OFELI

Modules
	Conservation Law Equations
	Conservation law equations.
	Electromagnetics
	Electromagnetic equations.
	General Purpose Equations
	Gathers equation related classes.
	Fluid Dynamics
	Fluid Dynamics equations.
	Laplace equation
	Laplace and Poisson equations.
	Porous Media problems
	Porous Media equation classes.
	Solid Mechanics
	Solid Mechanics finite element equations.
	Heat Transfer
	Heat Transfer equations.
	Input/Output
	Input/Output utility classes.
	Utilities
	Utility functions and classes.
	Physical properties of media
	Physical properties of materials and media.
	Global Variables
	All global variables in the library.
	Finite Element Mesh
	Mesh management classes
	Shape Function
	Shape function classes.
	Solver
	Solver functions and classes.
	Vector and Matrix
	Vector and matrix classes.

Files
file	ICPG1D.h
	Definition file for class ICPG1D.
file	ICPG2DT.h
	Definition file for class ICPG2DT.
file	ICPG3DT.h
	Definition file for class ICPG3DT.
file	LCL1D.h
	Definition file for class LCL1D.
file	LCL2DT.h
	Definition file for class LCL2DT.
file	LCL3DT.h
	Definition file for class LCL3DT.
file	Muscl.h
	Definition file for class Muscl.
file	Muscl1D.h
	Definition file for class Muscl1D.
file	Muscl2DT.h
	Definition file for class Muscl2DT.
file	Muscl3DT.h
	Definition file for class Muscl3DT.
file	BiotSavart.h
	Definition file for class BiotSavart.
file	EC2D1T3.h
	Definition file for class EC2D1T3.
file	EC2D2T3.h
	Definition file for class EC2D2T3.
file	Equa_Electromagnetics.h
	Definition file for class FE_Electromagnetics.
file	HelmholtzBT3.h
	Definition file for class HelmholtzBT3.
file	Equa.h
	Definition file for abstract class Equa.
file	Equation.h
	Definition file for class Equation.
file	Equa_Fluid.h
	Definition file for class Equa_Fluid.
file	NSP2DQ41.h
	Definition file for class NSP2DQ41.
file	TINS2DT3S.h
	Definition file for class TINS2DT3S.
file	TINS3DT4S.h
	Definition file for class TINS3DT4S.
file	Equa_Laplace.h
	Definition file for class Equa_Laplace.
file	Laplace1DL2.h
	Definition file for class Laplace1DL2.
file	Laplace1DL3.h
	Definition file for class Laplace1DL3.
file	Laplace2DT3.h
	Definition file for class Laplace2DT3.
file	Laplace2DT6.h
	Definition file for class Laplace2DT6.
file	Laplace3DT4.h
	Definition file for class Laplace3DT4.
file	SteklovPoincare2DBE.h
	Definition file for class SteklovPoincare2DBE.
file	Equa_Porous.h
	Definition file for class Equa_Porous.
file	WaterPorous1D.h
	Definition file for class WaterPorous1D.
file	WaterPorous2D.h
	Definition file for class WaterPorous2D.
file	Bar2DL2.h
	Definition file for class Bar2DL2.
file	Beam3DL2.h
	Definition file for class Beam3DL2.
file	Elas2DQ4.h
	Definition file for class Elas2DQ4.
file	Elas2DT3.h
	Definition file for class Elas2DT3.
file	Elas3DH8.h
	Definition file for class Elas3DH8.
file	Elas3DT4.h
	Definition file for class Elas3DT4.
file	Equa_Solid.h
	Definition file for class Equa_Solid.
file	DC1DL2.h
	Definition file for class DC1DL2.
file	DC2DT3.h
	Definition file for class DC2DT3.
file	DC2DT6.h
	Definition file for class DC2DT6.
file	DC3DAT3.h
	Definition file for class DC3DAT3.
file	DC3DT4.h
	Definition file for class DC3DT4.
file	Equa_Therm.h
	Definition file for class Equa_Therm.
file	PhaseChange.h
	Definition file for class PhaseChange and its parent abstract class.
file	Funct.h
	Definition file for class Funct.
file	IOField.h
	Definition file for class IOField.
file	IPF.h
	Definition file for class IPF.
file	output.h
	File that contains some output utility functions.
file	Prescription.h
	Definition file for class Prescription.
file	saveField.h
	Prototypes for functions to save mesh in various file formats.
file	saveField.h
	Prototypes for functions to save mesh in various file formats.
file	Tabulation.h
	Definition file for class Tabulation.
file	BMatrix.h
	Definition file for class BMatrix.
file	DMatrix.h
	Definition file for class DMatrix.
file	DSMatrix.h
	Definition file for abstract class DSMatrix.
file	LocalMatrix.h
	Definition file for class LocalMatrix.
file	LocalVect.h
	Definition file for class LocalVect.
file	Matrix.h
	Definition file for abstract class Matrix.
file	Point.h
	Definition file and implementation for class Point.
file	Point2D.h
	Definition file for class Point2D.
file	SkMatrix.h
	Definition file for class SkMatrix.
file	SkSMatrix.h
	Definition file for class SkSMatrix.
file	SpMatrix.h
	Definition file for class SpMatrix.
file	TrMatrix.h
	Definition file for class TrMatrix.
file	Domain.h
	Definition file for class Domain.
file	Edge.h
	Definition file for class Edge.
file	Element.h
	Definition file for class Element.
file	Figure.h
	Definition file for figure classes.
file	getMesh.h
	Definition file for mesh conversion functions.
file	Grid.h
	Definition file for class Grid.
file	Material.h
	Definition file for class Material.
file	Mesh.h
	Definition file for class Mesh.
file	MeshAdapt.h
	Definition file for class MeshAdapt.
file	MeshExtract.h
	Definition file for classes for extracting submeshes.
file	MeshUtil.h
	Definitions of utility functions for meshes.
file	Node.h
	Definition file for class Node.
file	saveMesh.h
	Prototypes for functions to save mesh in various file formats.
file	Side.h
	Definition file for class Side.
file	FEShape.h
	Definition file for class FEShape.
file	Hexa8.h
	Definition file for class Hexa8.
file	Line2.h
	Definition file for class Line2.
file	Line3.h
	Definition file for class Line3.
file	Penta6.h
	Definition file for class Penta6.
file	Quad4.h
	Definition file for class Quad4.
file	Tetra4.h
	Definition file for class Tetra4.
file	Triang3.h
	Definition file for class Triang3.
file	Triang6S.h
	Definition file for class Triang6S.
file	BiCG.h
	Solves an unsymmetric linear system of equations using the BiConjugate Gradient method.
file	BSpline.h
	Function to perform a B-spline interpolation.
file	CG.h
	Functions to solve a symmetric positive definite linear system of equations using the Conjugate Gradient method.
file	CGS.h
	Solves an unsymmetric linear system of equations using the Conjugate Gradient Squared method.
file	EigenProblemSolver.h
	Definition file for class EigenProblemSolver.
file	GMRes.h
	Function to solve a linear system of equations using the Generalized Minimum Residual method.
file	GS.h
	Function to solve a linear system of equations using the Gauss-Seidel method.
file	Integration.h
	Definition file for numerical integration class.
file	Jacobi.h
	Function to solve a linear system of equations using the Jacobi method.
file	MyNLAS.h
	Definition file for abstract class MyNLAS.
file	MyOpt.h
	Definition file for abstract class MyOpt.
file	ODESolver.h
	Definition file for class ODESolver.
file	Prec.h
	Definition file for preconditioning classes.
file	Richardson.h
	Function to solve a linear system of equations using the Richardson method.
file	SSOR.h
	Function to solve a linear system of equations using the Symmetric Successive Over Relaxation method.
file	TimeStepping.h
	Definition file for class TimeStepping.
file	constants.h
	File that contains some widely used constants.
file	Gauss.h
	Definition file for struct Gauss.
file	qksort.h
	File that contains template quick sorting function.
file	Timer.h
	Definition file for class Timer.
file	util.h
	File that contains various utility functions.

Classes
class	LocalVect< T_, N_ >
	Handles small size vectors like element vectors. More...
class	ICPG1D
	Class to solve the Inviscid compressible fluid flows (Euler equations) for perfect gas in 1-D. More...
class	ICPG2DT
	Class to solve the Inviscid compressible fluid flows (Euler equations) for perfect gas in 2-D. More...
class	ICPG3DT
	Class to solve the Inviscid compressible fluid flows (Euler equations) for perfect gas in 3-D. More...
class	LCL1D
	Class to solve the linear conservation law (Hyperbolic equation) in 1-D by a MUSCL Finite Volume scheme. More...
class	LCL2DT
	Class to solve the linear hyperbolic equation in 2-D by a MUSCL Finite Volume scheme on triangles. More...
class	LCL3DT
	Class to solve the linear conservation law equation in 3-D by a MUSCL Finite Volume scheme on tetrahedra. More...
class	Muscl
	Parent class for hyperbolic solvers with Muscl scheme. More...
class	Vect< T_ >
	To handle general purpose vectors. More...
class	Muscl1D
	Class for 1-D hyperbolic solvers with Muscl scheme. More...
class	Muscl2DT
	Class for 2-D hyperbolic solvers with Muscl scheme. More...
class	Muscl3DT
	Class for 3-D hyperbolic solvers with Muscl scheme using tetrahedra. More...
class	BiotSavart
	Class to compute the magnetic induction from the current density using the Biot-Savart formula. More...
class	EC2D1T3
	Eddy current problems in 2-D domains using solenoidal approximation. More...
class	EC2D2T3
	Eddy current problems in 2-D domains using transversal approximation. More...
class	Equa_Electromagnetics< NEN_, NEE_, NSN_, NSE_ >
	Abstract class for Electromagnetics Equation classes. More...
class	HelmholtzBT3
	Builds finite element arrays for Helmholtz equations in a bounded media using 3-Node triangles. More...
class	Equa
	Mother abstract class to describe equation. More...
class	Equation< NEN_, NEE_, NSN_, NSE_ >
	Abstract class for all equation classes. More...
class	Equa_Fluid< NEN_, NEE_, NSN_, NSE_ >
	Abstract class for Fluid Dynamics Equation classes. More...
class	NSP2DQ41
	Builds finite element arrays for incompressible Navier-Stokes equations in 2-D domains using Q1/P0 element and a penaly formulation for the incompressibility condition. More...
class	TINS2DT3S
	Builds finite element arrays for transient incompressible fluid flow using Navier-Stokes equations in 2-D domains. Numerical approximation uses stabilized 3-node triangle finite elements for velocity and pressure. 2nd-order projection scheme is used for time integration. More...
class	TINS3DT4S
	Builds finite element arrays for transient incompressible fluid flow using Navier-Stokes equations in 3-D domains. Numerical approximation uses stabilized 4-node tatrahedral finite elements for velocity and pressure. 2nd-order projection scheme is used for time integration. More...
class	FastMarching
	class for the fast marching algorithm on uniform grids More...
class	FastMarching1DG
	class for the fast marching algorithm on 1-D uniform grids More...
class	FastMarching2DG
	class for the fast marching algorithm on 2-D uniform grids More...
class	FastMarching3DG
	class for the fast marching algorithm on 3-D uniform grids More...
class	Equa_Laplace< NEN_, NEE_, NSN_, NSE_ >
	Abstract class for classes about the Laplace equation. More...
class	Laplace1DL2
	To build element equation for a 1-D elliptic equation using the 2-Node line element (P1). More...
class	Laplace1DL3
	To build element equation for the 1-D elliptic equation using the 3-Node line (P2). More...
class	Laplace2DT3
	To build element equation for the Laplace equation using the 2-D triangle element (P1). More...
class	Laplace2DT6
	To build element equation for the Laplace equation using the 2-D triangle element (P2). More...
class	SteklovPoincare2DBE
	Solver of the Steklov Poincare problem in 2-D geometries using piecewie constant boundary elemen. More...
class	Equa_Porous< NEN_, NEE_, NSN_, NSE_ >
	Abstract class for Porous Media Finite Element classes. More...
class	WaterPorous2D
	To solve water flow equations in porous media (1-D) More...
class	Bar2DL2
	To build element equations for Planar Elastic Bar element with 2 DOF (Degrees of Freedom) per node. More...
class	Beam3DL2
	To build element equations for 3-D beam equations using 2-node lines. More...
class	Elas2DQ4
	To build element equations for 2-D linearized elasticity using 4-node quadrilaterals. More...
class	Elas2DT3
	To build element equations for 2-D linearized elasticity using 3-node triangles. More...
class	Elas3DH8
	To build element equations for 3-D linearized elasticity using 8-node hexahedra. More...
class	Elas3DT4
	To build element equations for 3-D linearized elasticity using 4-node tetrahedra. More...
class	Equa_Solid< NEN_, NEE_, NSN_, NSE_ >
	Abstract class for Solid Mechanics Finite Element classes. More...
class	DC1DL2
	Builds finite element arrays for thermal diffusion and convection in 1-D using 2-Node elements. More...
class	DC2DT3
	Builds finite element arrays for thermal diffusion and convection in 2-D domains using 3-Node triangles. More...
class	DC2DT6
	Builds finite element arrays for thermal diffusion and convection in 2-D domains using 6-Node triangles. More...
class	DC3DAT3
	Builds finite element arrays for thermal diffusion and convection in 3-D domains with axisymmetry using 3-Node triangles. More...
class	DC3DT4
	Builds finite element arrays for thermal diffusion and convection in 3-D domains using 4-Node tetrahedra. More...
class	Equa_Therm< NEN_, NEE_, NSN_, NSE_ >
	Abstract class for Heat transfer Finite Element classes. More...
class	PhaseChange
	This class enables defining phase change laws for a given material. More...
class	Funct
	A simple class to parse real valued functions. More...
class	IOField
	Enables working with files in the XML Format. More...
class	IPF
	To read project parameters from a file in IPF format. More...
class	Prescription
	To prescribe various types of data by an algebraic expression. Data may consist in boundary conditions, forces, tractions, fluxes, initial condition. All these data types can be defined through an enumerated variable. More...
class	Tabulation
	To read and manipulate tabulated functions. More...
class	BMatrix< T_ >
	To handle band matrices. More...
class	DMatrix< T_ >
	To handle dense matrices. More...
class	DSMatrix< T_ >
	To handle symmetric dense matrices. More...
class	SkMatrix< T_ >
	To handle square matrices in skyline storage format. More...
class	SkSMatrix< T_ >
	To handle symmetric matrices in skyline storage format. More...
class	SpMatrix< T_ >
	To handle matrices in sparse storage format. More...
class	LocalMatrix< T_, NR_, NC_ >
	Handles small size matrices like element matrices, with a priori known size. More...
class	Matrix< T_ >
	Virtual class to handle matrices for all storage formats. More...
class	Point< T_ >
	Defines a point with arbitrary type coordinates. More...
class	Point2D< T_ >
	Defines a 2-D point with arbitrary type coordinates. More...
class	TrMatrix< T_ >
	To handle tridiagonal matrices. More...
class	Domain
	To store and treat finite element geometric information. More...
class	Edge
	To describe an edge. More...
class	Element
	To store and treat finite element geometric information. More...
class	Figure
	To store and treat a figure (or shape) information. More...
class	Rectangle
	To store and treat a rectangular figure. More...
class	Brick
	To store and treat a brick (parallelepiped) figure. More...
class	Circle
	To store and treat a circular figure. More...
class	Sphere
	To store and treat a sphere. More...
class	Ellipse
	To store and treat an ellipsoidal figure. More...
class	Triangle
	To store and treat a triangle. More...
class	Polygon
	To store and treat a polygonal figure. More...
class	Grid
	To manipulate structured grids. More...
class	Material
	To treat material data. This class enables reading material data in material data files. It also returns these informations by means of its members. More...
class	Mesh
	To store and manipulate finite element meshes. More...
class	MeshAdapt
	To adapt mesh in function of given solution. More...
class	NodeList
	Class to construct a list of nodes having some common properties. More...
class	ElementList
	Class to construct a list of elements having some common properties. More...
class	SideList
	Class to construct a list of sides having some common properties. More...
class	EdgeList
	Class to construct a list of edges having some common properties. More...
class	Node
	To describe a node. More...
class	Partition
	To partition a finite element mesh into balanced submeshes. More...
class	Side
	To store and treat finite element sides (edges in 2-D or faces in 3-D) More...
class	FEShape
	Parent class from which inherit all finite element shape classes. More...
class	triangle
	Defines a triangle. The reference element is the rectangle triangle with two unit edges. More...
class	Hexa8
	Defines a three-dimensional 8-node hexahedral finite element using Q1-isoparametric interpolation. More...
class	Line2
	To describe a 2-Node planar line finite element. More...
class	Line3
	To describe a 3-Node quadratic planar line finite element. More...
class	Penta6
	Defines a 6-node pentahedral finite element using P1 interpolation in local coordinates (s.x,s.y) and Q1 isoparametric interpolation in local coordinates (s.x,s.z) and (s.y,s.z). More...
class	Quad4
	Defines a 4-node quadrilateral finite element using Q1 isoparametric interpolation. More...
class	Tetra4
	Defines a three-dimensional 4-node tetrahedral finite element using P1 interpolation. More...
class	Triang3
	Defines a 3-Node (P1) triangle. More...
class	Triang6S
	Defines a 6-Node straight triangular finite element using P2 interpolation. More...
class	Prec< T_ >
	To set a preconditioner. More...
class	EigenProblemSolver
	Class to find eigenvalues and corresponding eigenvectors of a given matrix in a generalized eigenproblem, i.e. Find scalars l and non-null vectors v such that [K]{v} = l[M]{v} where [K] and [M] are symmetric matrices. The eigenproblem can be originated from a PDE. For this, we will refer to the matrices K and M as Stiffness and Mass matrices respectively. More...
class	Integration
	Class for numerical integration methods. More...
class	Iter< T_ >
	Class to drive an iterative process. More...
class	LinearSolver
	Class to solve systems of linear equations by direct or iterative methods. More...
class	MyNLAS
	Abstract class to define by user specified function. More...
class	MyOpt
	Abstract class to define by user specified optimization function. More...
class	ODESolver
	To solve a system of ordinary differential equations. More...
class	TimeStepping
	To solve time stepping problems, i.e. systems of linear ordinary differential equations of the form [A2]{y"} + [A1]{y'} + [A0]{y} = {b}. More...
class	Gauss
	Calculate data for Gauss integration. More...
class	Timer
	To handle elapsed time counting. More...

