LinearPDE2D Class Reference

Solves a generic linear PDE in 2-D using 3-Node triangular finite elements. More...

Inheritance diagram for LinearPDE2D:

Public Member Functions
	LinearPDE2D ()
	Default Constructor. Constructs an empty equation.
	LinearPDE2D (Mesh &ms)
	Constructor using Mesh data. More...
	LinearPDE2D (Mesh &ms, Vect< real_t > &u)
	Constructor using Mesh and initial condition. More...
	~LinearPDE2D ()
	Destructor.
void	Mat_00 (real_t coef=1.0)
	Add 0th order term, in time and space, to left-hand side coef More...
void	Mat_10 (real_t coef=1.0)
	Add 1st order term in time, 0th in space to left-hand side. More...
void	Mat_01 (real_t coef=1.0)
	Add Oth order term in time, 1st in space to left-hand side. More...
void	Mat_20 (real_t coef=1.0)
	Add 2nd order term in time, 0th in space to left-hand side. More...
void	Mat_02 (real_t coef=1.0)
	Add 0th order term in time, 2nd in space to left-hand side. More...
void	BodyRHS (const Vect< real_t > &f)
	Add body right-hand side term to right hand side. More...
void	BodyRHS (real_t f)
	Add body right-hand side term to right hand side. More...
void	BoundaryRHS (real_t flux)
	Add boundary right-hand side flux to right hand side. More...
void	BoundaryRHS (const Vect< real_t > &f)
	Add boundary right-hand side term to right hand side after multiplying it by coefficient coef More...
Point< real_t > &	Flux () const
	Return (constant) heat flux in element.
void	Grad (Vect< Point< real_t > > &g)
	Compute gradient of solution. More...
Point< real_t > &	Grad (const Vect< real_t > &u) const
	Return gradient of a vector in element. More...
void	setInput (EType opt, Vect< real_t > &u)
	Set equation input data. More...
Public Member Functions inherited from Equa_LinearPDE< 3, 2 >
	Equa_LinearPDE ()
	Default constructor. More...
virtual	~Equa_LinearPDE ()
	Destructor.
void	setNoLumping ()
	Set no lumping. More...
void	setStab ()
	Set stabilization for convection term. More...
void	set_00 (real_t a=1.0)
	Set coefficient for term (0,0): 0th order in time and space. More...
void	set_00 (Fct &f)
	Set coefficient for term (0,0): 0th order in time and space. More...
void	set_00 (const string &f)
	Set coefficient for term (0,0): 0th order in time and space. More...
void	set_10 (real_t a=1.0)
	Set coefficient for term (1,0): 1st order in time, 0th order in space. More...
void	set_10 (Fct &f)
	Set coefficient for term (1,0): 1st order in time, 0th order in space. More...
void	set_20 (real_t a=1.0)
	Set coefficient for term (2,0): 2nd order in time, 0th order in space. More...
void	set_20 (Fct &f)
	Set coefficient for term (2,0): 2nd order in time, 0th order in space. More...
void	set_01 (real_t a=1.0)
	Set coefficient for term (0,1): 0th order in time, 1st order in space. More...
void	set_01 (Point< real_t > &a)
	Set coefficient for term (0,1): 0th order in time, 1st order in space. More...
void	set_01 (Fct &f)
	Set coefficient for term (0,1): 0th order in time, 1st order in time and space. More...
void	set_01 (Vect< real_t > &a)
	Set coefficient for term (0,1): 0th order in time, 1st order in space. More...
void	set_02 (real_t a=1.0)
	Set coefficient for term (0,2): 0th order in time, 2nd order in space. More...
void	set_02 (Fct &f)
	Set coefficient for term (0,2): 0th order in time, 2nd order in time and space. More...
void	build ()
	Build the linear system of equations for the steady state case.
void	build (TimeStepping &s)
	Build the linear system of equations. More...
void	build (EigenProblemSolver &e)
	Build the linear system for an eigenvalue problem. More...
Public Member Functions inherited from Equation< NEN_, NEN_, NSN_, NSN_ >
	Equation ()
	Equation (Mesh &mesh)
	Constructor with mesh instance. More...
	Equation (Mesh &mesh, Vect< real_t > &u)
	Constructor with mesh instance and solution vector. More...
	Equation (Mesh &mesh, Vect< real_t > &u, real_t &init_time, real_t &final_time, real_t &time_step)
	Constructor with mesh instance, matrix and right-hand side. More...
	~Equation ()
	Destructor.
void	updateBC (const Element &el, const Vect< real_t > &bc)
	Update Right-Hand side by taking into account essential boundary conditions. More...
void	DiagBC (DOFSupport dof_type=NODE_DOF, int dof=0)
	Update element matrix to impose bc by diagonalization technique. More...
