Builds finite element arrays for thermal diffusion and convection in 2-D domains using 6-Node triangles. More...


Public Member Functions | |
DC2DT6 () | |
Default Constructor. More... | |
DC2DT6 (const Element *el) | |
Constructor for an element. More... | |
DC2DT6 (const Side *sd) | |
Constructor for a boundary side. More... | |
DC2DT6 (const Element *el, const Vect< real_t > &u, real_t time=0.) | |
Constructor for an element (Transient case). More... | |
DC2DT6 (const Element *el, const Vect< real_t > &u, real_t time, real_t deltat, int scheme) | |
Constructor for an element (transient case) with specification of time integration scheme. More... | |
DC2DT6 (const Side *sd, const Vect< real_t > &u, real_t time=0.) | |
Constructor for a boundary side (transient case). More... | |
DC2DT6 (const Side *sd, const Vect< real_t > &u, real_t time, real_t deltat, int scheme) | |
Constructor for a side (transient case) with specification of time integration scheme. More... | |
~DC2DT6 () | |
Destructor. | |
void | Diffusion (real_t coef=1) |
Add diffusion matrix to left hand side after multiplying it by coefficient coef More... | |
void | Convection (real_t coef=1) |
Add convection matrix to left-hand side after multiplying it by coefficient coef More... | |
void | Convection (Point< real_t > &v, real_t coef=1) |
Add convection matrix to left hand side after multiplying it by coefficient coef More... | |
void | Convection (const Vect< real_t > &v, real_t coef=1) |
Add convection matrix to left-hand side after multiplying it by coefficient coef More... | |
void | BodyRHS (const Vect< real_t > &b, int opt=GLOBAL_ARRAY) |
Add body right-hand side term to right hand side. More... | |
void | BoundaryRHS (const Vect< real_t > &b) |
Add boundary right-hand side term to right hand side after multiplying it by coefficient coef More... | |
virtual void | setStab () |
Set stabilized formulation. More... | |
virtual void | LCapacityToLHS (real_t coef=1) |
Add lumped capacity contribution to left-hand side. More... | |
virtual void | LCapacityToRHS (real_t coef=1) |
Add lumped capacity contribution to right-hand side. More... | |
virtual void | CapacityToLHS (real_t coef=1) |
Add consistent capacity contribution to left-hand side. More... | |
virtual void | CapacityToRHS (real_t coef=1) |
Add consistent capacity contribution to right-hand side. More... | |
void | setLumpedCapacity () |
Add lumped capacity contribution to left and right-hand sides taking into account time integration scheme. | |
void | setCapacity () |
Add consistent capacity contribution to left and right-hand sides taking into account time integration scheme. | |
virtual void | DiffusionToRHS (real_t coef=1.) |
Add diffusion term to right-hand side. | |
void | setDiffusion () |
Add diffusion contribution to left and/or right-hand side taking into account time integration scheme. | |
virtual void | ConvectionToRHS (real_t coef=1.) |
Add convection term to right-hand side. | |
void | setConvection () |
Add convection contribution to left and/or right-hand side taking into account time integration scheme. | |
void | build () |
Build the linear system of equations. More... | |
int | runTransient () |
Run one time step. More... | |
int | run () |
Run the equation. More... | |
void | setRhoCp (const real_t &rhocp) |
Set product of Density by Specific heat (constants) | |
void | setConductivity (const real_t &diff) |
Set (constant) thermal conductivity. | |
void | RhoCp (const string &exp) |
Set product of Density by Specific heat given by an algebraic expression. | |
void | Conduc (const string &exp) |
Set thermal conductivity given by an algebraic expression. | |
void | buildEigen (SkSMatrix< real_t > &K, SkSMatrix< real_t > &M) |
Build global stiffness and mass matrices for the eigen system. More... | |
void | buildEigen (SkSMatrix< real_t > &K, Vect< real_t > &M) |
Build global diffusion and capacity matrices for the eigen system. More... | |
void | updateBC (const Element &el, const Vect< real_t > &bc) |
Update Right-Hand side by taking into account essential boundary conditions. More... | |
void | updateBC (const Vect< real_t > &bc) |