Enumerations
enum	PDE_Terms {   CONSISTENT_MASS = 0x00001000 ,   LUMPED_MASS = 0x00002000 ,   MASS = 0x00002000 ,   CAPACITY = 0x00004000 ,   CONSISTENT_CAPACITY = 0x00004000 ,   LUMPED_CAPACITY = 0x00008000 ,   VISCOSITY = 0x00010000 ,   STIFFNESS = 0x00020000 ,   DIFFUSION = 0x00040000 ,   MOBILITY = 0x00040000 ,   CONVECTION = 0x00080000 ,   DEVIATORIC = 0x00100000 ,   DILATATION = 0x00200000 ,   ELECTRIC = 0x00400000 ,   MAGNETIC = 0x00800000 ,   LOAD = 0x01000000 ,   HEAT_SOURCE = 0x02000000 ,   BOUNDARY_TRACTION = 0x04000000 ,   HEAT_FLUX = 0x08000000 ,   CONTACT = 0x10000000 ,   BUOYANCY = 0x20000000 ,   LORENTZ_FORCE = 0x40000000 }
enum	Analysis {   STATIONARY = 0 ,   STEADY_STATE = 0 ,   TRANSIENT = 1 ,   TRANSIENT_ONE_STEP = 2 ,   OPTIMIZATION = 3 ,   EIGEN = 4 }
enum	TimeScheme {   NONE = 0 ,   FORWARD_EULER = 1 ,   BACKWARD_EULER = 2 ,   CRANK_NICOLSON = 3 ,   HEUN = 4 ,   NEWMARK = 5 ,   LEAP_FROG = 6 ,   ADAMS_BASHFORTH = 7 ,   AB2 = 7 ,   RUNGE_KUTTA = 8 ,   RK4 = 8 ,   RK3_TVD = 9 ,   BDF2 = 10 ,   BUILTIN = 11 }
enum	FEType {   FE_2D_3N ,   FE_2D_6N ,   FE_2D_4N ,   FE_3D_AXI_3N ,   FE_3D_4N ,   FE_3D_8N }
enum	AccessType
	Enumerated values for file access type.
enum	MatrixType {   DENSE = 1 ,   SKYLINE = 2 ,   SPARSE = 4 ,   DIAGONAL = 8 ,   TRIDIAGONAL = 16 ,   BAND = 32 ,   SYMMETRIC = 64 ,   UNSYMMETRIC = 128 ,   IDENTITY = 256 }
enum	Iteration {   DIRECT_SOLVER = 0 ,   CG_SOLVER = 1 ,   CGS_SOLVER = 2 ,   BICG_SOLVER = 3 ,   BICG_STAB_SOLVER = 4 ,   GMRES_SOLVER = 5 }
	Choose iterative solver for the linear system. More...
enum	Preconditioner {   IDENT_PREC = 0 ,   DIAG_PREC = 1 ,   DILU_PREC = 2 ,   ILU_PREC = 3 ,   SSOR_PREC = 4 }
	Choose preconditioner for the linear system. More...
enum	BCType {   PERIODIC_A = 9999 ,   PERIODIC_B = -9999 ,   CONTACT_BC = 9998 ,   CONTACT_M = 9997 ,   CONTACT_S = -9997 ,   SLIP = 9996 }
enum	EigenMethod {   SUBSPACE = 1 ,   QR = 2 }
enum	IntegrationScheme {   LEFT_RECTANGLE = 0 ,   RIGHT_RECTANGLE = 1 ,   MID_RECTANGLE = 2 ,   TRAPEZOIDAL = 3 ,   SIMPSON = 4 ,   GAUSS_LEGENDRE = 5 }

