To build element equation for the 1-D elliptic equation using the 3-Node line (P₂). More...

#include <Laplace1DL3.h>

Inheritance diagram for Laplace1DL3:

Public Member Functions
	Laplace1DL3 ()
	Default constructor. Initializes an empty equation.

	Laplace1DL3 (Mesh &ms)
	Constructor using mesh instance.

	Laplace1DL3 (Mesh &ms, Vect< real_t > &u)

	~Laplace1DL3 ()
	Destructor.

void	LHS ()
	Compute element matrix.

void	BodyRHS (const Vect< real_t > &f)
	Add Right-hand side contribution.

void	BoundaryRHS (const Vect< real_t > &h)
	Add Neumann contribution to Right-Hand Side.

void	setNeumann1D (real_t f, int lr)
	Set Traction data.

Public Member Functions inherited from Equa_Laplace< 3, 3, 1, 1 >
	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.

virtual void	buildEigen (int opt=0)
	Build matrices 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 1-D elliptic equation using the 3-Node line (P₂).

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Constructor & Destructor Documentation

◆ Laplace1DL3() [1/2]

Laplace1DL3 ( Mesh & ms )

Constructor using mesh instance.

Parameters

[in] ms Mesh instance

◆ Laplace1DL3() [2/2]

Laplace1DL3	(	Mesh &	ms,
		Vect< real_t > &	u
	)

Constructor using mesh instance and solution vector

Parameters

[in]	ms	Mesh instance
[in,out]	u	Vect instance that contains, after execution of run() the solution

Member Function Documentation

◆ BodyRHS()

void BodyRHS ( const Vect< real_t > & f )

virtual

Add Right-hand side contribution.

Parameters

[in] f Vector of right-hand side of the Poisson equation at nodes

Reimplemented from Equa_Laplace< 3, 3, 1, 1 >.

◆ BoundaryRHS()

void BoundaryRHS ( const Vect< real_t > & h )

virtual

Add Neumann contribution to Right-Hand Side.

Parameters

[in] h Vector with size the total number of nodes. The first entry stands for the force at the first node (Neumann condition) and the last entry is the force at the last node (Neumann condition)

Reimplemented from Equa_Laplace< 3, 3, 1, 1 >.

◆ setNeumann1D()

void setNeumann1D	(	real_t	f,
		int	lr
	)

Set Traction data.

Parameters

[in]	f	Value of traction (Neumann boundary condition)
[in]	lr	Option to choose location of the traction (`-1`: Left end, `1`: Right end)

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Laplace1DL3() [1/2]

◆ Laplace1DL3() [2/2]

Member Function Documentation

◆ BodyRHS()

◆ BoundaryRHS()

◆ setNeumann1D()