Update Right-Hand side by taking into account essential boundary conditions. More... | |
void | DiagBC (int 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 | ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be, int dof) |
Localize Element 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 | 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, int dof_type=NODE_FIELD, int flag=0) |
Localize Element Vector. More... | |
void | SideVector (const Vect< real_t > &b) |
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 (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 | ElementAssembly (Vect< real_t > &v) |
Assemble element vector 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 | 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 * | A () |
Return element matrix as a C-array. | |
real_t * | sA () |
Return side matrix as a C-array. | |
real_t * | b () |
Return element right-hand side as a C-array. | |
real_t * | sb () |
Return side right-hand side as a C-array. | |
real_t * | Prev () |
Return element matrix as a C-array. | |
LocalMatrix< real_t, NEE_, NEE_ > & | EA () |
Return element matrix as a LocalMatrix instance. | |
LocalMatrix< real_t, NSE_, NSE_ > & | SA () |
Return side matrix as a LocalMatrix instance. | |
LocalVect< real_t, NEE_ > & | Eb () |
Return element right-hand side as a LocalVect instance. | |
LocalVect< real_t, NEE_ > & | Ep () |
Return element matrix as a C-array. | |
void | setInitialSolution (const Vect< real_t > &u) |
Set initial solution (previous time step) | |
real_t | setMaterialProperty (const string &exp, const string &prop) |
Define a material property by an algebraic expression. More... | |
void | setMesh (class Mesh &m) |
Define mesh and renumber DOFs after removing imposed ones. | |
Mesh & | getMesh () const |
Return reference to Mesh instance. More... | |
LinearSolver< real_t > & | getLinearSolver () |
Return reference to linear solver instance. | |
void | setSolver (int ls, int pc=IDENT_PREC) |
Choose solver for the linear system. More... | |
int | solveEigenProblem (int nb_eigv, bool g=false) |
Compute eigenvalues and eigenvectors. More... | |
real_t | getEigenValue (int n) const |
Return the n-th eigenvalue. More... | |
void | getEigenVector (int n, Vect< real_t > &v) const |
Store the eigenvector corresponding to a given eigenvalue. More... | |
class Eigen & | getEigenSolver () |
Return reference to eigenproblem solver. | |
Protected Member Functions | |
void | setMaterial () |
Set material properties. | |
void | Init (const Element *el) |
Set element arrays to zero. | |
void | Init (const Side *sd) |
Set side arrays to zero. | |
Detailed Description
Builds finite element arrays for thermal diffusion and convection in 2-D domains using 6-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
DC2DT6 | ( | ) |
Default Constructor.
Constructs an empty equation.
Constructor for an element (Transient case).
- Parameters
-
[in] el Pointer to element. [in] u Vect instance that contains solution at previous time step. [in] time Current time value [Default: 0
].
Constructor for an element (transient case) with specification of time integration scheme.
- Parameters
-
[in] el Pointer to element. [in] u Vect instance that contains solution at previous time step. [in] time Current time value [Default: 1
][in] deltat Value of time step [in] scheme Time Integration Scheme: -
FORWARD_EULER
: Forward Euler scheme -
BACKWARD_EULER
: Backward Euler scheme, -
CRANK_NICOLSON
: Crank-Nicolson Euler scheme.
-
Constructor for a boundary side (transient case).
- Parameters
-
[in] sd Pointer to side. [in] u Vect instance that contains solution at previous time step. [in] time Current time value [Default: 0
].
Constructor for a side (transient case) with specification of time integration scheme.
- Parameters
-
[in] sd Pointer to side. [in] u Vect instance that contains solution at previous time step. [in] time Current time value [in] deltat Value of time step [in] scheme Time Integration Scheme: To be chosen among the enumerated values: -
FORWARD_EULER
: Forward Euler scheme -
BACKWARD_EULER
: Backward Euler scheme, -
CRANK_NICOLSON
: Crank-Nicolson Euler scheme.