Functions
T_ *	A ()
	Return element matrix. More...
T_ *	b ()
	Return element right-hand side. More...
T_ *	Prev ()
	Return element previous vector. More...
	IOField ()
	Default constructor.
	IOField (const string &file, AccessType access, bool compact=true)
	Constructor using file name. More...
	IOField (const string &mesh_file, const string &file, Mesh &ms, AccessType access, bool compact=true)
	Constructor using file name, mesh file and mesh. More...
	IOField (const string &file, Mesh &ms, AccessType access, bool compact=true)
	Constructor using file name and mesh. More...
	IOField (const string &file, AccessType access, const string &name)
	Constructor using file name and field name. More...
	~IOField ()
	Destructor.
void	setMeshFile (const string &file)
	Set mesh file. More...
void	open ()
	Open file. More...
void	open (const string &file, AccessType access)
	Open file. More...
void	close ()
	Close file.
void	put (Mesh &ms)
	Store mesh in file.
void	put (const Vect< real_t > &v)
	Store Vect instance v in file. More...
real_t	get (Vect< real_t > &v)
	Get Vect v instance from file. More...
int	get (Vect< real_t > &v, const string &name)
	Get Vect v instance from file if the field has the given name. More...
int	get (DMatrix< real_t > &A, const string &name)
	Get DMatrix A instance from file if the field has the given name. More...
int	get (DSMatrix< real_t > &A, const string &name)
	Get DSMatrix A instance from file if the field has the given name. More...
int	get (Vect< real_t > &v, real_t t)
	Get Vect v instance from file corresponding to a specific time value. More...
void	saveGMSH (string output_file, string mesh_file)
	Save field vectors in a file using GMSH format. More...
ostream &	operator<< (ostream &s, const complex_t &x)
	Output a complex number. More...
ostream &	operator<< (ostream &s, const std::string &c)
	Output a string. More...
template<class T_ >
ostream &	operator<< (ostream &s, const vector< T_ > &v)
	Output a vector instance. More...
template<class T_ >
ostream &	operator<< (ostream &s, const std::list< T_ > &l)
	Output a vector instance. More...
template<class T_ >
ostream &	operator<< (ostream &s, const std::pair< T_, T_ > &a)
	Output a pair instance. More...
void	saveField (const Vect< real_t > &v, const Mesh &mesh, string output_file, int opt)
	Save a vector to an output file in a given file format. More...
void	saveField (Vect< real_t > &v, const Grid &g, string output_file, int opt)
	Save a vector to an output file in a given file format, for a structured grid data. More...
void	saveGnuplot (Mesh &mesh, string input_file, string output_file, int f=1)
	Save a vector to an input Gnuplot file. More...
void	saveTecplot (Mesh &mesh, string input_file, string output_file, int f=1)
	Save a vector to an output file to an input Tecplot file. More...
void	saveVTK (Mesh &mesh, string input_file, string output_file, int f=1)
	Save a vector to an output VTK file. More...
void	saveGmsh (Mesh &mesh, string input_file, string output_file, int f=1)
	Save a vector to an output Gmsh file. More...
	Tabulation ()
	Default constructor.
	Tabulation (string file)
	Constructor using file name.
	~Tabulation ()
	Destructor.
void	setFile (string file)
	Set file name. More...
real_t	getValue (string funct, real_t x)
	Return the calculated value of the function. More...
real_t	getDerivative (string funct, real_t x)
	Return the derivative of the function at a given point. More...
real_t	getValue (string funct, real_t x, real_t y)
	Return the calculated value of the function. More...
real_t	getValue (string funct, real_t x, real_t y, real_t z)
	Return the calculated value of the function. More...
real_t	getValue (string funct, real_t x, real_t y, real_t z, real_t t)
	Return the calculated value of the function. More...
size_t	getNbFuncts () const
	Get the Number of read functions. More...
size_t	getNbVar (size_t n) const
	Get number of variables of a given function. More...
string	getFunctName (size_t n) const
	Get the name of a read function. More...
size_t	getSize (size_t n, size_t i) const
	Get number of points defining tabulation. More...
real_t	getMinVar (size_t n, size_t i) const
	Get minimal value of a variable. More...
real_t	getMaxVar (size_t n, size_t i) const
	Get maximal value of a variable. More...
ostream &	operator<< (ostream &s, const Tabulation &t)
	Output Tabulated function data.
template<class T_ >
BMatrix< T_ >	operator* (T_ a, const BMatrix< T_ > &A)
	Operator * (Premultiplication of matrix by constant) More...
template<class T_ >
ostream &	operator<< (ostream &s, const BMatrix< T_ > &a)
	Output matrix in output stream.
template<class T_ >
Vect< T_ >	operator* (const DMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...
template<class T_ >
ostream &	operator<< (ostream &s, const DMatrix< T_ > &a)
	Output matrix in output stream.
template<class T_ >
Vect< T_ >	operator* (const DSMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...
template<class T_ >
ostream &	operator<< (ostream &s, const DSMatrix< T_ > &a)
	Output matrix in output stream.
template<class T_ , size_t NR_, size_t NC_>
LocalMatrix< T_, NR_, NC_ >	operator* (T_ a, const LocalMatrix< T_, NR_, NC_ > &x)
	Operator * (Multiply matrix x by scalar a) More...
template<class T_ , size_t NR_, size_t NC_>
LocalVect< T_, NR_ >	operator* (const LocalMatrix< T_, NR_, NC_ > &A, const LocalVect< T_, NC_ > &x)
	Operator * (Multiply matrix A by vector x) More...
template<class T_ , size_t NR_, size_t NC_>
ostream &	operator<< (ostream &s, const LocalMatrix< T_, NR_, NC_ > &A)
	Output vector in output stream.
template<class T_ , size_t N_>
LocalVect< T_, N_ >	operator+ (const LocalVect< T_, N_ > &x, const LocalVect< T_, N_ > &y)
	Operator + (Add two vectors) More...
template<class T_ , size_t N_>
LocalVect< T_, N_ >	operator- (const LocalVect< T_, N_ > &x, const LocalVect< T_, N_ > &y)
	Operator - (Subtract two vectors) More...
template<class T_ , size_t N_>
LocalVect< T_, N_ >	operator* (T_ a, const LocalVect< T_, N_ > &x)
	Operator * (Premultiplication of vector by constant) More...
template<class T_ , size_t N_>
LocalVect< T_, N_ >	operator/ (T_ a, const LocalVect< T_, N_ > &x)
	Operator / (Division of vector by constant) More...
template<class T_ , size_t N_>
void	Scale (T_ a, LocalVect< T_, N_ > &x)
	Multiply vector x by constant a and store result in x.
template<class T_ , size_t N_>
ostream &	operator<< (ostream &s, const LocalVect< T_, N_ > &v)
	Output vector in output stream.
template<class T_ >
Point< T_ >	operator+ (const Point< T_ > &a, const Point< T_ > &b)
	Operator + More...
template<class T_ >
Point< T_ >	operator+ (const Point< T_ > &a, const T_ &x)
	Operator + More...
template<class T_ >
Point< T_ >	operator- (const Point< T_ > &a)
	Unary Operator - More...
template<class T_ >
Point< T_ >	operator- (const Point< T_ > &a, const Point< T_ > &b)
	Operator - More...
template<class T_ >
Point< T_ >	operator- (const Point< T_ > &a, const T_ &x)
	Operator - More...
template<class T_ >
Point< T_ >	operator* (const T_ &a, const Point< T_ > &b)
	Operator * More...
template<class T_ >
Point< T_ >	operator* (const int &a, const Point< T_ > &b)
	Operator *. More...
template<class T_ >
Point< T_ >	operator* (const Point< T_ > &b, const T_ &a)
	Operator / More...
template<class T_ >
Point< T_ >	operator* (const Point< T_ > &b, const int &a)
	Operator * More...
template<class T_ >
T_	operator* (const Point< T_ > &a, const Point< T_ > &b)
	Operator * More...
template<class T_ >
Point< T_ >	operator/ (const Point< T_ > &b, const T_ &a)
	Operator / More...
Point< real_t >	CrossProduct (const Point< real_t > &lp, const Point< real_t > &rp)
	Return Cross product of two vectors lp and rp
template<class T_ >
std::ostream &	operator<< (std::ostream &s, const Point< T_ > &a)
	Output point coordinates. More...
template<class T_ >
bool	operator== (const Point2D< T_ > &a, const Point2D< T_ > &b)
	Operator ==. More...
template<class T_ >
Point2D< T_ >	operator+ (const Point2D< T_ > &a, const Point2D< T_ > &b)
	Operator +. More...
template<class T_ >
Point2D< T_ >	operator+ (const Point2D< T_ > &a, const T_ &x)
	Operator +. More...
template<class T_ >
Point2D< T_ >	operator- (const Point2D< T_ > &a)
	Unary Operator - More...
template<class T_ >
Point2D< T_ >	operator- (const Point2D< T_ > &a, const Point2D< T_ > &b)
	Operator - More...
template<class T_ >
Point2D< T_ >	operator- (const Point2D< T_ > &a, const T_ &x)
	Operator - More...
template<class T_ >
Point2D< T_ >	operator* (const T_ &a, const Point2D< T_ > &b)
	Operator *. More...
template<class T_ >
Point2D< T_ >	operator* (const int &a, const Point2D< T_ > &b)
template<class T_ >
Point2D< T_ >	operator* (const Point2D< T_ > &b, const T_ &a)
	Operator / More...
template<class T_ >
Point2D< T_ >	operator* (const Point2D< T_ > &b, const int &a)
	Operator * More...
template<class T_ >
T_	operator* (const Point2D< T_ > &b, const Point2D< T_ > &a)
	Operator *. More...
template<class T_ >
Point2D< T_ >	operator/ (const Point2D< T_ > &b, const T_ &a)
	Operator / More...
bool	areClose (const Point2D< real_t > &a, const Point2D< real_t > &b, real_t toler=OFELI_TOLERANCE)
	Return true if both instances of class Point2D<real_t> are distant with less then toler [Default: OFELI_EPSMCH].
real_t	SqrDistance (const Point2D< real_t > &a, const Point2D< real_t > &b)
	Return squared euclidean distance between points a and b More...
real_t	Distance (const Point2D< real_t > &a, const Point2D< real_t > &b)
	Return euclidean distance between points a and b More...
template<class T_ >
std::ostream &	operator<< (std::ostream &s, const Point2D< T_ > &a)
	Output point coordinates. More...
template<class T_ >
Vect< T_ >	operator* (const SkMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...
template<class T_ >
ostream &	operator<< (ostream &s, const SkMatrix< T_ > &a)
	Output matrix in output stream. More...
template<class T_ >
Vect< T_ >	operator* (const SkSMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...
template<class T_ >
ostream &	operator<< (ostream &s, const SkSMatrix< T_ > &a)
	Output matrix in output stream. More...
	SpMatrix ()
	Default constructor. More...
	SpMatrix (size_t nr, size_t nc)
	Constructor that initializes current instance as a dense matrix. More...
	SpMatrix (size_t size, int is_diagonal=false)
	Constructor that initializes current instance as a dense matrix. More...
	SpMatrix (Mesh &mesh, size_t dof=0, int is_diagonal=false)
	Constructor using a Mesh instance. More...
	SpMatrix (const Vect< RC > &I, int opt=1)
	Constructor for a square matrix using non zero row and column indices. More...
	SpMatrix (const Vect< RC > &I, const Vect< T_ > &a, int opt=1)
	Constructor for a square matrix using non zero row and column indices. More...
	SpMatrix (size_t nr, size_t nc, const vector< size_t > &row_ptr, const vector< size_t > &col_ind)
	Constructor for a rectangle matrix. More...
	SpMatrix (size_t nr, size_t nc, const vector< size_t > &row_ptr, const vector< size_t > &col_ind, const vector< T_ > &a)
	Constructor for a rectangle matrix. More...
	SpMatrix (const vector< size_t > &row_ptr, const vector< size_t > &col_ind)
	Constructor for a rectangle matrix. More...
	SpMatrix (const vector< size_t > &row_ptr, const vector< size_t > &col_ind, const vector< T_ > &a)
	Constructor for a rectangle matrix. More...
	SpMatrix (const SpMatrix &m)
	Copy constructor.
	~SpMatrix ()
	Destructor.
void	Identity ()
	Define matrix as identity.
void	Dense ()
	Define matrix as a dense one.
void	Diagonal ()
	Define matrix as a diagonal one.
void	Diagonal (const T_ &a)
	Define matrix as a diagonal one with diagonal entries equal to a
void	Laplace1D (size_t n, real_t h)
	Sets the matrix as the one for the Laplace equation in 1-D. More...
void	Laplace2D (size_t nx, size_t ny)
	Sets the matrix as the one for the Laplace equation in 2-D. More...
void	setMesh (Mesh &mesh, size_t dof=0)
	Determine mesh graph and initialize matrix. More...
void	setOneDOF ()
	Activate 1-DOF per node option.
void	setSides ()
	Activate Sides option.
void	setDiag ()
	Store diagonal entries in a separate internal vector.
void	DiagPrescribe (Mesh &mesh, Vect< T_ > &b, const Vect< T_ > &u)
	Impose by a diagonal method an essential boundary condition. More...
void	DiagPrescribe (Vect< T_ > &b, const Vect< T_ > &u)
	Impose by a diagonal method an essential boundary condition using the Mesh instance provided by the constructor. More...
void	setSize (size_t size)
	Set size of matrix (case where it's a square matrix). More...
void	setSize (size_t nr, size_t nc)
	Set size (number of rows) of matrix. More...
void	setGraph (const Vect< RC > &I, int opt=1)
	Set graph of matrix by giving a vector of its nonzero entries. More...
Vect< T_ >	getRow (size_t i) const
	Get i-th row vector.
Vect< T_ >	getColumn (size_t j) const
	Get j-th column vector.
T_ &	operator() (size_t i, size_t j)
	Operator () (Non constant version) More...
T_	operator() (size_t i, size_t j) const
	Operator () (Constant version) More...
T_	operator() (size_t i) const
	Operator () with one argument (Constant version) More...
T_	operator[] (size_t i) const
	Operator [] (Constant version). More...
Vect< T_ >	operator* (const Vect< T_ > &x) const
	Operator * to multiply matrix by a vector. More...
SpMatrix< T_ > &	operator*= (const T_ &a)
	Operator *= to premultiply matrix by a constant. More...
void	getMesh (Mesh &mesh)
	Get mesh instance whose reference will be stored in current instance of SpMatrix.
void	Mult (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector and save in another one. More...
void	MultAdd (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector x and add to y. More...
void	MultAdd (T_ a, const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector a*x and add to y. More...
void	TMult (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply transpose of matrix by vector x and save in y. More...
void	Axpy (T_ a, const SpMatrix< T_ > &m)
	Add to matrix the product of a matrix by a scalar. More...
void	Axpy (T_ a, const Matrix< T_ > *m)
	Add to matrix the product of a matrix by a scalar. More...
void	set (size_t i, size_t j, const T_ &val)
	Assign a value to an entry of the matrix. More...
void	add (size_t i, size_t j, const T_ &val)
	Add a value to an entry of the matrix. More...
void	operator= (const T_ &x)
	Operator =. More...
size_t	getColInd (size_t i) const
	Return storage information. More...
size_t	getRowPtr (size_t i) const
	Return Row pointer at position i.
int	solve (const Vect< T_ > &b, Vect< T_ > &x, bool fact=false)
	Solve the linear system of equations. More...
void	setSolver (Iteration solver=CG_SOLVER, Preconditioner prec=DIAG_PREC, int max_it=1000, real_t toler=1.e-8)
	Choose solver and preconditioner for an iterative procedure. More...
void	clear ()
	brief Set all matrix entries to zero
T_ *	get () const
	Return C-Array. More...
T_	get (size_t i, size_t j) const
	Return entry (i,j) of matrix if this one is stored, 0 otherwise. More...
void	add (size_t i, const T_ &val)
	Add val to entry i.
template<class T_ >
Vect< T_ >	operator* (const SpMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...
template<class T_ >
ostream &	operator<< (ostream &s, const SpMatrix< T_ > &A)
	Output matrix in output stream. More...
	TrMatrix ()
	Default constructor. More...
	TrMatrix (size_t size)
	Constructor for a tridiagonal matrix with size rows.
	TrMatrix (const TrMatrix &m)
	Copy Constructor.
	~TrMatrix ()
	Destructor.
void	Identity ()
	Define matrix as identity matrix.
void	Diagonal ()
	Define matrix as a diagonal one.
void	Diagonal (const T_ &a)
	Define matrix as a diagona one and assign value a to all diagonal entries.
void	Laplace1D (real_t h)
	Define matrix as the one of 3-point finite difference discretization of the second derivative. More...
void	setSize (size_t size)
	Set size (number of rows) of matrix. More...
void	MultAdd (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector x and add result to y.
void	MultAdd (T_ a, const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector a*x and add result to y.
void	Mult (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector x and save result in y.
void	TMult (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply transpose of matrix by vector x and save result in y.
void	Axpy (T_ a, const TrMatrix< T_ > &m)
	Add to matrix the product of a matrix by a scalar. More...
void	Axpy (T_ a, const Matrix< T_ > *m)
	Add to matrix the product of a matrix by a scalar. More...
void	set (size_t i, size_t j, const T_ &val)
	Assign constant val to an entry (i,j) of the matrix.
void	add (size_t i, size_t j, const T_ &val)
	Add constant val value to an entry (i,j) of the matrix.
void	add (size_t i, const T_ &val)
	Add val to entry i.
T_	operator() (size_t i, size_t j) const
	Operator () (Constant version). More...
T_ &	operator() (size_t i, size_t j)
	Operator () (Non constant version). More...
TrMatrix< T_ > &	operator= (const TrMatrix< T_ > &m)
	Operator =. More...
TrMatrix< T_ > &	operator= (const T_ &x)
	Operator = Assign matrix to identity times x.
TrMatrix< T_ > &	operator*= (const T_ &x)
	Operator *=. More...
int	solve (Vect< T_ > &b, bool fact=true)
	Solve a linear system with current matrix (forward and back substitution). More...
int	solve (const Vect< T_ > &b, Vect< T_ > &x, bool fact=false)
	Solve a linear system with current matrix (forward and back substitution). More...
T_ *	get () const
	Return C-Array.
T_	get (size_t i, size_t j) const
	Return entry (i,j) of matrix.
template<class T_ >
Vect< T_ >	operator* (const TrMatrix< T_ > &A, const Vect< T_ > &b)
	Operator * (Multiply vector by matrix and return resulting vector. More...
template<class T_ >
TrMatrix< T_ >	operator* (T_ a, const TrMatrix< T_ > &A)
	Operator * (Premultiplication of matrix by constant) More...
template<class T_ >
ostream &	operator<< (ostream &s, const TrMatrix< T_ > &A)
	Output matrix in output stream. More...
template<class T_ >
Vect< T_ >	operator+ (const Vect< T_ > &x, const Vect< T_ > &y)
	Operator + (Addition of two instances of class Vect) More...
template<class T_ >
Vect< T_ >	operator- (const Vect< T_ > &x, const Vect< T_ > &y)
	Operator - (Difference between two vectors of class Vect) More...
template<class T_ >
Vect< T_ >	operator* (const T_ &a, const Vect< T_ > &x)
	Operator * (Premultiplication of vector by constant) More...
template<class T_ >
Vect< T_ >	operator* (const Vect< T_ > &x, const T_ &a)
	Operator * (Postmultiplication of vector by constant) More...
template<class T_ >
Vect< T_ >	operator/ (const Vect< T_ > &x, const T_ &a)
	Operator / (Divide vector entries by constant) More...
template<class T_ >
T_	Dot (const Vect< T_ > &x, const Vect< T_ > &y)
	Calculate dot product of two vectors. More...
real_t	Discrepancy (Vect< complex_t > &x, const Vect< complex_t > &y, int n, int type=1)
	Return discrepancy between 2 vectors x and y More...
template<class T_ >
ostream &	operator<< (ostream &s, const Vect< T_ > &v)
	Output vector in output stream. More...
ostream &	operator<< (ostream &s, const Edge &ed)
	Output edge data.
ostream &	operator<< (ostream &s, const Element &el)
	Output element data.
Figure	operator- (const Figure &f1, const Figure &f2)
	Function to define a Figure instance as the set subtraction of two Figure instances. More...
	Grid ()
	Construct a default grid with 10 intervals in each direction.
	Grid (real_t xm, real_t xM, size_t npx)
	Construct a 1-D structured grid given its extremal coordinates and number of intervals. More...
	Grid (real_t xm, real_t xM, real_t ym, real_t yM, size_t npx, size_t npy)
	Construct a 2-D structured grid given its extremal coordinates and number of intervals. More...
	Grid (Point< real_t > m, Point< real_t > M, size_t npx, size_t npy)
	Construct a 2-D structured grid given its extremal coordinates and number of intervals. More...
	Grid (real_t xm, real_t xM, real_t ym, real_t yM, real_t zm, real_t zM, size_t npx, size_t npy, size_t npz)
	Construct a 3-D structured grid given its extremal coordinates and number of intervals. More...
	Grid (Point< real_t > m, Point< real_t > M, size_t npx, size_t npy, size_t npz)
	Construct a 3-D structured grid given its extremal coordinates and number of intervals. More...
	~Grid ()
	Destructor.
void	setXMin (const Point< real_t > &x)
	Set min. coordinates of the domain. More...
void	setXMax (const Point< real_t > &x)
void	setDomain (real_t xmin, real_t xmax)
	Set Dimensions of the domain: 1-D case. More...
void	setDomain (real_t xmin, real_t xmax, real_t ymin, real_t ymax)
	Set Dimensions of the domain: 2-D case. More...
void	setDomain (real_t xmin, real_t xmax, real_t ymin, real_t ymax, real_t zmin, real_t zmax)
	Set Dimensions of the domain: 3-D case. More...
void	setDomain (Point< real_t > xmin, Point< real_t > xmax)
	Set Dimensions of the domain: 3-D case. More...
const Point< real_t > &	getXMin () const
	Return min. Coordinates of the domain.
const Point< real_t > &	getXMax () const
	Return max. Coordinates of the domain.
void	setN (size_t nx, size_t ny=0, size_t nz=0)
	Set number of grid intervals in the x, y and z-directions. More...
void	setNbDOF (size_t n)
	Set number of degrees of freedom for a node [Default: 1].
size_t	getNx () const
	Return number of grid intervals in the x-direction.
size_t	getNy () const
	Return number of grid intervals in the y-direction. More...
size_t	getNz () const
	Return number of grid intervals in the z-direction. More...
real_t	getHx () const
	Return grid size in the x-direction.
real_t	getHy () const
	Return grid size in the y-direction.
real_t	getHz () const
	Return grid size in the z-direction.
Point< real_t >	getCoord (size_t i) const
	Return coordinates a point with label i in a 1-D grid.
Point< real_t >	getCoord (size_t i, size_t j) const
	Return coordinates a point with label (i,j) in a 2-D grid.
Point< real_t >	getCoord (size_t i, size_t j, size_t k) const
	Return coordinates a point with label (i,j,k) in a 3-D grid.
size_t	getNbNodes () const
	Return total number of grid nodes.
size_t	getNbDOF () const
	Return total number of dof.
real_t	getX (size_t i) const
	Return x-coordinate of point with index i
real_t	getY (size_t j) const
	Return y-coordinate of point with index j
real_t	getZ (size_t k) const
	Return z-coordinate of point with index k
Point2D< real_t >	getXY (size_t i, size_t j) const
	Return coordinates of point with indices (i,j)
Point< real_t >	getXYZ (size_t i, size_t j, size_t k) const
	Return coordinates of point with indices (i,j,k)
real_t	getCenter (size_t i) const
	Return coordinates of center of a 1-D cell with indices i, i+1
Point< real_t >	getCenter (size_t i, size_t j) const
	Return coordinates of center of a 2-D cell with indices (i,j), (i+1,j), (i+1,j+1), (i,j+1)
Point< real_t >	getCenter (size_t i, size_t j, size_t k) const
	Return coordinates of center of a 3-D cell with indices (i,j,k), (i+1,j,k), (i+1,j+1,k), (i,j+1,k), (i,j,k+1), (i+1,j,k+1), (i+1,j+1,k+1), (i,j+1,k+1)
void	setCode (string exp, int code)
	Set a code for some grid points. More...
void	setCode (int side, int code)
	Set a code for grid points on sides. More...
int	getCode (int side) const
	Return code for a side number. More...
int	getCode (size_t i, size_t j) const
	Return code for a grid point. More...
int	getCode (size_t i, size_t j, size_t k) const
	Return code for a grid point. More...
size_t	getDim () const
	Return space dimension.
void	Deactivate (size_t i)
	Change state of a cell from active to inactive (1-D grid) More...
void	Deactivate (size_t i, size_t j)
	Change state of a cell from active to inactive (2-D grid) More...
void	Deactivate (size_t i, size_t j, size_t k)
	Change state of a cell from active to inactive (2-D grid) More...
int	isActive (size_t i) const
	Say if cell is active or not (1-D grid) More...
int	isActive (size_t i, size_t j) const
	Say if cell is active or not (2-D grid) More...
int	isActive (size_t i, size_t j, size_t k) const
	Say if cell is active or not (3-D grid) More...
ostream &	operator<< (ostream &s, const Grid &g)
	Output grid data.
ostream &	operator<< (ostream &s, const Material &m)
	Output material data.
ostream &	operator<< (ostream &s, const Mesh &ms)
	Output mesh data. More...
ostream &	operator<< (ostream &s, const MeshAdapt &a)
	Output MeshAdapt class data.
ostream &	operator<< (ostream &s, const NodeList &nl)
	Output NodeList instance. More...
ostream &	operator<< (ostream &s, const ElementList &el)
	Output ElementList instance. More...
ostream &	operator<< (ostream &s, const SideList &sl)
	Output SideList instance. More...
ostream &	operator<< (ostream &s, const EdgeList &el)
	Output EdgeList instance. More...
size_t	Label (const Element &el)
	Return label of a given element. More...
size_t	Label (const Side &sd)
	Return label of a given side. More...
size_t	Label (const Edge &ed)
	Return label of a given edge. More...
size_t	NodeLabel (const Side &sd, size_t n)
	Return global label of node local label in side. More...
int	Code (const Element &el)
	Return code of a given element. More...
int	Code (const Side &sd, size_t i=1)
	Return code of a given (degree of freedom of) side. More...
bool	operator== (const Element &el1, const Element &el2)
	Check equality between 2 elements. More...
bool	operator== (const Side &sd1, const Side &sd2)
	Check equality between 2 sides. More...
void	MeshToMesh (const Vect< real_t > &u1, Vect< real_t > &u2, size_t nx, size_t ny=0, size_t nz=0, size_t dof=1)
	Function to redefine a vector defined on a mesh to a new mesh. More...
void	MeshToMesh (Mesh &m1, Mesh &m2, const Vect< real_t > &u1, Vect< real_t > &u2, const Point< real_t > &xmin, const Point< real_t > &xmax, size_t nx, size_t ny, size_t nz, size_t dof=1)
	Function to redefine a vector defined on a mesh to a new mesh. More...
ostream &	operator<< (ostream &s, const Node &nd)
	Output node data. More...
void	saveGmsh (const string &file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in Gmsh format. More...
void	saveGnuplot (const string &file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in Gmsh format. More...
void	saveTecplot (const string &file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in Tecplot format. More...
void	saveVTK (const string &file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in VTK format. More...
ostream &	operator<< (ostream &s, const Side &sd)
	Output side data. More...
template<class T_ >
int	BiCG (const SpMatrix< T_ > &A, int prec, const Vect< T_ > &b, Vect< T_ > &x, int max_it, real_t toler)
	Biconjugate gradient solver function. More...
template<class T_ >
int	CG (const SpMatrix< T_ > &A, int prec, const Vect< T_ > &b, Vect< T_ > &x, int max_it, real_t toler)
	Conjugate gradient solver function. More...
template<class T_ >
int	CGS (const SpMatrix< T_ > &A, int prec, const Vect< T_ > &b, Vect< T_ > &x, int max_it, real_t toler)
	Conjugate Gradient Squared solver function. More...
ostream &	operator<< (ostream &s, const EigenProblemSolver &es)
	Output eigenproblem information.
template<class T_ >
int	GMRes (const SpMatrix< T_ > &A, int prec, const Vect< T_ > &b, Vect< T_ > &x, size_t m, int max_it, real_t toler)
	GMRes solver function. More...
ostream &	operator<< (ostream &s, const ODESolver &de)
	Output differential system information.
ostream &	operator<< (ostream &s, TimeStepping &ts)
	Output differential system information. More...
template<class T_ , class C_ >
void	qksort (std::vector< T_ > &a, int begin, int end, C_ compare)
	Function to sort a vector according to a key function. More...
real_t	Sgn (real_t a, real_t b)
	Return |a| if b>0, -|a| if not.
real_t	Abs2 (real_t a)
	Return square of real number a
real_t	Abs (complex_t a)
	Return modulus of complex number a
real_t	Abs (const Point< real_t > &p)
	Return norm of vector a
complex_t	Conjg (complex_t a)
	Return complex conjugate of complex number a
template<class T_ >
const T_ &	Max (const T_ &a, const T_ &b)
	Return maximum value of elements a and b
int	Max (int a, int b, int c)
	Return maximum value of integer numbers a, b and c
real_t	Min (real_t a, real_t b, real_t c)
	Return minimum value of real numbers a, b and c
int	Min (int a, int b, int c)
	Return minimum value of integer numbers a, b and c
real_t	Max (real_t a, real_t b, real_t c, real_t d)
	Return maximum value of integer numbers a, b, c and d
int	Max (int a, int b, int c, int d)
	Return maximum value of integer numbers a, b, c and d
real_t	Min (real_t a, real_t b, real_t c, real_t d)
	Return minimum value of real numbers a, b, c and d
int	Min (int a, int b, int c, int d)
	Return minimum value of integer numbers a, b, c and d
template<class T_ >
void	Scale (T_ a, const vector< T_ > &x, vector< T_ > &y)
	Mutiply vector x by a and save result in vector y More...
template<class T_ >
void	Scale (T_ a, const Vect< T_ > &x, Vect< T_ > &y)
	Mutiply vector x by a and save result in vector y More...
template<class T_ >
void	Scale (T_ a, vector< T_ > &x)
	Mutiply vector x by a More...
template<class T_ >
void	Xpy (const vector< T_ > &x, vector< T_ > &y)
	Add vector x to y More...
template<class T_ >
void	Axpy (size_t n, T_ a, T_ *x, T_ *y)
	Multiply array x by a and add result to y More...
template<class T_ >
void	Axpy (T_ a, const vector< T_ > &x, vector< T_ > &y)
	Multiply vector x by a and add result to y More...
template<class T_ >
void	Copy (size_t n, T_ *x, T_ *y)
	Copy array x to y n is the arrays size.
template<class T_ >
T_	Dot (size_t n, T_ *x, T_ *y)
	Return dot product of arrays x and y More...
real_t	Dot (const vector< real_t > &x, const vector< real_t > &y)
	Return dot product of vectors x and y. More...
real_t	operator* (const vector< real_t > &x, const vector< real_t > &y)
	Operator * (Dot product of 2 vector instances) More...
template<class T_ >
T_	Dot (const Point< T_ > &x, const Point< T_ > &y)
	Return dot product of x and y
template<class T_ >
void	clear (Vect< T_ > &v)
	Assign 0 to all entries of a vector. More...
real_t	Nrm2 (const vector< real_t > &x)
	Return 2-norm of vector x
template<class T_ >
real_t	Nrm2 (const Point< T_ > &a)
	Return 2-norm of a
	Iter ()
	Default Constructor. More...
	Iter (int max_it, real_t toler)
	Constructor with iteration parameters. More...
bool	check (Vect< T_ > &u, const Vect< T_ > &v, int opt=2)
	Check convergence. More...
bool	check (T_ &u, const T_ &v)
	Check convergence for a scalar case (one equation) More...

