Builds finite element arrays for thermal diffusion and convection in 2-D domains using 3-Node triangles. More...

#include <DC2DT3.h>

Inheritance diagram for DC2DT3:

Public Member Functions
	DC2DT3 ()
	Default Constructor. Constructs an empty equation.

	DC2DT3 (Mesh &ms)
	Constructor using Mesh data. More...

	DC2DT3 (Mesh &ms, Vect< real_t > &u)
	Constructor using Mesh and initial condition. More...

	~DC2DT3 ()
	Destructor.

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

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

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

void	Diffusion (const LocalMatrix< real_t, 2, 2 > &diff, real_t coef=1)
	Add diffusion matrix to element matrix after multiplying it by coefficient `coef` More...

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

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

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

void	LinearExchange (real_t coef, real_t T)
	Add an edge linear exchange term to left and right-hand sides. 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...

void	Periodic (real_t coef=1.e20)
	Add contribution of periodic boundary condition (by a penalty technique). 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 (EqDataType opt, Vect< real_t > &u)
	Set equation input data. More...

void	JouleHeating (const Vect< real_t > &sigma, const Vect< real_t > &psi)
	Set Joule heating term as source. More...

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

virtual	~Equa_Therm ()
	Destructor.

virtual void	setStab ()
	Set stabilized formulation. More...

virtual void	LCapacity (real_t coef=1)
	Add lumped capacity contribution to element matrix. More...

virtual void	Capacity (real_t coef=1)
	Add consistent capacity contribution to left-hand side. More...

virtual void	Diffusion (real_t coef=1.)
	Add diffusion term to element matrix.

virtual void	Convection (real_t coef=1.)
	Add convection term to element matrix.

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

virtual void	BoundaryRHS (const Vect< real_t > &f)
	Add boundary right-hand side term to right-hand side. More...

void	build ()
	Build the linear system of equations. More...

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

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

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. 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	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, std::valarray< 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	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be, int dof)
	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, std::valarray< 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	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	ElementAssembly (Vect< real_t > &v)
	Assemble element vector 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.

Additional Inherited Members
Protected Member Functions inherited from Equa_Therm< 3, 3, 2, 2 >
void	setMaterial ()
	Set material properties.

Detailed Description

Builds finite element arrays for thermal diffusion and convection in 2-D domains using 3-Node triangles.

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

◆ DC2DT3() [1/2]

DC2DT3 ( Mesh & ms )

Constructor using Mesh data.

Parameters

[in] ms Mesh instance

◆ DC2DT3() [2/2]

DC2DT3	(	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_Therm< 3, 3, 2, 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_Therm< 3, 3, 2, 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.

◆ 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< 3, 3, 2, 2 >.

◆ 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< 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< 3, 3, 2, 2 >.

◆ Diffusion() [1/2]

void Diffusion	(	const LocalMatrix< real_t, 2, 2 > &	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 LocalMatrix).
[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: 1]

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

◆ 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.

◆ JouleHeating()

void JouleHeating	(	const Vect< real_t > &	sigma,
		const Vect< real_t > &	psi
	)

Set Joule heating term as source.

Parameters

[in]	sigma	Vect instance containing electric conductivity (elementwise)
[in]	psi	Vect instance containing electric potential (elementwise)

◆ 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< 3, 3, 2, 2 >.

◆ LinearExchange()

void LinearExchange	(	real_t	coef,
		real_t	T
	)

Add an edge linear exchange term to left and right-hand sides.

Parameters

[in]	coef	Coefficient of exchange
[in]	T	External value for exchange

Remarks: This assumes a constant value of T

◆ 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]

◆ setInput()

void setInput	(	EqDataType	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) `VELOCITY_FIELD`: Velocity vector (for the convection term)
[in]	u	Vector containing input data

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DC2DT3() [1/2]

◆ DC2DT3() [2/2]

Member Function Documentation

◆ BodyRHS() [1/2]

◆ BodyRHS() [2/2]

◆ BoundaryRHS() [1/2]

◆ BoundaryRHS() [2/2]

◆ Capacity()

◆ Convection() [1/3]

◆ Convection() [2/3]

◆ Convection() [3/3]

◆ Diffusion() [1/2]

◆ Diffusion() [2/2]

◆ Grad() [1/2]

◆ Grad() [2/2]

◆ JouleHeating()

◆ LCapacity()

◆ LinearExchange()

◆ Periodic()

◆ setInput()