To build element equation for the Laplace equation using the 2-D triangle element (P₁). More...

#include <Laplace2DT3.h>

Inheritance diagram for Laplace2DT3:

Public Member Functions
	Laplace2DT3 ()
	Default constructor.

	Laplace2DT3 (Mesh &ms)
	Constructor with mesh.

	Laplace2DT3 (Mesh &ms, Vect< real_t > &u)
	Constructor using mesh and solution vector.

	Laplace2DT3 (Mesh &ms, Vect< real_t > &b, Vect< real_t > &Dbc, Vect< real_t > &Nbc, Vect< real_t > &u)
	Constructor that initializes a standard Poisson equation.

	~Laplace2DT3 ()
	Destructor.

void	LHS ()
	Add finite element matrix to left-hand side.

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

void	BoundaryRHS (const Vect< real_t > &h)
	Add boundary source term to right-hand side.

void	buildEigen (int opt=0)
	Build global stiffness and mass matrices for the eigen system.

void	Post (const Vect< real_t > &u, Vect< Point< real_t > > &p)
	Perform post calculations.

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

virtual	~Equa_Laplace ()
	Destructor.

void	build ()
	Build global matrix and right-hand side.

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

Public Member Functions inherited from Equation< NEN_, NEE_, NSN_, NSE_ >
	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	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	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be, int dof)
	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	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	ElementAssembly (Vect< real_t > &v)
	Assemble element vector 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

To build element equation for the Laplace equation using the 2-D triangle element (P₁).

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Constructor & Destructor Documentation

◆ Laplace2DT3() [1/3]

Laplace2DT3 ( Mesh & ms )

Constructor with mesh.

Parameters

[in] ms Mesh instance

◆ Laplace2DT3() [2/3]

Laplace2DT3	(	Mesh &	ms,
		Vect< real_t > &	u )

Constructor using mesh and solution vector.

Parameters

[in]	ms	Mesh instance
[in]	u	Problem right-hand side

◆ Laplace2DT3() [3/3]

Laplace2DT3	(	Mesh &	ms,
		Vect< real_t > &	b,
		Vect< real_t > &	Dbc,
		Vect< real_t > &	Nbc,
		Vect< real_t > &	u )

Constructor that initializes a standard Poisson equation.

This constructor sets data for the Poisson equation with mixed (Dirichlet and Neumann) boundary conditions.

Parameters

[in]	ms	Mesh instance
[in]	b	Vector containing the source term (right-hand side of the equation) at mesh nodes
[in]	Dbc	Vector containing prescribed values of the solution (Dirichlet boundary condition) at nodes with positive code. Its size is the total number of nodes
[in]	Nbc	Vector containing prescribed fluxes (Neumann boundary conditions) at sides, its size is the total number of sides
[in]	u	Vector to contain the finite element solution at nodes once the member function run() is called.

Member Function Documentation

◆ BodyRHS()

void BodyRHS ( const Vect< real_t > & f )

virtual

Add body source term to right-hand side.

Parameters

[in] f Vector containing the source given function at mesh nodes

Reimplemented from Equa_Laplace< 3, 3, 2, 2 >.

◆ BoundaryRHS()

void BoundaryRHS ( const Vect< real_t > & h )

virtual

Add boundary source term to right-hand side.

Parameters

[in] h Vector containing the source given function at mesh nodes

Reimplemented from Equa_Laplace< 3, 3, 2, 2 >.

◆ buildEigen()

void buildEigen ( int opt = 0 )

virtual

Build global stiffness and mass matrices for the eigen system.

Parameters

[in] opt Flag to choose a lumped mass matrix (0) or consistent (1) [Default: 0]

Reimplemented from Equa_Laplace< 3, 3, 2, 2 >.

◆ Post()

void Post	(	const Vect< real_t > &	u,
		Vect< Point< real_t > > &	p )

Perform post calculations.

Parameters

[in]	u	Solution at nodes
[out]	p	Vector containing gradient at elements

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Laplace2DT3() [1/3]

◆ Laplace2DT3() [2/3]

◆ Laplace2DT3() [3/3]

Member Function Documentation

◆ BodyRHS()

◆ BoundaryRHS()

◆ buildEigen()

◆ Post()