Detailed Description

Enumeration Type Documentation

Analysis

enum Analysis

Selects Analysis type

Enumerator
STATIONARY	Steady State analysis
STEADY_STATE	Steady state analysis
TRANSIENT	Transient problem
TRANSIENT_ONE_STEP	Transient problem, perform only one time step
OPTIMIZATION	Optimization problem
EIGEN	Eigenvalue problem

BCType

enum BCType

To select special boundary conditions.

Enumerator
PERIODIC_A	Periodic Boundary condition (first side)
PERIODIC_B	Periodic Boundary condition (second side)
CONTACT_BC	Contact Boundary conditions
CONTACT_M	Contact Boundary condition, set as master side
CONTACT_S	Contact Boundary condition, set as slave side
SLIP	Slip Boundary condition

EigenMethod

enum EigenMethod

Enumerator
SUBSPACE	Subspace iteration method (for symmetric matrices)
QR	QR reduction method (Martin, Parlett, Peters, Reinsch and Wilkinson.)

FEType

enum FEType

Choose Finite Element Type

Enumerator
FE_2D_3N	2-D elements, 3-Nodes (P1)
FE_2D_6N	2-D elements, 6-Nodes (P2)
FE_2D_4N	2-D elements, 4-Nodes (Q1)
FE_3D_AXI_3N	3-D Axisymmetric elements, 3-Nodes (P1)
FE_3D_4N	3-D elements, 4-Nodes (P1)
FE_3D_8N	3-D elements, 8-Nodes (Q1)

IntegrationScheme

enum IntegrationScheme

Choose numerical integration scheme

Enumerator
LEFT_RECTANGLE	Left rectangle integration formula
RIGHT_RECTANGLE	Right rectangle integration formula
MID_RECTANGLE	Midpoint (central) rectangle formula
TRAPEZOIDAL	Trapezoidal rule
SIMPSON	Simpson formula
GAUSS_LEGENDRE	Gauss-Legendre quadrature formulae

Iteration

enum Iteration

Choose iterative solver for the linear system.

Enumerator
DIRECT_SOLVER	Direct solver
CG_SOLVER	CG Method
CGS_SOLVER	CGS Metod
BICG_SOLVER	BiCG Method
BICG_STAB_SOLVER	BiCGStab Method
GMRES_SOLVER	GMRes Method

MatrixType

enum MatrixType

Choose matrix storage and type

Enumerator
DENSE	Dense storage
SKYLINE	Skyline storage
SPARSE	Sparse storage
DIAGONAL	Diagonal storage
TRIDIAGONAL	Tridiagonal storage
BAND	Band storage
SYMMETRIC	Symmetric matrix
UNSYMMETRIC	Unsymmetric matrix
IDENTITY	Identity matrix

PDE_Terms

enum PDE_Terms

Enumerate variable that selects various terms in partial differential equations

Enumerator
CONSISTENT_MASS	Consistent mass term
LUMPED_MASS	Lumped mass term
MASS	Consistent mass term
CAPACITY	Consistent capacity term
CONSISTENT_CAPACITY	Consistent capacity term
LUMPED_CAPACITY	Lumped capacity term
VISCOSITY	Viscosity term
STIFFNESS	Stiffness term
DIFFUSION	Diffusion term
MOBILITY	Mobility term
CONVECTION	Convection term
DEVIATORIC	Deviatoric term
DILATATION	Dilatational term
ELECTRIC	Electric term
MAGNETIC	Magnetic term
LOAD	Body load term
HEAT_SOURCE	Body heat source term
BOUNDARY_TRACTION	Boundary traction (pressure) term
HEAT_FLUX	Boundary heat flux term
CONTACT	Signorini contact
BUOYANCY	Buoyancy force term
LORENTZ_FORCE	Lorentz force term

Preconditioner

enum Preconditioner

Choose preconditioner for the linear system.

Enumerator
IDENT_PREC	Identity (No preconditioning)
DIAG_PREC	Diagonal preconditioner
DILU_PREC	DILU (Diagonal Incomplete factorization) preconditioner
ILU_PREC	ILU (Incomplete factorization) preconditioner
SSOR_PREC	SSOR preconditioner

TimeScheme

enum TimeScheme

Selects Time integration scheme

Enumerator
NONE	No time integration scheme
FORWARD_EULER	Forward Euler scheme (Explicit)
BACKWARD_EULER	Backward Euler scheme (Implicit)
CRANK_NICOLSON	Crank-Nicolson scheme
HEUN	Heun scheme
NEWMARK	Newmark scheme
LEAP_FROG	Leap Frog scheme
ADAMS_BASHFORTH	Adams-Bashforth scheme (2nd Order)
AB2	Adams-Bashforth scheme (2nd Order)
RUNGE_KUTTA	4-th Order Runge-Kutta scheme (4th Order)
RK4	4-th Order Runge-Kutta scheme
RK3_TVD	3-rd Order Runge-Kutta TVD scheme
BDF2	Backward Difference Formula (2nd Order)
BUILTIN	Builtin scheme, implemented in equation class

Function Documentation

Grid() [1/5]

Grid	(	Point< real_t >	m,
		Point< real_t >	M,
		size_t	npx,
		size_t	npy
	)

Construct a 2-D structured grid given its extremal coordinates and number of intervals.

Parameters

[in]	m	Minimal coordinate value
[in]	M	Maximal coordinate value
[in]	npx	Number of grid intervals in the x-direction
[in]	npy	Number of grid intervals in the y-direction

Grid() [2/5]

Grid	(	Point< real_t >	m,
		Point< real_t >	M,
		size_t	npx,
		size_t	npy,
		size_t	npz
	)

Construct a 3-D structured grid given its extremal coordinates and number of intervals.

Parameters

[in]	m	Minimal coordinate value
[in]	M	Maximal coordinate value
[in]	npx	Number of grid intervals in the x-direction
[in]	npy	Number of grid intervals in the y-direction
[in]	npz	Number of grid intervals in the z-direction

Grid() [3/5]

Grid	(	real_t	xm,
		real_t	xM,
		real_t	ym,
		real_t	yM,
		real_t	zm,
		real_t	zM,
		size_t	npx,
		size_t	npy,
		size_t	npz
	)

Construct a 3-D structured grid given its extremal coordinates and number of intervals.

Parameters

[in]	xm	Minimal value for x
[in]	xM	Maximal value for x
[in]	ym	Minimal value for y
[in]	yM	Maximal value for y
[in]	zm	Minimal value for z
[in]	zM	Maximal value for z
[in]	npx	Number of grid intervals in the x-direction
[in]	npy	Number of grid intervals in the y-direction
[in]	npz	Number of grid intervals in the z-direction

Grid() [4/5]

Grid	(	real_t	xm,
		real_t	xM,
		real_t	ym,
		real_t	yM,
		size_t	npx,
		size_t	npy
	)

Construct a 2-D structured grid given its extremal coordinates and number of intervals.