-
Member Function Documentation
|
virtual |
Add diffusion matrix to left hand side after multiplying it by coefficient coef
- Parameters
-
[in] coef Coefficient to multiply by added term [Default: 1
].
Reimplemented from Equa_Therm< real_t, 6, 6, 3, 3 >.
|
virtual |
Add convection matrix to left-hand side 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< real_t, 6, 6, 3, 3 >.
Add convection matrix to left hand side after multiplying it by coefficient coef
- Parameters
-
[in] v Constant velocity vector. [in] coef Coefficient to multiply by added term [Default: 1
].
Add convection matrix to left-hand side 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
].
void BodyRHS | ( | const Vect< real_t > & | b, |
int | opt = GLOBAL_ARRAY |
||
) |
Add body right-hand side term to right hand side.
- Parameters
-
[in] b Local vector (of size 6
) containing source at element nodes[in] opt Vector is local ( LOCAL_ARRAY
) with size 6 or global (GLOBAL_ARRAY
) with size = Number of nodes [Default:GLOBAL_ARRAY
].
Add boundary right-hand side term to right hand side after multiplying it by coefficient coef
- Parameters
-
[in] b Local vector (of size 3
) containing source at side nodes.
|
virtualinherited |
Set stabilized formulation.
Stabilized variational formulations are to be used when the Péclet number is large.
By default, no stabilization is used.
|
virtualinherited |
Add lumped capacity contribution to left-hand side.
- Parameters
-
[in] coef coefficient to multiply by the matrix before adding [Default: 1
]
|
virtualinherited |
Add lumped capacity contribution to right-hand side.
- Parameters
-
[in] coef coefficient to multiply by the vector before adding [Default: 1
]
|
virtualinherited |
Add consistent capacity contribution to left-hand side.
- Parameters
-
[in] coef coefficient to multiply by the matrix before adding [Default: 1
]
|
virtualinherited |
Add consistent capacity contribution to right-hand side.
- Parameters
-
[in] coef coefficient to multiply by the vector before adding [Default: 1
]
|
inherited |
Build the linear system of equations.
Before using this function, one must have properly selected appropriate options for:
- The choice of a steady state or transient analysis. By default, the analysis is stationary
- In the case of transient analysis, the choice of a time integration scheme and a lumped or consistent capacity matrix. If transient analysis is chosen, the lumped capacity matrix option is chosen by default, and the implicit Euler scheme is used by default for time integration.
|
inherited |
Run one time step.
This function performs one time step in equation solving. It is to be used only if a TRANSIENT analysis is required.
- Returns
- Return error from the linear system solver
|
inherited |
Run the equation.
If the analysis (see function setAnalysis) is STEADY_STATE
, then the function solves the stationary equation.
If the analysis is TRANSIENT
, then the function performs time stepping until the final time is reached.
Build global stiffness and mass matrices for the eigen system.
Case where the mass matrix is consistent
- Parameters
-
[in] K Stiffness matrix [in] M Consistent mass matrix
Build global diffusion and capacity matrices for the eigen system.
Case where the capacity matrix is lumped
- Parameters
-
[in] K Diffusion matrix [in] M Vector containing diagonal capacity matrix
Update Right-Hand side by taking into account essential boundary conditions.
- Parameters
-
[in] el Reference to current element instance [in] bc Vector that contains imposed values at all DOFs
Update Right-Hand side by taking into account essential boundary conditions.
- Parameters
-
[in] bc Vector that contains imposed values at all DOFs
- Remarks
- The current element is pointed by
_theElement
|
inherited |
Update element matrix to impose bc by diagonalization technique.
- Parameters
-
[in] dof_type DOF type option. To choose among the enumerated values: -
NODE_FIELD
, DOFs are supported by nodes [Default] -
ELEMENT_FIELD
, DOFs are supported by elements -
SIDE_FIELD
, DOFs are supported by sides
[in] dof DOF setting: -
= 0
, All DOFs are taken into account [Default] -
!= 0
, Only DOF No.dof
is handled in the system
-
Localize Element Vector from a Vect instance.
