implements a mixed-hybrid FE Darcy solver. More...

#include <DarcySolverLinear.hpp>

Inheritance diagram for DarcySolverLinear< MeshType >:

Collaboration diagram for DarcySolverLinear< MeshType >:

Public Types
typedef MeshType	mesh_Type
	Typedef for mesh template. More...

typedef LinearSolver	solver_Type
	Typedef for solver template. More...

typedef DarcySolverLinear< mesh_Type >	darcySolver_Type
	Self typedef. More...

typedef DarcyData< mesh_Type >	data_Type
	Typedef for the data type. More...

typedef std::shared_ptr< data_Type >	dataPtr_Type
	Shared pointer for the data type. More...

typedef BCHandler	bcHandler_Type
	Boundary condition handler. More...

typedef std::shared_ptr< bcHandler_Type >	bcHandlerPtr_Type
	Shared pointer to a boundary condition handler. More...

typedef std::shared_ptr< Epetra_Comm >	commPtr_Type
	Shared pointer to a MPI communicator. More...

typedef MapEpetra	map_Type
	Map type. More...

typedef std::shared_ptr< Displayer >	displayerPtr_Type
	Shared pointer to a displayer. More...

typedef FESpace< mesh_Type, map_Type >	fESpace_Type
	Finite element space. More...

typedef std::shared_ptr< fESpace_Type >	fESpacePtr_Type
	Shared pointer to a finite element space. More...

typedef FEScalarField< mesh_Type, map_Type >	scalarField_Type
	Scalar field. More...

typedef std::shared_ptr< scalarField_Type >	scalarFieldPtr_Type
	Shared pointer to a scalar field. More...

typedef FEVectorField< mesh_Type, map_Type >	vectorField_Type
	Vector field. More...

typedef std::shared_ptr< vectorField_Type >	vectorFieldPtr_Type
	Shared pointer to a scalar field. More...

typedef FEFunction< mesh_Type, map_Type, Real >	scalarFct_Type
	Scalar value function. More...

typedef std::shared_ptr< scalarFct_Type >	scalarFctPtr_Type
	Shared pointer to a scalar value function. More...

typedef FEFunction< mesh_Type, map_Type, Vector >	vectorFct_Type
	Vector value function. More...

typedef std::shared_ptr< vectorFct_Type >	vectorFctPtr_Type
	Shared pointer to a vector value function. More...

typedef FEFunction< mesh_Type, map_Type, Matrix >	matrixFct_Type
	Matrix value funcion. More...

typedef std::shared_ptr< matrixFct_Type >	matrixFctPtr_Type
	Shared pointer to a matrix value function. More...

typedef solver_Type::matrix_Type	matrix_Type
	Sparse and distributed matrix. More...

typedef solver_Type::matrixPtr_Type	matrixPtr_Type
	Shared pointer to a sparse and distributed matrix. More...

typedef solver_Type::vector_Type	vector_Type
	Distributed vector. More...

typedef solver_Type::vectorPtr_Type	vectorPtr_Type
	Shared pointer to a distributed vector. More...

typedef solver_Type::preconditionerPtr_Type	preconditionerPtr_Type
	Shared pointer to the preconditioner. More...

Constructors and destructor
	DarcySolverLinear ()
	Constructor for the class. More...

virtual	~DarcySolverLinear ()
	Virtual destructor. More...

Methods
void	buildSystem ()
	Build the global hybrid system, the right hand and apply the boundary conditions. More...

virtual void	setup ()
	Set up the linear solver and the preconditioner for the linear system. More...

void	solveLinearSystem ()
	Solve the global hybrid system. More...

void	computePrimalAndDual ()
	Compute primal and dual variables from the hybrid variable as a post process. More...

virtual void	solve ()
	Solve the Darcy problem grouping other public methods. More...

Set Methods
void	setData (dataPtr_Type &data)
	Set the data. More...

void	setBoundaryConditions (bcHandlerPtr_Type &bcHandler)
	Set the boundary conditions. More...

void	setScalarSource (const scalarFctPtr_Type &scalarSourceFct)
	Set scalar source term. More...

void	setVectorSource (const vectorFctPtr_Type &vectorSourceFct)
	Set vector source term. More...

virtual void	setInversePermeability (const matrixFctPtr_Type &invPermFct)
	Set inverse diffusion tensor. More...

void	setReactionTerm (const scalarFctPtr_Type &reactionTermFct)
	Set the coefficient for the reaction term. More...