Parameters

[in]	xm	Minimal value for x
[in]	xM	Maximal value for x
[in]	ym	Minimal value for y
[in]	yM	Maximal value for y
[in]	npx	Number of grid intervals in the x-direction
[in]	npy	Number of grid intervals in the y-direction

Grid() [5/5]

Grid	(	real_t	xm,
		real_t	xM,
		size_t	npx
	)

Construct a 1-D structured grid given its extremal coordinates and number of intervals.

Parameters

[in]	xm	Minimal value for x
[in]	xM	Maximal value for x
[in]	npx	Number of grid intervals in the x-direction

IOField() [1/4]

IOField	(	const string &	file,
		AccessType	access,
		bool	compact = true
	)

Constructor using file name.

Parameters

[in]	file	File name.
[in]	access	Access code. This number is to be chosen among two enumerated values: IOField::IN to read the file IOField::OUT to write on it
[in]	compact	Flag to choose a compact storage or not [Default: true]

IOField() [2/4]

IOField	(	const string &	file,
		AccessType	access,
		const string &	name
	)

Constructor using file name and field name.

Parameters

[in]	file	File that contains field stored or to store
[in]	access	Access code. This number is to be chosen among two enumerated values: IOField::IN to read the file IOField::OUT to write on it
[in]	name	Seek a specific field with given name

IOField() [3/4]

IOField	(	const string &	file,
		Mesh &	ms,
		AccessType	access,
		bool	compact = true
	)

Constructor using file name and mesh.

Parameters

[in]	file	File that contains field stored or to store
[in]	ms	Mesh instance
[in]	access	Access code. This number is to be chosen among two enumerated values: IOField::IN to read the file IOField::OUT to write on it
[in]	compact	Flag to choose a compact storage or not [Default: true]

IOField() [4/4]

IOField	(	const string &	mesh_file,
		const string &	file,
		Mesh &	ms,
		AccessType	access,
		bool	compact = true
	)

Constructor using file name, mesh file and mesh.

Parameters

[in]	mesh_file	File containing mesh
[in]	file	File that contains field stored or to store
[in]	ms	Mesh instance
[in]	access	Access code. This number is to be chosen among two enumerated values: IOField::IN to read the file IOField::OUT to write on it
[in]	compact	Flag to choose a compact storage or not [Default: true]

Iter() [1/2]

Iter

Default Constructor.

This constructor set default values: the maximal number of iterations is set to 100 and the tolerance to 1.e-8

Iter() [2/2]

Iter	(	int	max_it,
		real_t	toler
	)

Constructor with iteration parameters.

Parameters

[in]	max_it	Maximum number of iterations
[in]	toler	Tolerance value for convergence

SpMatrix() [1/10]

SpMatrix

(

)

Default constructor.

Initialize a zero-dimension matrix

SpMatrix() [2/10]

SpMatrix	(	const Vect< RC > &	I,
		const Vect< T_ > &	a,
		int	opt = 1
	)

Constructor for a square matrix using non zero row and column indices.

Parameters

[in]	I	Vector containing pairs of row and column indices
[in]	a	Vector containing matrix entries in the same order than the one given by I
[in]	opt	Flag indicating if vector I is cleaned and ordered (opt=1: default) or not (opt=0). In the latter case, this vector can have the same contents more than once and are not necessarily ordered

SpMatrix() [3/10]

SpMatrix	(	const Vect< RC > &	I,
		int	opt = 1
	)

Constructor for a square matrix using non zero row and column indices.

Parameters

[in]	I	Vector containing pairs of row and column indices
[in]	opt	Flag indicating if vectors I is cleaned and ordered (opt=1) or not (opt=0). In the latter case, this vector can have the same contents more than once and are not necessarily ordered

SpMatrix() [4/10]

SpMatrix	(	const vector< size_t > &	row_ptr,
		const vector< size_t > &	col_ind
	)

Constructor for a rectangle matrix.

Parameters

[in]	row_ptr	Vector of row pointers (See the above description of this class).
[in]	col_ind	Vector of column indices (See the above description of this class).

SpMatrix() [5/10]

SpMatrix	(	const vector< size_t > &	row_ptr,
		const vector< size_t > &	col_ind,
		const vector< T_ > &	a
	)

Constructor for a rectangle matrix.

Parameters

[in]	row_ptr	Vector of row pointers (See the above description of this class).
[in]	col_ind	Vector of column indices (See the above description of this class).
[in]	a	vector instance that contain matrix entries stored row by row. Number of rows is extracted from vector row_ptr.

SpMatrix() [6/10]

SpMatrix	(	Mesh &	mesh,
		size_t	dof = 0,
		int	is_diagonal = false
	)

Constructor using a Mesh instance.

Parameters

[in]	mesh	Mesh instance from which matrix graph is extracted.
[in]	dof	Option parameter, with default value 0. dof=1 means that only one degree of freedom for each node (or element or side) is taken to determine matrix structure. The value dof=0 means that matrix structure is determined using all DOFs.
[in]	is_diagonal	Boolean argument to say is the matrix is actually a diagonal matrix or not.

SpMatrix() [7/10]

SpMatrix	(	size_t	nr,
		size_t	nc
	)

Constructor that initializes current instance as a dense matrix.

Normally, for a dense matrix this is not the right class.

Parameters

[in]	nr	Number of matrix rows.
[in]	nc	Number of matrix columns.

SpMatrix() [8/10]

SpMatrix	(	size_t	nr,
		size_t	nc,
		const vector< size_t > &	row_ptr,
		const vector< size_t > &	col_ind
	)

Constructor for a rectangle matrix.

Parameters

[in]	nr	Number of rows
[in]	nc	Number of columns
[in]	row_ptr	Vector of row pointers (See the above description of this class).
[in]	col_ind	Vector of column indices (See the above description of this class).

SpMatrix() [9/10]

SpMatrix	(	size_t	nr,
		size_t	nc,
		const vector< size_t > &	row_ptr,
		const vector< size_t > &	col_ind,
		const vector< T_ > &	a
	)

Constructor for a rectangle matrix.

Parameters

[in]	nr	Number of rows
[in]	nc	Number of columns
[in]	row_ptr	Vector of row pointers (See the above description of this class).
[in]	col_ind	Vector of column indices (See the above description of this class).
[in]	a	vector instance containing matrix entries stored columnwise

SpMatrix() [10/10]

SpMatrix	(	size_t	size,
		int	is_diagonal = false
	)

Constructor that initializes current instance as a dense matrix.

Normally, for a dense matrix this is not the right class.

Parameters

[in]	size	Number of matrix rows (and columns).
[in]	is_diagonal	Boolean argument to say is the matrix is actually a diagonal matrix or not.

TrMatrix()

TrMatrix

(

)

Default constructor.

Initialize a zero dimension tridiagonal matrix

A()

T_ * OFELI::A

(

)

Return element matrix.

Matrix is returned as a C-array

add()

void add ( size_t  i, size_t  j, const T_ &  val  )

virtual

Add a value to an entry of the matrix.

Parameters

[in]	i	Row index
[in]	j	Column index
[in]	val	Constant value to add to a(i,j)

Implements Matrix< T_ >.

Axpy() [1/6]

void Axpy	(	size_t	n,
		T_	a,
		T_ *	x,
		T_ *	y
	)

Multiply array x by a and add result to y

n is the arrays size.

Axpy() [2/6]

void Axpy ( T_  a, const Matrix< T_ > *  m  )

virtual

Add to matrix the product of a matrix by a scalar.

Parameters

[in]	a	Scalar to premultiply
[in]	m	Pointer to Matrix by which a is multiplied. The result is added to current instance

Implements Matrix< T_ >.

Axpy() [3/6]

void Axpy ( T_  a, const Matrix< T_ > *  m  )

virtual

Add to matrix the product of a matrix by a scalar.

Parameters

[in]	a	Scalar to premultiply
[in]	m	Matrix by which a is multiplied. The result is added to current instance

Implements Matrix< T_ >.

Axpy() [4/6]

void Axpy	(	T_	a,
		const SpMatrix< T_ > &	m
	)

Add to matrix the product of a matrix by a scalar.

Parameters

[in]	a	Scalar to premultiply
[in]	m	Matrix by which a is multiplied. The result is added to current instance

Axpy() [5/6]

void Axpy	(	T_	a,
		const TrMatrix< T_ > &	m
	)

Add to matrix the product of a matrix by a scalar.

Parameters

[in]	a	Scalar to premultiply
[in]	m	Matrix by which a is multiplied. The result is added to current instance

Axpy() [6/6]

void Axpy	(	T_	a,
		const vector< T_ > &	x,
		vector< T_ > &	y
	)

Multiply vector x by a and add result to y

x and y are instances of class vector<T_>

b()

T_ * OFELI::b

(

)

Return element right-hand side.

Right-hand side is returned as a C-array

BiCG()

int BiCG	(	const SpMatrix< T_ > &	A,
		int	prec,
		const Vect< T_ > &	b,
		Vect< T_ > &	x,
		int	max_it,
		real_t	toler
	)

Biconjugate gradient solver function.

This function uses the preconditioned Biconjugate Conjugate Gradient algorithm to solve a linear system with a sparse matrix.
The global variable Verbosity enables choosing output message level

• Verbosity < 2 : No output message
• Verbosity > 1 : Notify executing the function CG
• Verbosity > 2 : Notify convergence with number of performed iterations or divergence
• Verbosity > 3 : Output each iteration number and residual
• Verbosity > 6 : Print final solution if convergence
• Verbosity > 10 : Print obtained solution at each iteration

Parameters

[in]	A	Problem matrix (Instance of class SpMatrix).
[in]	prec	Enum variable selecting a preconditioner, among the values IDENT_PREC, DIAG_PREC, ILU_PREC or SSOR_PREC
[in]	b	Right-hand side vector (class Vect)
[in,out]	x	Vect instance containing initial solution guess in input and solution of the linear system in output (If iterations have succeeded).
[in]	max_it	Maximum number of iterations.
	toler	[in] Tolerance for convergence (measured in relative weighted 2-Norm).

Returns

Number of performed iterations,

Template Parameters

<T_>	Data type (double, float, complex<double>, ...)

Author

Rachid Touzani

Copyright

GNU Lesser Public License

CG()

int CG	(	const SpMatrix< T_ > &	A,
		int	prec,
		const Vect< T_ > &	b,
		Vect< T_ > &	x,
		int	max_it,
		real_t	toler
	)

Conjugate gradient solver function.

This function uses the preconditioned Conjugate Gradient algorithm to solve a linear system with a sparse matrix.
The global variable Verbosity enables choosing output message level

• Verbosity < 2 : No output message
• Verbosity > 1 : Notify executing the function CG
• Verbosity > 2 : Notify convergence with number of performed iterations or divergence
• Verbosity > 3 : Output each iteration number and residual
• Verbosity > 6 : Print final solution if convergence
• Verbosity > 10 : Print obtained solution at each iteration

Parameters

[in]	A	Problem matrix (Instance of abstract class SpMatrix).
[in]	prec	Enum variable selecting a preconditioner, among the values IDENT_PREC, DIAG_PREC, ILU_PREC or SSOR_PREC
[in]	b	Right-hand side vector (class Vect)
[in,out]	x	Vect instance containing initial solution guess in input and solution of the linear system in output (If iterations have succeeded).
[in]	max_it	Maximum number of iterations.
[in]	toler	Tolerance for convergence (measured in relative weighted 2-Norm).

Returns

Number of performed iterations,

Template Parameters

<T_>	Data type (double, float, complex<double>, ...)

Author

Rachid Touzani

Copyright

GNU Lesser Public License

CGS()

int CGS	(	const SpMatrix< T_ > &	A,
		int	prec,
		const Vect< T_ > &	b,
		Vect< T_ > &	x,
		int	max_it,
		real_t	toler
	)

Conjugate Gradient Squared solver function.

This function uses the preconditioned Conjugate Gradient Squared algorithm to solve a linear system with a sparse matrix.
The global variable Verbosity enables choosing output message level

• Verbosity < 2 : No output message
• Verbosity > 1 : Notify executing the function CG
• Verbosity > 2 : Notify convergence with number of performed iterations or divergence
• Verbosity > 3 : Output each iteration number and residual
• Verbosity > 6 : Print final solution if convergence
• Verbosity > 10 : Print obtained solution at each iteration

Parameters

[in]	A	Problem matrix (Instance of class SpMatrix).
[in]	prec	Enum variable selecting a preconditioner, among the values IDENT_PREC, DIAG_PREC, ILU_PREC or SSOR_PREC
[in]	b	Right-hand side vector (class Vect)
[in,out]	x	Vect instance containing initial solution guess in input and solution of the linear system in output (If iterations have succeeded).
[in]	max_it	Maximum number of iterations.
[in]	toler	Tolerance for convergence (measured in relative weighted 2-Norm).

Returns

Number of performed iterations

Template Parameters

<T_>	Data type (real_t, float, complex<real_t>, ...)

Author

Rachid Touzani

Copyright

GNU Lesser Public License

check() [1/2]

bool check	(	T_ &	u,
		const T_ &	v
	)

Check convergence for a scalar case (one equation)

Parameters

[in,out]	u	Solution at previous iteration
[in]	v	Solution at current iteration

Returns

true if convergence criterion is satisfied, false if not

After checking, this function copied v into u.

check() [2/2]

bool check	(	Vect< T_ > &	u,
		const Vect< T_ > &	v,
		int	opt = 2
	)

Check convergence.

Parameters

[in,out]	u	Solution vector at previous iteration
[in]	v	Solution vector at current iteration
[in]	opt	Vector norm for convergence checking 1: 1-norm, 2: 2-norm, 0: Max. norm [Default: 2]

Returns

true if convergence criterion is satisfied, false if not

After checking, this function copied v into u.

clear()

void clear

(

Vect< T_ > &

v

)

Assign 0 to all entries of a vector.

Parameters

[in]

v

Vector to clear

Code() [1/2]

int Code

(

const Element &

el

)

Return code of a given element.

Parameters

[in]

el

Reference to Element instance

Returns

Code of element

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Code() [2/2]

int Code	(	const Side &	sd,
		size_t	i = 1
	)

Return code of a given (degree of freedom of) side.

Parameters

[in]	sd	Reference to Side instance
[in]	i	Label of dof [Default: 1]

Returns

Code of dof of side

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Deactivate() [1/3]

void Deactivate

(

size_t

i

)

Change state of a cell from active to inactive (1-D grid)

Parameters

[in]

i

grid cell to remove

Deactivate() [2/3]

void Deactivate	(	size_t	i,
		size_t	j
	)

Change state of a cell from active to inactive (2-D grid)

Parameters

[in]	i	i-th index for grid cell to remove. If this value is 0, all cells (*,j) are deactivated
[in]	j	j-th index for grid cell to remove If this value is 0, all cells (i,*) are deactivated

Remarks

if i and j have value 0 all grid cells are deactivated !!

