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

#include <LinearPDE2D.h>

Inheritance diagram for LinearPDE2D:

Public Member Functions
	LinearPDE2D ()
	Default Constructor. Constructs an empty equation.

	LinearPDE2D (Mesh &ms)
	Constructor using Mesh data.

	LinearPDE2D (Mesh &ms, Vect< real_t > &u)
	Constructor using Mesh and initial condition.

	~LinearPDE2D ()
	Destructor.

void	Mat_00 (real_t coef=1.0)
	Add 0th order term, in time and space, to left-hand side `coef`

void	Mat_10 (real_t coef=1.0)
	Add 1st order term in time, 0th in space to left-hand side.

void	Mat_01 (real_t coef=1.0)
	Add Oth order term in time, 1st in space to left-hand side.

void	Mat_20 (real_t coef=1.0)
	Add 2nd order term in time, 0th in space to left-hand side.

void	Mat_02 (real_t coef=1.0)
	Add 0th order term in time, 2nd in space to left-hand side.

void	BodyRHS (const Vect< real_t > &f)
	Add body right-hand side term to right hand side.

void	BodyRHS (real_t f)
	Add body right-hand side term to right hand side.

void	BoundaryRHS (real_t flux)
	Add boundary right-hand side flux to right hand side.

void	BoundaryRHS (const Vect< real_t > &f)
	Add boundary right-hand side term to right hand side after multiplying it by coefficient `coef`

Point< real_t > &	Flux () const
	Return (constant) heat flux in element.

void	Grad (Vect< Point< real_t > > &g)
	Compute gradient of solution.

Point< real_t > &	Grad (const Vect< real_t > &u) const
	Return gradient of a vector in element.

void	setInput (EType opt, Vect< real_t > &u)
	Set equation input data.

Public Member Functions inherited from Equa_LinearPDE< 3, 2 >
	Equa_LinearPDE ()
	Default constructor.

virtual	~Equa_LinearPDE ()
	Destructor.

void	setNoLumping ()
	Set no lumping.

void	setStab ()
	Set stabilization for convection term.

void	set_00 (real_t a=1.0)
	Set coefficient for term (0,0): 0th order in time and space.

void	set_00 (Fct &f)
	Set coefficient for term (0,0): 0th order in time and space.

void	set_00 (const string &f)
	Set coefficient for term (0,0): 0th order in time and space.

void	set_10 (real_t a=1.0)
	Set coefficient for term (1,0): 1st order in time, 0th order in space.

void	set_10 (Fct &f)
	Set coefficient for term (1,0): 1st order in time, 0th order in space.

void	set_20 (real_t a=1.0)
	Set coefficient for term (2,0): 2nd order in time, 0th order in space.

void	set_20 (Fct &f)
	Set coefficient for term (2,0): 2nd order in time, 0th order in space.

void	set_01 (real_t a=1.0)
	Set coefficient for term (0,1): 0th order in time, 1st order in space.

void	set_01 (Point< real_t > &a)
	Set coefficient for term (0,1): 0th order in time, 1st order in space.

void	set_01 (Fct &f)
	Set coefficient for term (0,1): 0th order in time, 1st order in time and space.

void	set_01 (Vect< real_t > &a)
	Set coefficient for term (0,1): 0th order in time, 1st order in space.

void	set_02 (real_t a=1.0)
	Set coefficient for term (0,2): 0th order in time, 2nd order in space.

void	set_02 (Fct &f)
	Set coefficient for term (0,2): 0th order in time, 2nd order in time and space.

void	build ()
	Build the linear system of equations for the steady state case.

void	build (TimeStepping &s)
	Build the linear system of equations.

void	build (EigenProblemSolver &e)
	Build the linear system for an eigenvalue problem.

Public Member Functions inherited from Equation< NEN_, NEN_, NSN_, NSN_ >
	Equation ()

	Equation (Mesh &mesh)
	Constructor with mesh instance.

	Equation (Mesh &mesh, Vect< real_t > &u)
	Constructor with mesh instance and solution vector.

	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.

	~Equation ()
	Destructor.

void	updateBC (const Element &el, const Vect< real_t > &bc)
	Update Right-Hand side by taking into account essential boundary conditions.

void	DiagBC (DOFSupport dof_type=NODE_DOF, int dof=0)
	Update element matrix to impose bc by diagonalization technique.

void	LocalNodeVector (Vect< real_t > &b)
	Localize element vector from a Vect instance.

void	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEE_ > &be)
	Localize element vector from a Vect instance.

void	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be, int dof)
	Localize Element Vector from a Vect instance.

void	SideNodeVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &bs)
	Localize side vector from a Vect instance.

void	SideSideVector (const Vect< real_t > &b, vector< real_t > &bs)
	Localize side vector from a Vect instance.

void	ElementNodeVectorSingleDOF (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be)
	Localize Element Vector from a Vect instance.

void	ElementSideVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &be)
	Localize Element Vector from a Vect instance.

void	ElementVector (const Vect< real_t > &b, DOFSupport dof_type=NODE_DOF, int flag=0)
	Localize element vector.

void	SideVector (const Vect< real_t > &b, vector< real_t > &sb)
	Localize side vector.

void	ElementNodeCoordinates ()
	Localize coordinates of element nodes.

void	SideNodeCoordinates ()
	Localize coordinates of side nodes.

void	ElementAssembly (Matrix< real_t > *A)
	Assemble element matrix into global one.

void	ElementAssembly (BMatrix< real_t > &A)
	Assemble element matrix into global one.

void	ElementAssembly (SkSMatrix< real_t > &A)
	Assemble element matrix into global one.

void	ElementAssembly (SkMatrix< real_t > &A)
	Assemble element matrix into global one.

void	ElementAssembly (SpMatrix< real_t > &A)
	Assemble element matrix into global one.

void	ElementAssembly (TrMatrix< real_t > &A)
	Assemble element matrix into global one.

void	ElementAssembly (Vect< real_t > &v)
	Assemble element vector into global one.

void	DGElementAssembly (Matrix< real_t > *A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.

void	DGElementAssembly (SkSMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.

void	DGElementAssembly (SkMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.

void	DGElementAssembly (SpMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.

void	DGElementAssembly (TrMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.

void	SideAssembly (Matrix< real_t > *A)
	Assemble side (edge or face) matrix into global one.

void	SideAssembly (SkSMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one.

void	SideAssembly (SkMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one.

void	SideAssembly (SpMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one.

void	SideAssembly (Vect< real_t > &v)
	Assemble side (edge or face) vector into global one.

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.

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.

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.

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.

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.

void	setMatrixType (int t)
	Choose type of matrix.

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.

int	solveLinearSystem (Vect< real_t > &b, Vect< real_t > &x)
	Solve the linear system with given right-hand side.

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 ( 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 >.

◆ BoundaryRHS() [2/2]

void BoundaryRHS ( real_t flux )

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

Parameters

[in] flux Vector containing source at side nodes.

◆ Grad() [1/2]

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

◆ Grad() [2/2]

void Grad ( Vect< Point< real_t > > & g )

Compute gradient of solution.

Parameters

[in] g Elementwise vector containing gradient of solution.

◆ 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

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ LinearPDE2D() [1/2]

◆ LinearPDE2D() [2/2]

Member Function Documentation

◆ BodyRHS() [1/2]

◆ BodyRHS() [2/2]

◆ BoundaryRHS() [1/2]

◆ BoundaryRHS() [2/2]

◆ Grad() [1/2]

◆ Grad() [2/2]

◆ Mat_00()

◆ Mat_01()

◆ Mat_02()

◆ Mat_10()

◆ Mat_20()

◆ setInput()