void	setHybridField (const scalarFieldPtr_Type &hybridField)
	Set the hybrid field vector. More...

void	setPrimalField (const scalarFieldPtr_Type &primalField)
	Set the primal field vector. More...

void	setDualField (const scalarFieldPtr_Type &dualField)
	Set the dual field vector. More...

void	setFields (const scalarFieldPtr_Type &dualField, const scalarFieldPtr_Type &primalField, const scalarFieldPtr_Type &hybridField)
	Set the fields. More...

void	setDisplayer (const displayerPtr_Type &displayer)
	Set the displayer and, implicitly, the communicator. More...

void	setCommunicator (const commPtr_Type &comm)
	Set the communicator and, implicitly, the displayer. More...

Get Methods
const scalarFieldPtr_Type &	hybridFieldPtr () const
	Returns pointer to the hybrid solution field. More...

scalarFieldPtr_Type &	hybridFieldPtr ()
	Returns pointer to the hybrid solution field. More...

const scalarFieldPtr_Type &	primalFieldPtr () const
	Returns pointer to the primal solution field. More...

scalarFieldPtr_Type &	primalFieldPtr ()
	Returns pointer to the primal solution field. More...

const scalarFieldPtr_Type &	dualFieldPtr () const
	Returns pointer to the dual solution field. More...

scalarFieldPtr_Type &	dualFieldPtr ()
	Returns pointer to the dual solution field. More...

const vectorPtr_Type &	residualPtr () const

vectorPtr_Type &	residualPtr ()

const bcHandlerPtr_Type &	boundaryConditionHandlerPtr () const
	Returns boundary conditions handler. More...

bcHandlerPtr_Type &	boundaryConditionHandlerPtr ()
	Returns boundary conditions handler. More...

const map_Type &	getMap () const
	Returns Epetra local map. More...

const commPtr_Type &	getCommPtr () const
	Returns Epetra communicator. More...

Private Constructors
	DarcySolverLinear (const darcySolver_Type &)
	Inhibited copy constructor. More...

Private Operators
darcySolver_Type &	operator= (const darcySolver_Type &)
	Inhibited assign operator. More...

Protected Methods
virtual void	preLoopElementsComputation ()
	Perform all the operations before doing the loop on volume elements. More...

void	computeConstantMatrices (MatrixElemental &elmatMix)
	Pre-computes local (element independant) matrices. More...

virtual void	localMatrixComputation (const UInt &iElem, MatrixElemental &elmatMix, MatrixElemental &elmatReactionTerm)
	Computes local (element dependent) matrices. More...

virtual void	localVectorComputation (const UInt &iElem, VectorElemental &elvecMix)
	Computes local (element dependent) vectors. More...

void	staticCondensation (MatrixElemental &localMatrixHybrid, VectorElemental &localVectorHybrid, MatrixElemental &elmatMix, MatrixElemental &elmatReactionTerm, VectorElemental &elvecMix)
	Performs static condensation. More...

void	localComputePrimalAndDual (VectorElemental &localSolution, MatrixElemental &elmatMix, MatrixElemental &elmatReactionTerm, VectorElemental &elvecMix)
	Compute locally, as a post process, the primal and dual variable given the hybrid. More...

virtual void	postComputePrimalAndDual ()
	Do some computation after the calculation of the primal and dual variable. More...

virtual void	resetVariables ()
	Update all problem variables. More...

void	applyBoundaryConditions ()
	Apply the boundary condition. More...

template<typename MatrixType >
void	symmetrizeMatrix (Int N, MatrixType &A)
	Make matrix symmetric. More...

Parallel stuff
displayerPtr_Type	M_displayer
	Displayer for parallel cout. More...

Data of the problem
dataPtr_Type	M_data
	Data for Darcy solvers. More...

scalarFctPtr_Type	M_scalarSourceFct
	Source function. More...

vectorFctPtr_Type	M_vectorSourceFct
	Vector source function. More...

scalarFctPtr_Type	M_reactionTermFct
	Reaction term function. More...

matrixFctPtr_Type	M_inversePermeabilityFct
	Inverse of the permeability tensor. More...

bcHandlerPtr_Type	M_boundaryConditionHandler
	Bondary conditions handler. More...

Solution fields stuff
scalarFieldPtr_Type	M_primalField
	Primal solution. More...

scalarFieldPtr_Type	M_dualField
	Dual solution. More...

scalarFieldPtr_Type	M_hybridField
	Hybrid solution. More...