Deactivate() [3/3]

void Deactivate	(	size_t	i,
		size_t	j,
		size_t	k
	)

Change state of a cell from active to inactive (2-D grid)

Parameters

[in]	i	i-th index for grid cell to remove. If this value is 0, all cells (*,j,k) are deactivated
[in]	j	j-th index for grid cell to remove If this value is 0, all cells (i,*,k) are deactivated
[in]	k	k-th index for grid cell to remove If this value is 0, all cells (i,j,*) are deactivated

DiagPrescribe() [1/2]

void DiagPrescribe	(	Mesh &	mesh,
		Vect< T_ > &	b,
		const Vect< T_ > &	u
	)

Impose by a diagonal method an essential boundary condition.

This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).

Parameters

[in]	mesh	Mesh instance from which information is extracted.
[in,out]	b	Vect instance that contains right-hand side.
[in]	u	Vect instance that conatins imposed valued at DOFs where they are to be imposed.

DiagPrescribe() [2/2]

void DiagPrescribe	(	Vect< T_ > &	b,
		const Vect< T_ > &	u
	)

Impose by a diagonal method an essential boundary condition using the Mesh instance provided by the constructor.

This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).

Parameters

[in,out]	b	Vect instance that contains right-hand side.
[in]	u	Vect instance that conatins imposed valued at DOFs where they are to be imposed.

Discrepancy()

real_t Discrepancy	(	Vect< complex_t > &	x,
		const Vect< complex_t > &	y,
		int	n,
		int	type = 1
	)

Return discrepancy between 2 vectors x and y

Parameters

[in,out]	x	First vector (Instance of class Vect). On output, x is assigned the vector y
[in]	y	Second vector (Instance of class Vect)
[in]	n	Type of norm 1: Weighted 1-Norm 2: Weighted 2-Norm 0: Max-Norm
[in]	type	Discrepancy type (0: Absolute, 1: Relative [Default])

Returns

Computed discrepancy value

Distance()

real_t Distance	(	const Point2D< real_t > &	a,
		const Point2D< real_t > &	b
	)

Return euclidean distance between points a and b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Dot() [1/3]

T_ Dot	(	const Vect< T_ > &	x,
		const Vect< T_ > &	y
	)

Calculate dot product of two vectors.

Returns

Dot (inner or scalar) product Calculate dot (scalar) product of two vectors

Dot() [2/3]

double Dot	(	const vector< real_t > &	x,
		const vector< real_t > &	y
	)

Return dot product of vectors x and y.

x and y are instances of class vector<double>

Dot() [3/3]

T_ Dot	(	size_t	n,
		T_ *	x,
		T_ *	y
	)

Return dot product of arrays x and y

n is the arrays size.

get() [1/7]

T_ * get

(

)

const

Return C-Array.

Non zero terms of matrix is stored row by row.

get() [2/7]

int get	(	DMatrix< real_t > &	A,
		const string &	name
	)

Get DMatrix A instance from file if the field has the given name.

First time step is read from the XML file.

Parameters

[in,out]	A	DMatrix instance
[in]	name	Name to seek in the XML file

get() [3/7]

int get	(	DSMatrix< real_t > &	A,
		const string &	name
	)

Get DSMatrix A instance from file if the field has the given name.

First time step is read from the XML file.

Parameters

[in,out]	A	DSMatrix instance
[in]	name	Name to seek in the XML file

get() [4/7]

T_ get ( size_t  i, size_t  j  ) const

virtual

Return entry (i,j) of matrix if this one is stored, 0 otherwise.

Parameters

[in]	i	Row index (Starting from 1)
[in]	j	Column index (Starting from 1)

Implements Matrix< T_ >.

get() [5/7]

real_t get

(

Vect< real_t > &

v

)

Get Vect v instance from file.

First time step is read from the XML file.

get() [6/7]

int get	(	Vect< real_t > &	v,
		const string &	name
	)

Get Vect v instance from file if the field has the given name.

First time step is read from the XML file.

Parameters

[in,out]	v	Vect instance
[in]	name	Name to seek in the XML file

get() [7/7]

int get	(	Vect< real_t > &	v,
		real_t	t
	)

Get Vect v instance from file corresponding to a specific time value.

The sought vector corresponding to the time value is read from the XML file.

Parameters

[in,out]	v	Vector instance
[in]	t	Time value

getCode() [1/3]

int getCode

(

int

side

)

const

Return code for a side number.

Parameters

[in]

side

Side for which code is returned. Possible values are: MIN_X, MAX_X, MIN_Y, MAX_Y, MIN_Z, MAX_Z

getCode() [2/3]

int getCode	(	size_t	i,
		size_t	j
	)		const

Return code for a grid point.

Parameters

[in]	i	i-th index for node for which code is to be returned.
[in]	j	j-th index for node for which code is to be returned.

getCode() [3/3]

int getCode	(	size_t	i,
		size_t	j,
		size_t	k
	)		const

Return code for a grid point.

Parameters

[in]	i	i-th index for node for which code is to be returned.
[in]	j	j-th index for node for which code is to be returned.
[in]	k	k-th index for node for which code is to be returned.

getColInd()

size_t getColInd ( size_t  i ) const

virtual

Return storage information.

Returns

Column index of the i-th stored element in matrix

Reimplemented from Matrix< T_ >.

getDerivative()

real_t getDerivative	(	string	funct,
		real_t	x
	)

Return the derivative of the function at a given point.

Case of a function of one variable

Parameters

[in]	funct	Name of the function to be evaluated, as read from input file
[in]	x	Value of the variable

Returns

Derivative value

getFunctName()

string getFunctName

(

size_t

n

)

const

Get the name of a read function.

Parameters

[in]

n

index of function

Returns

Name of function

getMaxVar()

real_t getMaxVar	(	size_t	n,
		size_t	i
	)		const

Get maximal value of a variable.

Parameters

[in]	n	index of function
[in]	i	index of variable (between 1 and 3)

Returns

getMinVar()

real_t getMinVar	(	size_t	n,
		size_t	i
	)		const

Get minimal value of a variable.

Parameters

[in]	n	index of function
[in]	i	index of variable (Between 1 and 3)

Returns

Minimal value

getNbFuncts()

size_t getNbFuncts

(

)

const

Get the Number of read functions.

Returns

size_t Number of functions

getNbVar()

size_t getNbVar

(

size_t

n

)

const

Get number of variables of a given function.

Parameters

[in]

n

index of function

Returns

Number of variables

getNy()

size_t getNy

(

)

const

Return number of grid intervals in the y-direction.

ny=0 for 1-D domains (segments)

getNz()

size_t getNz

(

)

const

Return number of grid intervals in the z-direction.

nz=0 for 1-D (segments) and 2-D domains (rectangles)

getSize()

size_t getSize	(	size_t	n,
		size_t	i
	)		const

Get number of points defining tabulation.

Parameters

[in]	n	index of function (Starting from 1)
[in]	i	index of variable (Between 1 and 3)

Returns

Size

getValue() [1/4]

real_t getValue	(	string	funct,
		real_t	x
	)

Return the calculated value of the function.

Case of a function of one variable

Parameters

[in]	funct	Name of the function to be evaluated, as read from input file
[in]	x	Value of the variable

Returns

Computed value of the function

getValue() [2/4]

real_t getValue	(	string	funct,
		real_t	x,
		real_t	y
	)

Return the calculated value of the function.

Case of a function of two variables

Parameters

[in]	funct	Name of the function to be evaluated, as read from input file
[in]	x	Value of the first variable
[in]	y	Value of the second variable

Returns

Computed value of the function

getValue() [3/4]

real_t getValue	(	string	funct,
		real_t	x,
		real_t	y,
		real_t	z
	)

Return the calculated value of the function.

Case of a function of three variables

Parameters

[in]	funct	Name of the funct to be evaluated, as read from input file
[in]	x	Value of the first variable
[in]	y	Value of the second variable
[in]	z	Value of the third variable

Returns

Computed value of the function

getValue() [4/4]

real_t getValue	(	string	funct,
		real_t	x,
		real_t	y,
		real_t	z,
		real_t	t
	)

Return the calculated value of the function.

Case of a function of three variables

Parameters

[in]	funct	Name of the funct to be evaluated, as read from input file
[in]	x	Value of the first variable
[in]	y	Value of the second variable
[in]	z	Value of the third variable
[in]	t	Value of the fourth variable

Returns

Computed value of the function

GMRes()

int GMRes	(	const SpMatrix< T_ > &	A,
		int	prec,
		const Vect< T_ > &	b,
		Vect< T_ > &	x,
		size_t	m,
		int	max_it,
		real_t	toler
	)

GMRes solver function.

This function uses the preconditioned GMRES algorithm to solve a linear system with a sparse matrix.
The global variable Verbosity enables choosing output message level

• Verbosity < 2 : No output message
• Verbosity > 1 : Notify executing the function CG
• Verbosity > 2 : Notify convergence with number of performed iterations or divergence
• Verbosity > 3 : Output each iteration number and residual
• Verbosity > 6 : Print final solution if convergence
• Verbosity > 10 : Print obtained solution at each iteration

Parameters

[in]	A	Problem matrix (Instance of class SpMatrix).
[in]	prec	Enum variable selecting a preconditioner, among the values IDENT_PREC, DIAG_PREC, ILU_PREC or SSOR_PREC
[in]	b	Right-hand side vector (class Vect)
[in,out]	x	Vect instance containing initial solution guess in input and solution of the linear system in output (If iterations have succeeded).
[in]	m	Number of subspaces to generate for iterations.
[in]	max_it	Maximum number of iterations.
[in]	toler	Tolerance for convergence (measured in relative weighted 2-Norm).

Returns

Number of performed iterations,

Template Parameters

<T_>	Data type (double, float, complex<double>, ...)

Author

Rachid Touzani

Copyright

GNU Lesser Public License

isActive() [1/3]

int isActive

(

size_t

i

)

const

Say if cell is active or not (1-D grid)

Parameters

[in]

i

Index of cell

Returns

1 if cell is active, 0 if not

isActive() [2/3]

int isActive	(	size_t	i,
		size_t	j
	)		const

Say if cell is active or not (2-D grid)

Parameters

[in]	i	i-th index of cell
[in]	j	j-th index of cell

Returns

1 if cell is active, 0 if not

isActive() [3/3]

int isActive	(	size_t	i,
		size_t	j,
		size_t	k
	)		const

Say if cell is active or not (3-D grid)

Parameters

[in]	i	i-th index of cell
[in]	j	j-th index of cell
[in]	k	k-th index of cell

Returns

1 if cell is active, 0 if not

Label() [1/3]

size_t Label

(

const Edge &

ed

)

Return label of a given edge.

Parameters

[in]

ed

Reference to Edge instance

Returns

Label of edge

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Label() [2/3]

size_t Label

(

const Element &

el

)

Return label of a given element.

Parameters

[in]

el

Reference to Element instance

Returns

Label of element

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Label() [3/3]

size_t Label

(

const Side &

sd

)

Return label of a given side.

Parameters

[in]

sd

Reference to Side instance

Returns

Label of side

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Laplace1D() [1/2]

void Laplace1D

(

real_t

h

)

Define matrix as the one of 3-point finite difference discretization of the second derivative.

Parameters

[in]

h

mesh size

Laplace1D() [2/2]

void Laplace1D	(	size_t	n,
		real_t	h
	)

Sets the matrix as the one for the Laplace equation in 1-D.

The matrix is initialized as the one resulting from P₁ finite element discretization of the classical elliptic operator -u'' = f with homogeneous Dirichlet boundary conditions

Remarks

This function is available for real valued matrices only.

Parameters

[in]	n	Size of matrix (Number of rows)
[in]	h	Mesh size (assumed constant)

Laplace2D()

void Laplace2D	(	size_t	nx,
		size_t	ny
	)

Sets the matrix as the one for the Laplace equation in 2-D.

The matrix is initialized as the one resulting from P₁ finite element discretization of the classical elliptic operator -Delta u = f with homogeneous Dirichlet boundary conditions

Remarks

This function is available for real valued matrices only.

Parameters

[in]	nx	Number of unknowns in the x-direction
[in]	ny	Number of unknowns in the y-direction

Remarks

The number of rows is equal to nx*ny

MeshToMesh() [1/2]

void MeshToMesh	(	const Vect< real_t > &	u1,
		Vect< real_t > &	u2,
		size_t	nx,
		size_t	ny = 0,
		size_t	nz = 0,
		size_t	dof = 1
	)

Function to redefine a vector defined on a mesh to a new mesh.

The program interpolates (piecewise linear) first the vector on a finer structured grid. Then the values on the new mesh nodes are computed.

Remarks

For efficiency the number of grid cells must be large enough so that interpolation provides efficient accuracy

Parameters

[in]	u1	Input vector of nodal values defined on first mesh. This vector instance must contain Mesh instance
[out]	u2	Output vector of nodal values defined on second mesh. This vector instance must contain Mesh instance
[in]	nx	Number of cells in the x-direction in the fine structured grid
[in]	ny	Number of cells in the y-direction in the fine structured grid The default value of ny is 0, i.e. a 1-D grid
[in]	nz	Number of cells in the z-direction in the fine structured grid The default value of nz is 0, i.e. a 1-D or 2-D grid
[in]	dof	Label of degree of freedom of vector u. Only this dof is considered. [Default: 1]

Note

The input vector u1 is a one degree of freedom per node vector, i.e. its size must be equal (or greater than) the total number of nodes of mesh m1. The size of vector u2 is deduced from the mesh m2

Author

Rachid Touzani

Copyright

GNU Lesser Public License

MeshToMesh() [2/2]

void MeshToMesh	(	Mesh &	m1,
		Mesh &	m2,
		const Vect< real_t > &	u1,
		Vect< real_t > &	u2,
		const Point< real_t > &	xmin,
		const Point< real_t > &	xmax,
		size_t	nx,
		size_t	ny,
		size_t	nz,
		size_t	dof = 1
	)

Function to redefine a vector defined on a mesh to a new mesh.

The program interpolates (piecewise linear) first the vector on a finer structured grid. Then the values on the new mesh nodes are computed. In this function the grid rectangle is defined so that this one can cover only a submesh of m1.

Remarks

For efficiency the number of grid cells must be large enough so that interpolation provides efficient accuracy

Parameters

[in]	m1	Reference to the first mesh instance
[out]	m2	Reference to the second mesh instance
[in]	u1	Input vector of nodal values defined on first mesh
[out]	u2	Output vector of nodal values defined on second mesh
[in]	xmin	Point instance containing minimal coordinates of the rectangle that defines the grid
[in]	xmax	Point instance containing maximal coordinates of the rectangle that defines the grid
[in]	nx	Number of cells in the x-direction in the fine structured grid
[in]	ny	Number of cells in the y-direction in the fine structured grid The default value of ny is 0, i.e. a 1-D grid
[in]	nz	Number of cells in the z-direction in the fine structured grid The default value of nz is 0, i.e. a 1-D or 2-D grid
[in]	dof	Label of degree of freedom of vector u. Only this dof is considered. [Default: 1]

Note

The input vector u1 is a one degree of freedom per node vector, i.e. its size must be equal (or greater than) the total number of nodes of mesh m1. The size of vector u2 is deduced from the mesh m2

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Mult()

void Mult ( const Vect< T_ > &  x, Vect< T_ > &  y  ) const

virtual

Multiply matrix by vector and save in another one.