void	LocalNodeVector (Vect< real_t > &b)
	Localize element vector from a Vect instance. More...
void	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEE_ > &be)
	Localize element vector from a Vect instance. More...
void	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be, int dof)
	Localize Element Vector from a Vect instance. More...
void	SideNodeVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &bs)
	Localize side vector from a Vect instance. More...
void	SideSideVector (const Vect< real_t > &b, vector< real_t > &bs)
	Localize side vector from a Vect instance. More...
void	ElementNodeVectorSingleDOF (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be)
	Localize Element Vector from a Vect instance. More...
void	ElementSideVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &be)
	Localize Element Vector from a Vect instance. More...
void	ElementVector (const Vect< real_t > &b, DOFSupport dof_type=NODE_DOF, int flag=0)
	Localize element vector. More...
void	SideVector (const Vect< real_t > &b, vector< real_t > &sb)
	Localize side vector. More...
void	ElementNodeCoordinates ()
	Localize coordinates of element nodes. More...
void	SideNodeCoordinates ()
	Localize coordinates of side nodes. More...
void	ElementAssembly (Matrix< real_t > *A)
	Assemble element matrix into global one. More...
void	ElementAssembly (BMatrix< real_t > &A)
	Assemble element matrix into global one. More...
void	ElementAssembly (SkSMatrix< real_t > &A)
	Assemble element matrix into global one. More...
void	ElementAssembly (SkMatrix< real_t > &A)
	Assemble element matrix into global one. More...
void	ElementAssembly (SpMatrix< real_t > &A)
	Assemble element matrix into global one. More...
void	ElementAssembly (TrMatrix< real_t > &A)
	Assemble element matrix into global one. More...
void	ElementAssembly (Vect< real_t > &v)
	Assemble element vector into global one. More...
void	DGElementAssembly (Matrix< real_t > *A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
void	DGElementAssembly (SkSMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
void	DGElementAssembly (SkMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
void	DGElementAssembly (SpMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
void	DGElementAssembly (TrMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
void	SideAssembly (Matrix< real_t > *A)
	Assemble side (edge or face) matrix into global one. More...
void	SideAssembly (SkSMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one. More...
void	SideAssembly (SkMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one. More...
void	SideAssembly (SpMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one. More...
void	SideAssembly (Vect< real_t > &v)
	Assemble side (edge or face) vector into global one. More...
void	AxbAssembly (const Element &el, const Vect< real_t > &x, Vect< real_t > &b)
	Assemble product of element matrix by element vector into global vector. More...
void	AxbAssembly (const Side &sd, const Vect< real_t > &x, Vect< real_t > &b)
	Assemble product of side matrix by side vector into global vector. More...
size_t	getNbNodes () const
	Return number of element nodes.
size_t	getNbEq () const
	Return number of element equations.
real_t	setMaterialProperty (const string &exp, const string &prop)
	Define a material property by an algebraic expression. More...
Public Member Functions inherited from Equa
	Equa ()
	Default constructor.
virtual	~Equa ()
	Destructor.
void	setMesh (Mesh &m)
	Define mesh and renumber DOFs after removing imposed ones.
Mesh &	getMesh () const
	Return reference to Mesh instance. More...
LinearSolver &	getLinearSolver ()
	Return reference to linear solver instance.
Matrix< real_t > *	getMatrix () const
	Return pointer to matrix.
void	setSolver (Iteration ls, Preconditioner pc=IDENT_PREC)
	Choose solver for the linear system. More...
void	setMatrixType (int t)
	Choose type of matrix. More...
int	solveLinearSystem (Matrix< real_t > *A, Vect< real_t > &b, Vect< real_t > &x)
	Solve the linear system with given matrix and right-hand side. More...
int	solveLinearSystem (Vect< real_t > &b, Vect< real_t > &x)
	Solve the linear system with given right-hand side. More...
void	LinearSystemInfo ()
	Print info on linear system solver.