Algebraic stuff
matrixPtr_Type	M_matrHybrid
	Hybrid matrix. More...

vectorPtr_Type	M_rhs
	Right hand side. More...

vectorPtr_Type	M_residual
	Residual. More...

solver_Type	M_linearSolver
	Linear solver. More...

preconditionerPtr_Type	M_prec
	Epetra preconditioner for the linear system. More...

Detailed Description

template<typename MeshType>
class LifeV::DarcySolverLinear< MeshType >

implements a mixed-hybrid FE Darcy solver.

Author: A. Fumagalli aless.nosp@m.io.f.nosp@m.umaga.nosp@m.lli@.nosp@m.mail..nosp@m.poli.nosp@m.mi.it

See also: For applications related to two-phase flow see [8]

This class implements a Darcy solver.

The classical formulation of this problem is a couple of differential equations of first order with two unknowns: $p \in C^1 (\Omega )$ , being the pressure or the primal unknown, and $\sigma \in (C^1( \Omega ) )^n$ , being the Darcy velocity or the total flux or the dual unknown, such that

$\left\{ \begin{array}{l l l} \Lambda^{-1} \sigma + \nabla p = f_v & \mathrm{in} & \Omega\,, \vspace{0.2cm} \\ \nabla \cdot \sigma + \pi p - f = 0 & \mathrm{in} & \Omega\,, \vspace{0.2cm} \\ p = g_D & \mathrm{on} & \Gamma_D\,,\vspace{0.2cm} \\ \sigma \cdot n + h p = g_R & \mathrm{on} & \Gamma_R\,. \end{array} \right.$

The first equation is the Darcy equation and the second equation is the conservation law.
The data in the system are:

$\Lambda$ the permeability tensor;
the scalar source term;
the vector source term;
$\pi$ the reaction coefficient;
$\Gamma_D$ the subset of the boundary of $\Omega$ with Dirichlet boundary conditions;
Dirichlet boundary condition data;
$\Gamma_R$ that is the part of the boundary of $\Omega$ with Robin, or Neumann, boundary conditions;
and Robin boundary condition data;

We suppose that $\partial \Omega = \Gamma_D \cup \Gamma_R$ and $\Gamma_D \cap \Gamma_R = \emptyset$ .
Using the hybridization procedure, and introducing a new variable, we may split the problem from the entire domain to problems in each elements of the triangulation $\mathcal{T}_h$ , then we may write the weak formulation for the dual problem. The new variable is the hybrid unknown $\lambda$ , e.g. "the trace" of pressure of the primal unknown, it is the Lagrange multipliers forcing the continuity of the flux across each faces or edges in the triangulation. We introduce the following functional spaces, the first is the space of the primal variable, the third for the dual variable, the fourth for the hybrid variable.

$\begin{array}{l} V = L^2 (\Omega ) \,,\vspace{0.2cm} \\ H(div, K) = \displaystyle \left\{ \tau \in ( L^2(K))^n : \nabla \cdot \tau \in L^2(K)\right\}\,, \vspace{0.2cm}\\ Z = \displaystyle \left\{ \tau \in L^2(\Omega) : \tau\vert_K \in H(div, K) \, \forall K \in \mathcal{T}_h \right\}\,, \vspace{0.2cm}\\ \Lambda = \displaystyle \left\{ \lambda \in \prod_{K \in \mathcal{T}_h} H^{1/2} (\partial K): \lambda_K = \lambda_{K'} \ ,\, \mathrm{on} \,\, e_{K\cap K'} \, \forall K \in \mathcal{T}_h,\, \lambda = g_D \,\, \mathrm{on} \,\, \Gamma_D \right\}\,. \end{array}$

Introducing the following bilinear forms and functionals

$\begin{array}{l l} a(\sigma, \tau) = \displaystyle \sum_{K \in \mathcal{T}_h}\int_K \Lambda^{-1} \sigma \cdot \tau \,, & b(p, \tau) = \displaystyle -\sum_{K \in \mathcal{T}_h} \int_K p \nabla \cdot \tau\,, \vspace{0.2cm}\\ c(\lambda, \tau) = \displaystyle \sum_{K \in \mathcal{T}_h} \int_{\partial K} \lambda \tau \cdot n\,,& d(p, q) = \displaystyle \sum_{K \in \mathcal{T}_h} \int_{\partial K} \pi p q \,,\vspace{0.2cm}\\ h(\lambda, \mu) = \displaystyle \sum_{K \in \mathcal{T}_h} \int_{\partial K \cap \Gamma_R} h \mu \lambda \,,& F(q) = \displaystyle \sum_{K \in \mathcal{T}_h} \int_K f q\,,\vspace{0.2cm}\\ F_v(\tau) = \displaystyle \sum_{K \in \mathcal{T}_h} \int_K f_v \tau \,, \vspace{0.2cm}\,,& G(\mu) = \displaystyle \sum_{K \in \mathcal{T}_h} \int_{\partial K \cap \Gamma_R} g \mu\,, \end{array}$

we obtain the Darcy problem in the weak form: find $(\sigma, \, p, \, \lambda) \in Z \times V \times \Lambda$ such that