Parameters

[in]	x	Vector to multiply by matrix
[out]	y	Vector that contains on output the result.

Implements Matrix< T_ >.

MultAdd() [1/2]

void MultAdd ( const Vect< T_ > &  x, Vect< T_ > &  y  ) const

virtual

Multiply matrix by vector x and add to y.

Parameters

[in]	x	Vector to multiply by matrix
[out]	y	Vector to add to the result. y contains on output the result.

Implements Matrix< T_ >.

MultAdd() [2/2]

void MultAdd ( T_  a, const Vect< T_ > &  x, Vect< T_ > &  y  ) const

virtual

Multiply matrix by vector a*x and add to y.

Parameters

[in]	a	Constant to multiply by matrix
[in]	x	Vector to multiply by matrix
[out]	y	Vector to add to the result. y contains on output the result.

Implements Matrix< T_ >.

NodeLabel()

size_t NodeLabel	(	const Side &	sd,
		size_t	n
	)

Return global label of node local label in side.

Parameters

[in]	sd	Reference to Side instance
[in]	n	Local label of node in side

Returns

Global label of node

Author

Rachid Touzani

Copyright

GNU Lesser Public License

open() [1/2]

void open

(

)

Open file.

Case where file name has been previously given (in the constructor).

open() [2/2]

void open	(	const string &	file,
		AccessType	access
	)

Open file.

Parameters

[in]	file	File name.
[in]	access	Access code. This number is to be chosen among two enumerated values: IOField::IN to read the file IOField::OUT to write on it

operator()() [1/5]

T_ operator()

(

size_t

i

)

const

Operator () with one argument (Constant version)

Returns i-th position in the array storing matrix entries. The first entry is at location 1. Entries are stored row by row.

operator()() [2/5]

T_ & operator() ( size_t  i, size_t  j  )

virtual

Operator () (Non constant version)

Parameters

[in]	i	Row index
[in]	j	Column index

Implements Matrix< T_ >.

operator()() [3/5]

T_ & operator() ( size_t  i, size_t  j  )

virtual

Operator () (Non constant version).

Parameters

[in]	i	Row index
[in]	j	Column index

Implements Matrix< T_ >.

operator()() [4/5]

T_ operator() ( size_t  i, size_t  j  ) const

virtual

Operator () (Constant version)

Parameters

[in]	i	Row index
[in]	j	Column index

Implements Matrix< T_ >.

operator()() [5/5]

T_ operator() ( size_t  i, size_t  j  ) const

virtual

Operator () (Constant version).

Parameters

[in]	i	Row index
[in]	j	Column index

Implements Matrix< T_ >.

operator*() [1/25]

Vect< T_ > operator*	(	const DMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	DMatrix instance to multiply by vector
[in]	b	Vect instance

Returns

Vect instance containing A*b

operator*() [2/25]

Vect< T_ > operator*	(	const DSMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	DSMatrix instance to multiply by vector
[in]	b	Vect instance

Returns

Vect instance containing A*b

operator*() [3/25]

Point2D< T_ > operator*	(	const int &	a,
		const Point2D< T_ > &	b
	)

Operator *.

Return point b divided by integer constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [4/25]

Point< T_ > operator*	(	const int &	a,
		const Point< T_ > &	b
	)

Operator *.

Return point b divided by integer constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [5/25]

LocalVect< T_, NR_, NC_ > operator*	(	const LocalMatrix< T_, NR_, NC_ > &	x,
		const LocalVect< T_, NC_ > &	x
	)

Operator * (Multiply matrix A by vector x)

This function performs a matrix-vector product and returns resulting vector as a reference to LocalVect instance

Returns

A*x

operator*() [6/25]

Point2D< T_ > operator*	(	const Point2D< T_ > &	b,
		const int &	a
	)

Operator *

Return point b postmultiplied by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [7/25]

T_ operator*	(	const Point2D< T_ > &	b,
		const Point2D< T_ > &	a
	)

Operator *.

Return point b postmultiplied by integer constant a.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [8/25]

Point2D< T_ > operator*	(	const Point2D< T_ > &	b,
		const T_ &	a
	)

Operator /

Return point b postmultiplied by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [9/25]

T_ operator*	(	const Point< T_ > &	b,
		const Point< T_ > &	a
	)

Operator *

Return inner (scalar) product of points a and b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [10/25]

Point< T_ > operator*	(	const Point< T_ > &	b,
		const int &	a
	)

Operator *

Return point b postmultiplied by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [11/25]

Point< T_ > operator*	(	const Point< T_ > &	b,
		const T_ &	a
	)

Operator /

Return point b multiplied by constant a

operator*() [12/25]

Vect< T_ > operator*	(	const SkMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	SkMatrix instance to multiply by vector
[in]	b	Vect instance

Returns

Vect instance containing A*b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [13/25]

Vect< T_ > operator*	(	const SkSMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	SkSMatrix instance to multiply by vector
[in]	b	Vect instance

Returns

Vect instance containing A*b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [14/25]

Vect< T_ > operator*	(	const SpMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	SpMatrix instance to multiply by vector
[in]	b	Vect instance

Returns

Vect instance containing A*b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [15/25]

Point2D< T_ > operator*	(	const T_ &	a,
		const Point2D< T_ > &	b
	)

Operator *.

Return point b premultiplied by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [16/25]

Point< T_ > operator*	(	const T_ &	a,
		const Point< T_ > &	b
	)

Operator *

Return point b premultiplied by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [17/25]

Vect< T_ > operator*	(	const T_ &	a,
		const Vect< T_ > &	x
	)

Operator * (Premultiplication of vector by constant)

Returns

a*x

operator*() [18/25]

Vect< T_ > operator*	(	const TrMatrix< T_ > &	A,
		const Vect< T_ > &	b
	)

Operator * (Multiply vector by matrix and return resulting vector.

Parameters

[in]	A	TrMatrix instance to multiply by vector
[in]	b	Vect instance

Returns

Vect instance containing A*b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*() [19/25]

Vect< T_ > operator*

(

const Vect< T_ > &

x

)

const

Operator * to multiply matrix by a vector.

Parameters

[in]

x

Vect instance to multiply by

Returns

Vector product of matrix by x

operator*() [20/25]

Vect< T_ > operator*	(	const Vect< T_ > &	x,
		const T_ &	a
	)

Operator * (Postmultiplication of vector by constant)

Returns

x*a

operator*() [21/25]

real_t operator*	(	const vector< real_t > &	x,
		const vector< real_t > &	y
	)

Operator * (Dot product of 2 vector instances)

Returns

x.y

operator*() [22/25]

BMatrix< T_ > operator*	(	T_	a,
		const BMatrix< T_ > &	A
	)

Operator * (Premultiplication of matrix by constant)

Returns

a*A

operator*() [23/25]

LocalMatrix< T_, NR_, NC_ > operator*	(	T_	a,
		const LocalMatrix< T_, NR_, NC_ > &	x
	)

Operator * (Multiply matrix x by scalar a)

Returns

a*x

operator*() [24/25]

LocalVect< T_, N_ > operator*	(	T_	a,
		const LocalVect< T_, N_ > &	x
	)

Operator * (Premultiplication of vector by constant)

Returns

a*x

operator*() [25/25]

TrMatrix< T_ > operator*	(	T_	a,
		const TrMatrix< T_ > &	A
	)

Operator * (Premultiplication of matrix by constant)

Returns

a*A

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator*=() [1/2]

SpMatrix< T_ > & operator*=

(

const T_ &

a

)

Operator *= to premultiply matrix by a constant.

Parameters

[in]

a

Constant to multiply matrix by

Returns

Resulting matrix

operator*=() [2/2]

TrMatrix< T_ > & operator*=

(

const T_ &

x

)

Operator *=.

Premultiply matrix entries by constant value x.

operator+() [1/6]

LocalVect< T_, N_ > operator+	(	const LocalVect< T_, N_ > &	x,
		const LocalVect< T_, N_ > &	y
	)

Operator + (Add two vectors)

Returns

x+y

operator+() [2/6]

Point2D< T_ > operator+	(	const Point2D< T_ > &	a,
		const Point2D< T_ > &	b
	)

Operator +.

Return sum of two points a and b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator+() [3/6]

Point2D< T_ > operator+	(	const Point2D< T_ > &	a,
		const T_ &	x
	)

Operator +.

Translate a by x

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator+() [4/6]

Point< T_ > operator+	(	const Point< T_ > &	a,
		const Point< T_ > &	b
	)

Operator +

Return sum of two points a and b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator+() [5/6]

Point< T_ > operator+	(	const Point< T_ > &	a,
		const T_ &	x
	)

Operator +

Translate a by x

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator+() [6/6]

Vect< T_ > operator+	(	const Vect< T_ > &	x,
		const Vect< T_ > &	y
	)

Operator + (Addition of two instances of class Vect)

Returns

x + y

operator-() [1/9]

Figure operator-	(	const Figure &	f1,
		const Figure &	f2
	)

Function to define a Figure instance as the set subtraction of two Figure instances.

Parameters

[in]	f1	First Figure instance to subtract from
[in]	f2	Second Figure instance to subtract

Returns

Updated resulting Figure instance

operator-() [2/9]

LocalVect< T_, N_ > operator-	(	const LocalVect< T_, N_ > &	x,
		const LocalVect< T_, N_ > &	y
	)

Operator - (Subtract two vectors)

Returns

x-y

operator-() [3/9]

Point2D< T_ > operator-

(

const Point2D< T_ > &

a

)

Unary Operator -

Return minus a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator-() [4/9]

Point2D< T_ > operator-	(	const Point2D< T_ > &	a,
		const Point2D< T_ > &	b
	)

Operator -

Return point a minus point b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator-() [5/9]

Point2D< T_ > operator-	(	const Point2D< T_ > &	a,
		const T_ &	x
	)

Operator -

Translate a by -x

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator-() [6/9]

Point< T_ > operator-

(

const Point< T_ > &

a

)

Unary Operator -

Return minus a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator-() [7/9]

Point< T_ > operator-	(	const Point< T_ > &	a,
		const Point< T_ > &	b
	)

Operator -

Return point a minus point b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator-() [8/9]

Point< T_ > operator-	(	const Point< T_ > &	a,
		const T_ &	x
	)

Operator -

Translate a by -x

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator-() [9/9]

Vect< T_ > operator-	(	const Vect< T_ > &	x,
		const Vect< T_ > &	y
	)

Operator - (Difference between two vectors of class Vect)

Returns

x - y

operator/() [1/4]

Point2D< T_ > operator/	(	const Point2D< T_ > &	b,
		const T_ &	a
	)

Operator /

Return point b divided by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator/() [2/4]

Point< T_ > operator/	(	const Point< T_ > &	b,
		const T_ &	a
	)

Operator /

Return point b divided by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator/() [3/4]

Vect< T_ > operator/	(	const Vect< T_ > &	x,
		const T_ &	a
	)

Operator / (Divide vector entries by constant)

Returns

x/a

operator/() [4/4]

LocalVect< T_, N_ > operator/	(	T_	a,
		const LocalVect< T_, N_ > &	x
	)

Operator / (Division of vector by constant)

Returns

x/a

operator<<() [1/20]

ostream & operator<<	(	ostream &	s,
		const complex_t &	x
	)

Output a complex number.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [2/20]

ostream & operator<<	(	ostream &	s,
		const EdgeList &	el
	)

Output EdgeList instance.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [3/20]

ostream & operator<<	(	ostream &	s,
		const ElementList &	el
	)

Output ElementList instance.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [4/20]

ostream & operator<<	(	ostream &	s,
		const Mesh &	ms
	)

Output mesh data.

Level of mesh output depends on the global variable Verbosity

• If Verbosity=0 or Verbosity=1, this function outputs only principal mesh parameters: number of nodes, number of elements, ...
• If Verbosity>1, this function outputs in addition the list of 10 first nodes, elements and sides
• If Verbosity>2, this function outputs in addition the list of 50 first nodes, elements and sides
• If Verbosity>3, this function outputs all mesh data

operator<<() [5/20]

ostream & operator<<	(	ostream &	s,
		const Node &	nd
	)

Output node data.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [6/20]

ostream & operator<<	(	ostream &	s,
		const NodeList &	nl
	)

Output NodeList instance.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [7/20]

ostream & operator<<	(	ostream &	s,
		const Side &	sd
	)

Output side data.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [8/20]

ostream & operator<<	(	ostream &	s,
		const SideList &	sl
	)

Output SideList instance.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [9/20]

ostream & operator<<	(	ostream &	s,
		const SkMatrix< T_ > &	a
	)

Output matrix in output stream.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [10/20]

ostream & operator<<	(	ostream &	s,
		const SkSMatrix< T_ > &	a
	)

Output matrix in output stream.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [11/20]

ostream & operator<<	(	ostream &	s,
		const SpMatrix< T_ > &	A
	)

Output matrix in output stream.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [12/20]

ostream & operator<<	(	ostream &	s,
		const std::list< T_ > &	l
	)

Output a vector instance.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [13/20]

ostream & operator<<	(	ostream &	s,
		const std::pair< T_, T_ > &	a
	)

Output a pair instance.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [14/20]

ostream & operator<<	(	ostream &	s,
		const std::string &	c
	)

Output a string.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [15/20]

ostream & operator<<	(	ostream &	s,
		const TrMatrix< T_ > &	a
	)

Output matrix in output stream.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [16/20]

ostream & operator<<	(	ostream &	s,
		const Vect< T_ > &	v
	)

Output vector in output stream.

Level of vector output depends on the global variable Verbosity

• If Verbosity=0, this function outputs vector size only.
• If Verbosity>0, this function outputs vector size, vector name, value of time, and number of components
• If Verbosity>1, this function outputs in addition the first 10 entries in vector
• If Verbosity>2, this function outputs in addition the first 50 entries in vector
• If Verbosity>3, this function outputs in addition the first 100 entries in vector
• If Verbosity>4, this function outputs all vector entries

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [17/20]

ostream & operator<<	(	ostream &	s,
		const vector< T_ > &	v
	)

Output a vector instance.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [18/20]

ostream & operator<<	(	ostream &	s,
		TimeStepping &	ts
	)

Output differential system information.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [19/20]

ostream & operator<<	(	std::ostream &	s,
		const Point2D< T_ > &	a
	)

Output point coordinates.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator<<() [20/20]

ostream & operator<<	(	std::ostream &	s,
		const Point< T_ > &	a
	)

Output point coordinates.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator=() [1/2]

void operator=

(

const T_ &

x

)

Operator =.

Assign constant value x to all matrix entries.

operator=() [2/2]

TrMatrix< T_ > & operator=

(

const TrMatrix< T_ > &

m

)

Operator =.

Copy matrix m to current matrix instance.

operator==() [1/3]

operator==	(	const Element &	el1,
		const Element &	el2
	)

Check equality between 2 elements.

Parameters

[in]	el1	Reference to first Side instance
[in]	el2	Reference to second Side instance

Returns

true is elements are equal, i.e. if they have the same nodes, false if not.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator==() [2/3]

bool operator==	(	const Point2D< T_ > &	a,
		const Point2D< T_ > &	b
	)

Operator ==.

Return true if a=b, false if not.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator==() [3/3]

bool operator==	(	const Side &	sd1,
		const Side &	sd2
	)

Check equality between 2 sides.