- Parameters
-
[in] b Reference to global vector to be localized. The resulting local vector can be accessed by attribute ePrev. This member function is to be used if a constructor with Element was invoked.
Localize Element Vector from a Vect instance.
- Parameters
-
[in] b Global vector to be localized. [out] be Local vector, the length of which is the total number of element equations.
- Remarks
- All degrees of freedom are transferred to the local vector
|
inherited |
Localize Element Vector from a Vect instance.
- Parameters
-
[in] b Global vector to be localized. [out] be Local vector, the length of which is the total number of element equations. [in] dof Degree of freedom to transfer to the local vector
- Remarks
- Only yhe dega dof is transferred to the local vector
|
inherited |
Localize Element Vector from a Vect instance.
- Parameters
-
[in] b Global vector to be localized. [out] be Local vector, the length of which is the total number of element equations.
- Remarks
- Vector
b
is assumed to contain only one degree of freedom by node.
Localize Element Vector from a Vect instance.
- Parameters
-
[in] b Global vector to be localized. [out] be Local vector, the length of which is
Localize Element Vector.
- Parameters
-
[in] b Global vector to be localized [in] dof_type DOF type option. To choose among the enumerated values: -
NODE_FIELD
, DOFs are supported by nodes [Default] -
ELEMENT_FIELD
, DOFs are supported by elements -
SIDE_FIELD
, DOFs are supported by sides
[in] flag Option to set: -
= 0
, All DOFs are taken into account [Default] -
!= 0
, Only DOF numberdof
is handled in the system
ePrev
. -
- Remarks
- This member function is to be used if a constructor with Element was invoked. It uses the Element pointer
_theElement
Localize Side Vector.
- Parameters
-
[in] b Global vector to be localized -
NODE_FIELD
, DOFs are supported by nodes [ default ] -
ELEMENT_FIELD
, DOFs are supported by elements -
SIDE_FIELD
, DOFs are supported by sides
ePrev
. -
- Remarks
- This member function is to be used if a constructor with Side was invoked. It uses the Side pointer
_theSide
|
inherited |
Localize coordinates of element nodes.
Coordinates are stored in array _x[0], _x[1], ...
which are instances of class Point<real_t>
- Remarks
- This member function uses the Side pointer
_theSide
|
inherited |
Localize coordinates of side nodes.
Coordinates are stored in array _x[0], _x[1], ...
which are instances of class Point<real_t>
- Remarks
- This member function uses the Element pointer
_theElement
Assemble element matrix into global one.
- Parameters
-
A Pointer to global matrix (abstract class: can be any of classes SkSMatrix, SkMatrix, SpMatrix)
- Warning
- The element pointer is given by the global variable
theElement
Assemble element matrix into global one.
- Parameters
-
A Global matrix stored as an SkSMatrix instance
- Warning
- The element pointer is given by the global variable
theElement
Assemble element matrix into global one.
- Parameters
-
[in] A Global matrix stored as an SkMatrix instance
- Warning
- The element pointer is given by the global variable
theElement
Assemble element matrix into global one.
- Parameters
-
[in] A Global matrix stored as an SpMatrix instance
- Warning
- The element pointer is given by the global variable
theElement
Assemble element matrix into global one.
- Parameters
-
[in] A Global matrix stored as an TrMatrix instance
- Warning
- The element pointer is given by the global variable
theElement
Assemble element vector into global one.
- Parameters
-
[in] v Global vector (Vect instance)
- Warning
- The element pointer is given by the global variable
theElement
Assemble element matrix into global one for the Discontinuous Galerkin approximation.
- Parameters
-
A Pointer to global matrix (abstract class: can be any of classes SkSMatrix, SkMatrix, SpMatrix)
- Warning
- The element pointer is given by the global variable
theElement
Assemble element matrix into global one for the Discontinuous Galerkin approximation.