$\left\{ \begin{array}{l l} a(\sigma, \tau) + b(p, \tau) + c(\lambda, \tau) = F_v(\tau)\,, & \forall \tau \in Z \,,\vspace{0.2cm}\\ b(q, \sigma) - d(p,q) = - F(q)\,, & \forall q \in V \,,\vspace{0.2cm}\\ c(\mu, \sigma) + h(\lambda, \mu) = G(\mu) \,, & \forall \mu \in \Lambda\,. \end{array} \right.$

At discrete level we introduce the polynomial space, of degree $ r $ , that approximate the finite dimensional spaces introduced above $V_h \subset V$ , $Z_h \subset Z$ and $\Lambda_h \subset \Lambda$

$\begin{array}{l} V_h = \displaystyle \left\{ v_h \in V: v_h|_K \in P_r (K)\, \forall K \in \mathcal{T}_h \right\}\,, \vspace{0.2cm}\\ Z_h = \displaystyle \left\{ \tau_h \in Z: \tau_h|_K \in RT_r(K) \, \forall K \in \mathcal{T}_h \right\} \,, \vspace{0.2cm} \\ \Lambda_h = \displaystyle \left\{ \lambda_h \in \Lambda: \lambda_h|_{\partial K} \in R_r( \partial K ) \, \forall K \in \mathcal{T}_h\right\}\,, \end{array}$

where $ P_r(K) $ is the space of polynomial of degree $ r $ in the element $ K $ , $ RT_r(K) $ is the space of polynomial of Raviart-Thomas of degrees $ r $ in the element $ K $ and $R_r(\partial K)$ is the space of polynomial of degree $ r $ definite on each of the boundary of the element $ K $ and discontinuous from one edge to the other.
The finite dimensional problem is: find $(\sigma_h,\, p_h, \, \lambda_h) \in Z_h \times V_h \times \Lambda_h$ such that

$\left\{ \begin{array}{l l} a(\sigma_h, \tau_h) + b(p_h, \tau_h) + c(\lambda_h, \tau_h) = F_v(\tau_h) \,, & \forall \tau_h \in Z_h \,,\vspace{0.2cm}\\ b(q_h, \sigma_h) - d(p_h, q_h)= -F(q_h)\,, & \forall q_h \in V_h \,,\vspace{0.2cm}\\ c(\mu_h, \sigma_h) + h(\lambda_h, \mu_h) = G(\mu_h) \,, & \forall \mu_h \in \Lambda_h\,. \end{array} \right.$

To solve the problem we use the static condensation procedure, i.e. the unknowns in the discrete weak system are not independent and $ p_K $ , $\sigma_K$ may be written in function of $\lambda_K$ alone. We introduce the following local matrices

$\begin{array}{l l l} \left[ A \right]_{ij} = \displaystyle \int_K \Lambda^{-1} \psi_j \cdot \psi_i \,, & \left[ B \right]_{ij} = \displaystyle - \int_K \phi_j \nabla \cdot \psi_i \,, & \left[ C \right]_{ij} = \displaystyle \int_{\partial K} \xi_i \psi_j \cdot n \,, \vspace{0.2cm} \\ \left[ D \right]_{ij} = \displaystyle \int_K \pi \phi_j \phi_i\,, & \left[ H \right]_{ij} = \displaystyle \int_{\partial K \cap \Gamma_R} h \xi_i \xi_j\,, & \left[ F \right]_{j} = \displaystyle \int_K f \phi_j\,, \vspace{0.2cm} \\ \left[ F_v \right]_{j} = \displaystyle \int_K f_v \cdot \psi_j\,,& \left[ G \right]_{j} = \displaystyle \int_{\partial K \cap \Gamma_R } g \xi_j\,, \end{array}$

where we avoid to write the dependence on the triangle $ K $ in all the matrices and vectors.
The local matrix formulation of the finite dimensional problem is

