Solves a generic linear PDE in 2-D using 3-Node triangular finite elements. More...
#include <LinearPDE2D.h>

Public Member Functions | |
LinearPDE2D () | |
Default Constructor. Constructs an empty equation. | |
LinearPDE2D (Mesh &ms) | |
Constructor using Mesh data. More... | |
LinearPDE2D (Mesh &ms, Vect< real_t > &u) | |
Constructor using Mesh and initial condition. More... | |
~LinearPDE2D () | |
Destructor. | |
void | Mat_00 (real_t coef=1.0) |
Add 0th order term, in time and space, to left-hand side coef More... | |
void | Mat_10 (real_t coef=1.0) |
Add 1st order term in time, 0th in space to left-hand side. More... | |
void | Mat_01 (real_t coef=1.0) |
Add Oth order term in time, 1st in space to left-hand side. More... | |
void | Mat_20 (real_t coef=1.0) |
Add 2nd order term in time, 0th in space to left-hand side. More... | |
void | Mat_02 (real_t coef=1.0) |
Add 0th order term in time, 2nd in space to left-hand side. 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... | |
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... | |
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Equa_LinearPDE () | |
Default constructor. More... | |
virtual | ~Equa_LinearPDE () |
Destructor. | |
void | setNoLumping () |
Set no lumping. More... | |
void | setStab () |
Set stabilization for convection term. More... | |
void | set_00 (real_t a=1.0) |
Set coefficient for term (0,0): 0th order in time and space. More... | |
void | set_00 (Fct &f) |
Set coefficient for term (0,0): 0th order in time and space. More... | |
void | set_00 (const string &f) |
Set coefficient for term (0,0): 0th order in time and space. More... | |
void | set_10 (real_t a=1.0) |
Set coefficient for term (1,0): 1st order in time, 0th order in space. More... | |
void | set_10 (Fct &f) |
Set coefficient for term (1,0): 1st order in time, 0th order in space. More... | |
void | set_20 (real_t a=1.0) |
Set coefficient for term (2,0): 2nd order in time, 0th order in space. More... | |
void | set_20 (Fct &f) |
Set coefficient for term (2,0): 2nd order in time, 0th order in space. More... | |
void | set_01 (real_t a=1.0) |
Set coefficient for term (0,1): 0th order in time, 1st order in space. More... | |
void | set_01 (Point< real_t > &a) |
Set coefficient for term (0,1): 0th order in time, 1st order in space. More... | |
void | set_01 (Fct &f) |
Set coefficient for term (0,1): 0th order in time, 1st order in time and space. More... | |
void | set_01 (Vect< real_t > &a) |
Set coefficient for term (0,1): 0th order in time, 1st order in space. More... | |
void | set_02 (real_t a=1.0) |
Set coefficient for term (0,2): 0th order in time, 2nd order in space. More... | |
void | set_02 (Fct &f) |
Set coefficient for term (0,2): 0th order in time, 2nd order in time and space. More... | |
virtual void | Mat_00 (real_t coef=1.0) |
Add 0th order term, in time and space, to left-hand side. More... | |
virtual void | Mat_10 (real_t coef=1.0) |
Add 1st order term in time, 0th in space to left-hand side. More... | |
virtual void | Mat_20 (real_t coef=1.0) |
Add 2nd order term in time, 0th in space to left-hand side. More... | |
virtual void | Mat_01 (real_t coef=1.0) |
Add 0th order term in time, 1st in space to left-hand side. More... | |
virtual void | Mat_02 (real_t coef=1.0) |
Add 0th order term in time, 2nd in space to left-hand side. More... | |
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 for the steady state case. | |
void | build (TimeStepping &s) |
Build the linear system of equations. More... | |
void | build (EigenProblemSolver &e) |
Build the linear system for an eigenvalue problem. More... | |
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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 | ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be, int dof) |
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 | 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 | 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 | setMaterialProperty (const string &exp, const string &prop) |
Define a material property by an algebraic expression. More... | |
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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. | |
Detailed Description
Solves a generic linear PDE in 2-D using 3-Node triangular finite elements.
This class handles the scalar linear equation: a d^2u/dt^2 + b du/dt - div(c Grad u) + d.Grad u + eu = f in a given interval, with Dirichlet and/or Neumann boundary conditions. The coefficients a, b, c, d, e can be constants or given functions of space and time
Numerical solution uses the P1 finite element method for space discretization. For transient (time-dependent) problems, the class TimeStepping must be used. For eigenproblems, the class EigenProblemSolver must be used.
Constructor & Destructor Documentation
◆ LinearPDE2D() [1/2]
LinearPDE2D | ( | Mesh & | ms | ) |
◆ LinearPDE2D() [2/2]
LinearPDE2D | ( | Mesh & | ms, |
Vect< real_t > & | u | ||
) |
Member Function Documentation
◆ BodyRHS() [1/2]
Add body right-hand side term to right hand side.
- Parameters
-
[in] f Vector containing source at nodes.
Reimplemented from Equa_LinearPDE< 3, 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]
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_LinearPDE< 3, 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.
◆ Grad() [1/2]
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]
Compute gradient of solution.
- Parameters
-
[in] g Elementwise vector containing gradient of solution.
◆ Mat_00()
|
virtual |
Add 0th order term, in time and space, to left-hand side coef
- Parameters
-
[in] coef Coefficient to multiply by added term [default: 1
]
Reimplemented from Equa_LinearPDE< 3, 2 >.
◆ Mat_01()
|
virtual |
Add Oth order term in time, 1st in space to left-hand side.
- Parameters
-
[in] coef Coefficient to multiply by added term [default: 1
]
Reimplemented from Equa_LinearPDE< 3, 2 >.
◆ Mat_02()
|
virtual |
Add 0th order term in time, 2nd in space to left-hand side.
- Parameters
-
[in] coef Coefficient to multiply by added term [default: 1
]
Reimplemented from Equa_LinearPDE< 3, 2 >.
◆ Mat_10()
|
virtual |
Add 1st order term in time, 0th in space to left-hand side.
- Parameters
-
[in] coef Coefficient to multiply by added term [default: 1
]
Reimplemented from Equa_LinearPDE< 3, 2 >.
◆ Mat_20()
|
virtual |
Add 2nd order term in time, 0th in space to left-hand side.
- Parameters
-
[in] coef Coefficient to multiply by added term [default: 1
]
Reimplemented from Equa_LinearPDE< 3, 2 >.
◆ 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)
[in] u Vector containing input data -