Builds finite element arrays for thermal diffusion and convection in 3-D domains using 4-Node tetrahedra. More...

#include <DC3DT4.h>

Inheritance diagram for DC3DT4:

Public Member Functions
	DC3DT4 ()
	Default Constructor.

	DC3DT4 (Mesh &ms)
	Constructor using Mesh data.

	DC3DT4 (Mesh &ms, Vect< real_t > &u)
	Constructor using Mesh and initial condition.

	~DC3DT4 ()
	Destructor.

void	LCapacity (real_t coef=1)
	Add lumped capacity matrix to element matrix after multiplying it by coefficient `coef`

void	Capacity (real_t coef=1)
	Add consistent capacity matrix to element matrix after multiplying it by coefficient `coef`

void	Diffusion (real_t coef=1)
	Add diffusion matrix to element matrix after multiplying it by coefficient `coef`.

void	Diffusion (const DMatrix< real_t > &diff, real_t coef=1)
	Add diffusion matrix to element matrix after multiplying it by coefficient `coef`

void	Convection (real_t coef=1)
	Add convection matrix to element matrix after multiplying it by coefficient `coef`

void	Convection (const Point< real_t > &v, real_t coef=1)
	Add convection matrix to element matrix after multiplying it by coefficient `coef`

void	Convection (const Vect< Point< real_t > > &v, real_t coef=1)
	Add convection matrix to element matrix after multiplying it by coefficient `coef`

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

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

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

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

void	Periodic (real_t coef=1.e20)
	Add contribution of periodic boundary condition (by a penalty technique).

Public Member Functions inherited from Equa_Therm< 4, 4, 3, 3 >
	Equa_Therm ()
	Default constructor.

virtual	~Equa_Therm ()
	Destructor.

virtual void	setStab ()
	Set stabilized formulation.

void	build ()
	Build the linear system of equations.

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

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

void	setRho (const real_t &rho)
	Set Density (constant)

void	setCp (const real_t &cp)
	Set Specific heat (constant)

void	setConductivity (const real_t &diff)
	Set (constant) thermal conductivity.

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.

Additional Inherited Members
Protected Member Functions inherited from Equa_Therm< 4, 4, 3, 3 >
void	setMaterial ()
	Set material properties.

Detailed Description

Builds finite element arrays for thermal diffusion and convection in 3-D domains using 4-Node tetrahedra.

Note that members calculating element arrays have as an argument a real coef that will be multiplied by the contribution of the current element. This makes possible testing different algorithms.

Constructor & Destructor Documentation

◆ DC3DT4() [1/3]

DC3DT4 ( )

Default Constructor.

Constructs an empty equation.

◆ DC3DT4() [2/3]

DC3DT4 ( Mesh & ms )

Constructor using Mesh data.

Parameters

[in] ms Mesh instance

◆ DC3DT4() [3/3]

DC3DT4	(	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()

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_Therm< 4, 4, 3, 3 >.

◆ 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

Case where body source is given by a vector

Parameters

[in] f Vector containing source at nodes.

Reimplemented from Equa_Therm< 4, 4, 3, 3 >.

◆ 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.

◆ Capacity()

void Capacity ( real_t coef = 1 )

virtual

Add consistent capacity matrix to element matrix after multiplying it by coefficient coef

Parameters

[in] coef Coefficient to multiply by added term [Default: 1].

Reimplemented from Equa_Therm< 4, 4, 3, 3 >.

◆ Convection() [1/3]

void Convection	(	const Point< real_t > &	v,
		real_t	coef = `1`
	)

Add convection matrix to element matrix after multiplying it by coefficient coef

Parameters

[in]	v	Constant velocity vector
[in]	coef	Coefficient to multiply by added term [Default: `1`].

◆ Convection() [2/3]

void Convection	(	const Vect< Point< real_t > > &	v,
		real_t	coef = `1`
	)

Add convection matrix to element matrix after multiplying it by coefficient coef

Case where velocity field is given by a vector v.

Parameters

[in]	v	Velocity vector.
[in]	coef	Coefficient to multiply by added term [Default: `1`].

◆ Convection() [3/3]

void Convection ( real_t coef = 1 )

virtual

Add convection matrix to element matrix after multiplying it by coefficient coef

Case where velocity field has been previouly defined

Parameters

[in] coef Coefficient to multiply by added term [Default: 1].

Reimplemented from Equa_Therm< 4, 4, 3, 3 >.

◆ Diffusion() [1/2]

void Diffusion	(	const DMatrix< real_t > &	diff,
		real_t	coef = `1`
	)

Add diffusion matrix to element matrix after multiplying it by coefficient coef

Case where the diffusivity matrix is given as an argument.

Parameters

[in]	diff	Diffusion matrix (class DMatrix).
[in]	coef	Coefficient to multiply by added term [Default: `1`].

◆ Diffusion() [2/2]

void Diffusion ( real_t coef = 1 )

virtual

Add diffusion matrix to element matrix after multiplying it by coefficient coef.

Parameters

[in] coef Coefficient to multiply by added term (default value = 1).

Reimplemented from Equa_Therm< 4, 4, 3, 3 >.

◆ Grad()

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

Compute gradient of solution.

Parameters

[in] g Elementwise vector containing gradient of solution.

◆ LCapacity()

void LCapacity ( real_t coef = 1 )

virtual

Add lumped capacity matrix to element matrix after multiplying it by coefficient coef

Parameters

[in] coef Coefficient to multiply by added term [Default: 1].

Reimplemented from Equa_Therm< 4, 4, 3, 3 >.

◆ Periodic()

void Periodic ( real_t coef = 1.e20 )

Add contribution of periodic boundary condition (by a penalty technique).

Boundary nodes where periodic boundary conditions are to be imposed must have codes equal to PERIODIC_A on one side and PERIODIC_B on the opposite side.

Parameters

[in] coef Value of penalty parameter [Default: 1.e20].

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DC3DT4() [1/3]

◆ DC3DT4() [2/3]

◆ DC3DT4() [3/3]

Member Function Documentation

◆ BodyRHS()

◆ BoundaryRHS() [1/2]

◆ BoundaryRHS() [2/2]

◆ Capacity()

◆ Convection() [1/3]

◆ Convection() [2/3]

◆ Convection() [3/3]

◆ Diffusion() [1/2]

◆ Diffusion() [2/2]

◆ Grad()

◆ LCapacity()

◆ Periodic()