- Parameters
-
A Global matrix stored as an SkSMatrix instance
- Warning
- The element pointer is given by the global variable
theElement
Assemble element matrix into global one for the Discontinuous Galerkin approximation.
- Parameters
-
[in] A Global matrix stored as an SkMatrix instance
- Warning
- The element pointer is given by the global variable
theElement
Assemble element matrix into global one for the Discontinuous Galerkin approximation.
- Parameters
-
[in] A Global matrix stored as an SpMatrix instance
- Warning
- The element pointer is given by the global variable
theElement
Assemble element matrix into global one for the Discontinuous Galerkin approximation.
- Parameters
-
[in] A Global matrix stored as an TrMatrix instance
- Warning
- The element pointer is given by the global variable
theElement
Assemble side (edge or face) matrix into global one.
- Parameters
-
A Pointer to global matrix (abstract class: can be any of classes SkSMatrix, SkMatrix, SpMatrix)
- Warning
- The side pointer is given by the global variable
theSide
Assemble side (edge or face) matrix into global one.
- Parameters
-
[in] A Global matrix stored as an SkSMatrix instance
- Warning
- The side pointer is given by the global variable
theSide
Assemble side (edge or face) matrix into global one.
- Parameters
-
[in] A Global matrix stored as an SkMatrix instance
- Warning
- The side pointer is given by the global variable
theSide
Assemble side (edge or face) matrix into global one.
- Parameters
-
[in] A Global matrix stored as an SpMatrix instance
- Warning
- The side pointer is given by the global variable
theSide
Assemble side (edge or face) vector into global one.
- Parameters
-
[in] v Global vector (Vect instance)
- Warning
- The side pointer is given by the global variable
theSide
Assemble product of element matrix by element vector into global vector.
- Parameters
-
[in] el Reference to Element instance [in] x Global vector to multiply by (Vect instance) [out] b Global vector to add (Vect instance)
Assemble product of side matrix by side vector into global vector.
- Parameters
-
[in] sd Reference to Side instance [in] x Global vector to multiply by (Vect instance) [out] b Global vector (Vect instance)
|
inherited |
Define a material property by an algebraic expression.
- Parameters
-
[in] exp Algebraic expression [in] prop Property name
- Returns
- Return value in expression evaluation:
-
=0
, Normal evaluation -
!=0
, An error message is displayed
-
|
inherited |
Return reference to Mesh instance.
- Returns
- Reference to Mesh instance
|
inherited |
Choose solver for the linear system.
- Parameters
-
[in] ls Solver of the linear system. To choose among the enumerated values: DIRECT_SOLVER
,CG_SOLVER
,GMRES_SOLVER
-
DIRECT_SOLVER
, Use a facorization solver [default] -
CG_SOLVER
, Conjugate Gradient iterative solver -
CGS_SOLVER
, Squared Conjugate Gradient iterative solver -
BICG_SOLVER
, BiConjugate Gradient iterative solver -
BICG_STAB_SOLVER
, BiConjugate Gradient Stabilized iterative solver -
GMRES_SOLVER
, GMRES iterative solver -
QMR_SOLVER
, QMR iterative solver
[in] pc Preconditioner to associate to the iterative solver. If the direct solver was chosen for the first argument this argument is not used. Otherwise choose among the enumerated values: -
IDENT_PREC
, Identity preconditioner (no preconditioning [default]) -
DIAG_PREC
, Diagonal preconditioner -
ILU_PREC
, Incomplete LU factorization preconditioner
-
|
inherited |
Compute eigenvalues and eigenvectors.
Eigenvalues and vectors are computed using the Bathe's subspace iteration method.
- Parameters
-
[in] nb_eigv Number of eigenvalues to compute [in] g Option to choose whether to solve a generalized eigenvalue problem (true) or a standard one (false). The generalized eigenvalue problem corresponds to the case where a consistent mass matrix (rather than a lumped one) is computed. Default value is false.
|
inherited |
Return the n-th eigenvalue.
This functions works only if the member function getEigen was called with an argument nb_eigv
greater or equal to n
. Otherwise it returns 0
.