Detailed Description

Solves a generic linear PDE in 2-D using 3-Node triangular finite elements.

This class handles the scalar linear equation: a d^2u/dt^2 + b du/dt - div(c Grad u) + d.Grad u + eu = f in a given interval, with Dirichlet and/or Neumann boundary conditions. The coefficients a, b, c, d, e can be constants or given functions of space and time

Numerical solution uses the P1 finite element method for space discretization. For transient (time-dependent) problems, the class TimeStepping must be used. For eigenproblems, the class EigenProblemSolver must be used.

Constructor & Destructor Documentation

LinearPDE2D() [1/2]

LinearPDE2D

(

Mesh &

ms

)

Constructor using Mesh data.

Parameters

[in]

ms

Mesh instance

LinearPDE2D() [2/2]

LinearPDE2D	(	Mesh &	ms,
		Vect< real_t > &	u
	)

Constructor using Mesh and initial condition.

Parameters

[in]	ms	Mesh instance
[in]	u	Vect instance containing initial solution

Member Function Documentation

BodyRHS() [1/2]

void BodyRHS ( const Vect< real_t > &  f )

virtual

Add body right-hand side term to right hand side.

Parameters

[in]

f

Vector containing source at nodes.

Reimplemented from Equa_LinearPDE< 3, 2 >.

BodyRHS() [2/2]

void BodyRHS

(

real_t

f

)

Add body right-hand side term to right hand side.

Case where the body right-hand side is piecewise constant.

Parameters

[in]

f

Value of thermal source (Constant in element).

BoundaryRHS() [1/2]

void BoundaryRHS

(

real_t

flux

)

Add boundary right-hand side flux to right hand side.

Parameters

[in]

flux

Vector containing source at side nodes.

BoundaryRHS() [2/2]

void BoundaryRHS ( const Vect< real_t > &  f )

virtual

Add boundary right-hand side term to right hand side after multiplying it by coefficient coef

Parameters

[in]

f

Vector containing source at nodes

Reimplemented from Equa_LinearPDE< 3, 2 >.

Grad() [1/2]

void Grad

(

Vect< Point< real_t > > &

g

)

Compute gradient of solution.

Parameters

[in]

g

Elementwise vector containing gradient of solution.

Grad() [2/2]

Point<real_t>& Grad

(

const Vect< real_t > &

u

)

const

Return gradient of a vector in element.

Parameters

[in]

u

Global vector for which gradient is computed. Vector u has as size the total number of nodes

Mat_00()

void Mat_00 ( real_t  coef = 1.0 )

virtual

Add 0th order term, in time and space, to left-hand side coef

Parameters

[in]

coef

Coefficient to multiply by added term [default: 1]

Reimplemented from Equa_LinearPDE< 3, 2 >.

Mat_01()

void Mat_01 ( real_t  coef = 1.0 )

virtual

Add Oth order term in time, 1st in space to left-hand side.

Parameters

[in]

coef

Coefficient to multiply by added term [default: 1]

Reimplemented from Equa_LinearPDE< 3, 2 >.

Mat_02()

void Mat_02 ( real_t  coef = 1.0 )

virtual

Add 0th order term in time, 2nd in space to left-hand side.

Parameters

[in]

coef

Coefficient to multiply by added term [default: 1]

Reimplemented from Equa_LinearPDE< 3, 2 >.

Mat_10()

void Mat_10 ( real_t  coef = 1.0 )

virtual

Add 1st order term in time, 0th in space to left-hand side.

Parameters

[in]

coef

Coefficient to multiply by added term [default: 1]

Reimplemented from Equa_LinearPDE< 3, 2 >.

Mat_20()

void Mat_20 ( real_t  coef = 1.0 )

virtual

Add 2nd order term in time, 0th in space to left-hand side.

Parameters

[in]

coef

Coefficient to multiply by added term [default: 1]

Reimplemented from Equa_LinearPDE< 3, 2 >.

setInput()

void setInput	(	EType	opt,
		Vect< real_t > &	u
	)

Set equation input data.

Parameters

[in]	opt	Parameter to select type of input (enumerated values) INITIAL_FIELD: Initial temperature BOUNDARY_CONDITION_DATA: Boundary condition (Dirichlet) SOURCE_DATA: Heat source FLUX_DATA: Heat flux (Neumann boundary condition)
[in]	u	Vector containing input data