$\left\{ \begin{array}{l} A \sigma_K + B p_K + C \lambda_K = F_v\,, \vspace{0.2cm} \\ B^T \sigma_K - D p_K = -F \,, \vspace{0.2cm}\\ C^T \sigma_K + H \lambda_K = G\,. \end{array} \right.$

Or alternatively

$\begin{array}{l l l} \left[ \begin{array}{c c c} A & B & C \vspace{0.2cm} \\ B^T & -D & 0 \vspace{0.2cm} \\ C^T & 0 & H \end{array} \right] \, \cdot & \left[ \begin{array}{c} \sigma_K \vspace{0.2cm}\\ p_K \vspace{0.2cm}\\ \lambda_K \end{array} \right] \, & = \left[ \begin{array}{c} F_v \vspace{0.2cm}\\ -F \vspace{0.2cm}\\ G \end{array} \right]\,. \end{array}$

Introducing the local hybrid matrix and local hybrid right hand side

$\begin{array}{l} L_K = - C^T A^{-1} C + C^T A^{-1} B \left( B^T A^{-1} B + D \right)^{-1} B^T A^{-1} C + H \,, \vspace{0.2cm} \\ r_K = G + C^T A^{-1} B \left( B^T A^{-1} B + D \right)^{-1} F + C^T A^{-1} B \left( B^T A^{-1} B + D \right)^{-1} B^T A^{-1} F_v - C^T A^{-1} F_v \,, \end{array}$

Imposing that at each edge or face the hybrid unknown is single value we obtain a linear system for the hybrid unknown

$L \lambda = r \,.$

We recover the primal and dual variable as a post-process from the hybrid variable at element level, so we have

$\begin{array}{l} p_K = \left( B^T A^{-1} B + D \right)^{-1} \left( F + B^T A^{-1} F_v - B^T A^{-1} C \lambda_K \right)\,, \vspace{0.2cm} \\ \sigma_K = -A^{-1} \left( B p_K - F_v + C \lambda_K \right) \,. \end{array}$

Note: In the code we do not use the matrix and the vector , because all the boundary conditions are imposed via BCHandler class.; Example of usage can be found in darcy_nonlinear and darcy_linear. Coupled with an hyperbolic solver in impes.

Todo:: Insert any scientific publications that use this solver.

Bug:: If the save flag for the exporter is setted to 0 the program fails.

Definition at line 245 of file DarcySolverLinear.hpp.

Member Typedef Documentation

◆ mesh_Type

typedef MeshType mesh_Type

Typedef for mesh template.

Definition at line 254 of file DarcySolverLinear.hpp.

◆ solver_Type

typedef LinearSolver solver_Type

Typedef for solver template.

Definition at line 257 of file DarcySolverLinear.hpp.

◆ darcySolver_Type

typedef DarcySolverLinear< mesh_Type > darcySolver_Type

Self typedef.

Definition at line 260 of file DarcySolverLinear.hpp.

◆ data_Type

typedef DarcyData< mesh_Type > data_Type

Typedef for the data type.

Definition at line 263 of file DarcySolverLinear.hpp.

◆ dataPtr_Type

typedef std::shared_ptr< data_Type > dataPtr_Type

Shared pointer for the data type.

Definition at line 266 of file DarcySolverLinear.hpp.

◆ bcHandler_Type

typedef BCHandler bcHandler_Type

Boundary condition handler.

Definition at line 269 of file DarcySolverLinear.hpp.

◆ bcHandlerPtr_Type

typedef std::shared_ptr< bcHandler_Type > bcHandlerPtr_Type

Shared pointer to a boundary condition handler.

Definition at line 272 of file DarcySolverLinear.hpp.

◆ commPtr_Type

typedef std::shared_ptr< Epetra_Comm > commPtr_Type

Shared pointer to a MPI communicator.

Definition at line 275 of file DarcySolverLinear.hpp.

◆ map_Type

typedef MapEpetra map_Type

Map type.

Definition at line 278 of file DarcySolverLinear.hpp.

◆ displayerPtr_Type

typedef std::shared_ptr< Displayer > displayerPtr_Type

Shared pointer to a displayer.

Definition at line 281 of file DarcySolverLinear.hpp.

◆ fESpace_Type

typedef FESpace< mesh_Type, map_Type > fESpace_Type

Finite element space.

Definition at line 284 of file DarcySolverLinear.hpp.

◆ fESpacePtr_Type

typedef std::shared_ptr< fESpace_Type > fESpacePtr_Type

Shared pointer to a finite element space.