Parameters

[in]	sd1	Reference to first Side instance
[in]	sd2	Reference to second Side instance

Returns

true is sides are equal, i.e. if they have the same nodes, false if not.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

operator[]()

T_ operator[]

(

size_t

i

)

const

Operator [] (Constant version).

Returns i-th position in the array storing matrix entries. The first entry is at location 0. Entries are stored row by row.

Prev()

T_ * OFELI::Prev

(

)

Return element previous vector.

This is the vector given in time dependent constructor. It is returned as a C-array.

put()

void put

(

const Vect< real_t > &

v

)

Store Vect instance v in file.

Parameters

[in]

v

Vect instance to store

qksort()

void qksort	(	std::vector< T_ > &	a,
		int	begin,
		int	end,
		C_	compare
	)

Function to sort a vector according to a key function.

qksort uses the famous quick sorting algorithm.

Parameters

[in,out]	a	Vector to sort.
[in]	begin	index of starting index (0 for the beginning of the vector)
[in]	end	index of ending index
[in]	compare	A function object that implements the ordering. The user must provide this function that returns a boolean function that is true if the first argument is less than the second and false if not.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

saveField() [1/2]

void saveField	(	const Vect< real_t > &	v,
		const Mesh &	mesh,
		string	output_file,
		int	opt
	)

Save a vector to an output file in a given file format.

Case where the vector does not contain mesh information

Parameters

[in]	v	Vect instance to save
[in]	mesh	Mesh instance
[in]	output_file	Output file where to save the vector
[in]	opt	Option to choose file format to save. This is to be chosen among enumerated values: GMSH, GNUPLOT, MATLAB, TECPLOT, VTK

Author

Rachid Touzani

Copyright

GNU Lesser Public License

saveField() [2/2]

void saveField	(	Vect< real_t > &	v,
		const Grid &	g,
		string	output_file,
		int	opt = VTK
	)

Save a vector to an output file in a given file format, for a structured grid data.

Parameters

[in]	v	Vect instance to save
[in]	g	Grid instance
[in]	output_file	Output file where to save the vector
[in]	opt	Option to choose file format to save. This is to be chosen among enumerated values: GMSH, VTK

Author

Rachid Touzani

Copyright

GNU Lesser Public License

saveGmsh() [1/2]

void saveGmsh	(	const string &	file,
		const Mesh &	mesh
	)

This function outputs a Mesh instance in a file in Gmsh format.

Note

Gmsh is a free mesh generator that can be downloaded from the site: http://www.geuz.org/gmsh/

Parameters

[in]	file	Output file in Gmsh format.
[in]	mesh	Mesh instance to save.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

saveGmsh() [2/2]

void saveGmsh	(	Mesh &	mesh,
		string	input_file,
		string	output_file,
		int	f = 1
	)

Save a vector to an output Gmsh file.

Gmsh is a free mesh generator and postprocessor that can be downloaded from the site:
http://www.geuz.org/gmsh/

Parameters

[in]	mesh	Reference to Mesh instance
[in]	input_file	Input file (OFELI XML file containing a field).
[in]	output_file	Output file (Gmsh format file)
[in]	f	Field is stored each f time step [Default: 1]

Author

Rachid Touzani

Copyright

GNU Lesser Public License

saveGMSH()

void saveGMSH	(	string	output_file,
		string	mesh_file
	)

Save field vectors in a file using GMSH format.

This member function enables avoiding the use of cfield. It must be used once all field vectors have been stored in output file. It closes this file and copies its contents to a GMSH file.

Parameters

[in]	output_file	Output file name where to store using GMSH format
[in]	mesh_file	File containing mesh data

saveGnuplot() [1/2]

void saveGnuplot	(	const string &	file,
		const Mesh &	mesh
	)

This function outputs a Mesh instance in a file in Gmsh format.

Note

Gnuplot is a command-line driven program for producing 2D and 3D plots. It is under the GNU General Public License. Available information can be found in the site:
http://www.gnuplot.info/

Parameters

[out]	file	Output file in Gnuplot format.
[in]	mesh	Mesh instance to save.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

saveGnuplot() [2/2]

void saveGnuplot	(	Mesh &	mesh,
		string	input_file,
		string	output_file,
		int	f = 1
	)

Save a vector to an input Gnuplot file.

Gnuplot is a command-line driven program for producing 2D and 3D plots. It is under the GNU General Public License. Available information can be found in the site:
http://www.gnuplot.info/

Parameters

[in]	mesh	Reference to Mesh instance
[in]	input_file	Input file (OFELI XML file containing a field).
[in]	output_file	Output file (gnuplot format file)
[in]	f	Field is stored each f time step [Default: 1]

Author

Rachid Touzani

Copyright

GNU Lesser Public License

saveTecplot() [1/2]

void saveTecplot	(	const string &	file,
		const Mesh &	mesh
	)

This function outputs a Mesh instance in a file in Tecplot format.

Note

Tecplot is high quality post graphical commercial processing program developed by Amtec. Available information can be found in the site:
http://www.tecplot.com

Parameters

[out]	file	Output file in Tecplot format.
[in]	mesh	Mesh instance to save.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

saveTecplot() [2/2]

void saveTecplot	(	Mesh &	mesh,
		string	input_file,
		string	output_file,
		int	f = 1
	)

Save a vector to an output file to an input Tecplot file.

Tecplot is high quality post graphical commercial processing program developed by Amtec. Available information can be found in the site: http://www.tecplot.com

Parameters

[in]	mesh	Reference to Mesh instance
[in]	input_file	Input file (OFELI XML file containing a field).
[in]	output_file	Output file (gnuplot format file)
[in]	f	Field is stored each f time step [Default: 1]

Author

Rachid Touzani

Copyright

GNU Lesser Public License

saveVTK() [1/2]

void saveVTK	(	const string &	file,
		const Mesh &	mesh
	)

This function outputs a Mesh instance in a file in VTK format.

Note

The Visualization ToolKit (VTK) is an open source, freely available software system for 3D computer graphics. Available information can be found in the site:
http://public.kitware.com/VTK/

Parameters

[out]	file	Output file in VTK format.
[in]	mesh	Mesh instance to save.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

saveVTK() [2/2]

saveVTK	(	Mesh &	mesh,
		string	input_file,
		string	output_file,
		int	f = 1
	)

Save a vector to an output VTK file.

The Visualization ToolKit (VTK) is an open source, freely available software system for 3D computer graphics. Available information can be found in the site:
http://public.kitware.com/VTK/

Parameters

[in]	mesh	Reference to Mesh instance
[in]	input_file	Input file (OFELI XML file containing a field).
[in]	output_file	Output file (VTK format file)
[in]	f	Field is stored each f time step [Default: 1]

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Scale() [1/3]

void Scale	(	T_	a,
		const Vect< T_ > &	x,
		Vect< T_ > &	y
	)

Mutiply vector x by a and save result in vector y

x and y are instances of class Vect<T_>

Scale() [2/3]

void Scale	(	T_	a,
		const vector< T_ > &	x,
		vector< T_ > &	y
	)

Mutiply vector x by a and save result in vector y

x and y are instances of class vector<T_>

Scale() [3/3]

void Scale	(	T_	a,
		vector< T_ > &	x
	)

Mutiply vector x by a

x is an instance of class vector<T_>

set()

void set ( size_t  i, size_t  j, const T_ &  val  )

virtual

Assign a value to an entry of the matrix.

Parameters

[in]	i	Row index
[in]	j	Column index
[in]	val	Value to assign to a(i,j)

Implements Matrix< T_ >.

setCode() [1/2]

void setCode	(	int	side,
		int	code
	)

Set a code for grid points on sides.

Parameters

[in]	side	Side for which code is assigned. Possible values are: MIN_X, MAX_X, MIN_Y, MAX_Y, MIN_Z, MAX_Z
[in]	code	Code to assign.

setCode() [2/2]

void setCode	(	string	exp,
		int	code
	)

Set a code for some grid points.

Parameters

[in]	exp	Regular expression that determines the set of grid points on which the code is applied.
[in]	code	Code to assign.

setDomain() [1/4]

void setDomain	(	Point< real_t >	xmin,
		Point< real_t >	xmax
	)

Set Dimensions of the domain: 3-D case.

Parameters

[in]	xmin	Minimal coordinate value
[in]	xmax	Maximal coordinate value

setDomain() [2/4]

void setDomain	(	real_t	xmin,
		real_t	xmax
	)

Set Dimensions of the domain: 1-D case.

Parameters

[in]	xmin	Minimal value of x-coordinate
[in]	xmax	Maximal value of x-coordinate

setDomain() [3/4]

void setDomain	(	real_t	xmin,
		real_t	xmax,
		real_t	ymin,
		real_t	ymax
	)

Set Dimensions of the domain: 2-D case.

Parameters

[in]	xmin	Minimal value of x-coordinate
[in]	xmax	Maximal value of x-coordinate
[in]	ymin	Minimal value of y-coordinate
[in]	ymax	Maximal value of y-coordinate

setDomain() [4/4]

void setDomain	(	real_t	xmin,
		real_t	xmax,
		real_t	ymin,
		real_t	ymax,
		real_t	zmin,
		real_t	zmax
	)

Set Dimensions of the domain: 3-D case.

Parameters

[in]	xmin	Minimal value of x-coordinate
[in]	xmax	Maximal value of x-coordinate
[in]	ymin	Minimal value of y-coordinate
[in]	ymax	Maximal value of y-coordinate
[in]	zmin	Minimal value of z-coordinate
[in]	zmax	Maximal value of z-coordinate

setFile()

void setFile

(

string

file

)

Set file name.

This function is to be used when the default constructor is invoked.

setGraph()

void setGraph	(	const Vect< RC > &	I,
		int	opt = 1
	)

Set graph of matrix by giving a vector of its nonzero entries.

Parameters

[in]	I	Vector containing pairs of row and column indices
[in]	opt	Flag indicating if vector I is cleaned and ordered (opt=1: default) or not (opt=0). In the latter case, this vector can have the same contents more than once and are not necessarily ordered

setMesh()

void setMesh	(	Mesh &	mesh,
		size_t	dof = 0
	)

Determine mesh graph and initialize matrix.

This member function is called by constructor with the same arguments

Parameters

[in]	mesh	Mesh instance for which matrix graph is determined.
[in]	dof	Option parameter, with default value 0. dof=1 means that only one degree of freedom for each node (or element or side) is taken to determine matrix structure. The value dof=0 means that matrix structure is determined using all DOFs.

setMeshFile()

void setMeshFile

(

const string &

file

)

Set mesh file.

Parameters

[in]

file

Mesh file

setN()

void setN	(	size_t	nx,
		size_t	ny = 0,
		size_t	nz = 0
	)

Set number of grid intervals in the x, y and z-directions.

Number of points is the number of intervals plus one in each direction

Parameters

[in]	nx	Number of grid intervals in the x-direction
[in]	ny	Number of grid intervals in the y-direction (Default=0: 1-D grid)
[in]	nz	Number of grid intervals in the z-direction (Default=0: 1-D or 2-D grid)

Remarks

: The size of the grid (xmin and xmax) must have been defined before.

setSize() [1/3]

void setSize	(	size_t	nr,
		size_t	nc
	)

Set size (number of rows) of matrix.

Parameters

[in]	nr	Number of rows
[in]	nc	Number of columns

setSize() [2/3]

void setSize

(

size_t

size

)

Set size of matrix (case where it's a square matrix).

Parameters

[in]

size

Number of rows and columns.

setSize() [3/3]

void setSize

(

size_t

size

)

Set size (number of rows) of matrix.

Parameters

[in]

size

Number of rows and columns.

setSolver()

void setSolver	(	Iteration	solver = CG_SOLVER,
		Preconditioner	prec = DIAG_PREC,
		int	max_it = 1000,
		real_t	toler = 1.e-8
	)

Choose solver and preconditioner for an iterative procedure.

Parameters

[in]	solver	Option to choose iterative solver in an enumerated variable CG_SOLVER: Conjugate Gradient [default] CGS_SOLVER: Squared conjugate gradient BICG_SOLVER: Biconjugate gradient BICG_STAB_SOLVER: Biconjugate gradient stabilized GMRES_SOLVER: Generalized Minimal Residual Default value is CG_SOLVER
[in]	prec	Option to choose preconditioner in an enumerated variable IDENT_PREC: Identity preconditioner (no preconditioning) DIAG_PREC: Diagonal preconditioner [default] SSOR_PREC: SSOR (Symmetric Successive Over Relaxation) preconditioner DILU_PREC: ILU (Diagonal Incomplete factorization) preconditioner ILU_PREC: ILU (Incomplete factorization) preconditioner Default value is DIAG_PREC
[in]	max_it	Maximum number of allowed iterations. Default value is 1000.
[in]	toler	Tolerance for convergence. Default value is 1.e-8

setXMax()

void setXMax

(

const Point< real_t > &

x

)

Set max. coordinates of the domain.

Parameters

[in]

x

Maximal values of coordinates

setXMin()

void setXMin

(

const Point< real_t > &

x

)

Set min. coordinates of the domain.

Parameters

[in]

x

Minimal values of coordinates

solve() [1/3]

int solve ( const Vect< T_ > &  b, Vect< T_ > &  x, bool  fact = false  )

virtual

Solve the linear system of equations.

The default parameters are:

• CG_SOLVER for solver
• DIAG_PREC for preconditioner
• Max. Number of iterations is 1000
• Tolerance is 1.e-8

To change these values, call function setSolver before this function

Parameters

[in]	b	Vector that contains right-hand side
[out]	x	Vector that contains the obtained solution
[in]	fact	Unused argument

Returns

Number of actual performed iterations

Implements Matrix< T_ >.

solve() [2/3]

int solve ( const Vect< T_ > &  b, Vect< T_ > &  x, bool  fact = false  )

virtual

Solve a linear system with current matrix (forward and back substitution).

Parameters

[in]	b	Vect instance that contains right-hand side.
[out]	x	Vect instance that contains solution.
[in]	fact	Unused argument

Returns

• 0 if solution was normally performed,
• n if the n-th pivot is null.

Warning: Matrix is modified after this function.

Implements Matrix< T_ >.

solve() [3/3]

int solve ( Vect< T_ > &  b, bool  fact = true  )

virtual

Solve a linear system with current matrix (forward and back substitution).

Parameters

[in,out]	b	Vect instance that contains right-hand side on input and solution on output.
[in]	fact	Ununsed argument

Returns

• 0 if solution was normally performed,
• n if the n-th pivot is null.

Warning: Matrix is modified after this function.

Implements Matrix< T_ >.

SqrDistance()

real_t SqrDistance	(	const Point2D< real_t > &	a,
		const Point2D< real_t > &	b
	)

Return squared euclidean distance between points a and b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

TMult()

void TMult ( const Vect< T_ > &  x, Vect< T_ > &  y  ) const

virtual

Multiply transpose of matrix by vector x and save in y.

Parameters

[in]	x	Vector to multiply by matrix
[out]	y	Vector that contains on output the result.

Implements Matrix< T_ >.

Xpy()

void Xpy	(	const vector< T_ > &	x,
		vector< T_ > &	y
	)

Add vector x to y

x and y are instances of class vector<T_>