Definition at line 287 of file DarcySolverLinear.hpp.

◆ scalarField_Type

typedef FEScalarField< mesh_Type, map_Type > scalarField_Type

Scalar field.

Definition at line 290 of file DarcySolverLinear.hpp.

◆ scalarFieldPtr_Type

typedef std::shared_ptr< scalarField_Type > scalarFieldPtr_Type

Shared pointer to a scalar field.

Definition at line 293 of file DarcySolverLinear.hpp.

◆ vectorField_Type

typedef FEVectorField< mesh_Type, map_Type > vectorField_Type

Vector field.

Definition at line 296 of file DarcySolverLinear.hpp.

◆ vectorFieldPtr_Type

typedef std::shared_ptr< vectorField_Type > vectorFieldPtr_Type

Shared pointer to a scalar field.

Definition at line 299 of file DarcySolverLinear.hpp.

◆ scalarFct_Type

typedef FEFunction< mesh_Type, map_Type, Real > scalarFct_Type

Scalar value function.

Definition at line 302 of file DarcySolverLinear.hpp.

◆ scalarFctPtr_Type

typedef std::shared_ptr< scalarFct_Type > scalarFctPtr_Type

Shared pointer to a scalar value function.

Definition at line 305 of file DarcySolverLinear.hpp.

◆ vectorFct_Type

typedef FEFunction< mesh_Type, map_Type, Vector > vectorFct_Type

Vector value function.

Definition at line 308 of file DarcySolverLinear.hpp.

◆ vectorFctPtr_Type

typedef std::shared_ptr< vectorFct_Type > vectorFctPtr_Type

Shared pointer to a vector value function.

Definition at line 311 of file DarcySolverLinear.hpp.

◆ matrixFct_Type

typedef FEFunction< mesh_Type, map_Type, Matrix > matrixFct_Type

Matrix value funcion.

Definition at line 314 of file DarcySolverLinear.hpp.

◆ matrixFctPtr_Type

typedef std::shared_ptr< matrixFct_Type > matrixFctPtr_Type

Shared pointer to a matrix value function.

Definition at line 317 of file DarcySolverLinear.hpp.

◆ matrix_Type

typedef solver_Type::matrix_Type matrix_Type

Sparse and distributed matrix.

Definition at line 320 of file DarcySolverLinear.hpp.

◆ matrixPtr_Type

typedef solver_Type::matrixPtr_Type matrixPtr_Type

Shared pointer to a sparse and distributed matrix.

Definition at line 323 of file DarcySolverLinear.hpp.

◆ vector_Type

typedef solver_Type::vector_Type vector_Type

Distributed vector.

Definition at line 326 of file DarcySolverLinear.hpp.

◆ vectorPtr_Type

typedef solver_Type::vectorPtr_Type vectorPtr_Type

Shared pointer to a distributed vector.

Definition at line 329 of file DarcySolverLinear.hpp.

◆ preconditionerPtr_Type

typedef solver_Type::preconditionerPtr_Type preconditionerPtr_Type

Shared pointer to the preconditioner.

Definition at line 332 of file DarcySolverLinear.hpp.

Constructor & Destructor Documentation

◆ DarcySolverLinear() [1/2]

DarcySolverLinear ( )

inline

Constructor for the class.

Definition at line 340 of file DarcySolverLinear.hpp.

◆ ~DarcySolverLinear()

virtual ~DarcySolverLinear ( )

inlinevirtual

Virtual destructor.

Definition at line 343 of file DarcySolverLinear.hpp.

◆ DarcySolverLinear() [2/2]

DarcySolverLinear ( const darcySolver_Type & )

protected

Inhibited copy constructor.

Member Function Documentation

◆ buildSystem()

void buildSystem ( )

Build the global hybrid system, the right hand and apply the boundary conditions.

Loop on all the volume elements.

End of loop volume operation.

Definition at line 812 of file DarcySolverLinear.hpp.

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◆ setup()

void setup ( )

virtual

Set up the linear solver and the preconditioner for the linear system.

Reimplemented in DarcySolverTransient< MeshType >, DarcySolverTransientNonLinear< MeshType >, and DarcySolverNonLinear< MeshType >.

Definition at line 933 of file DarcySolverLinear.hpp.

◆ solveLinearSystem()

void solveLinearSystem ( )

Solve the global hybrid system.

Definition at line 954 of file DarcySolverLinear.hpp.

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◆ computePrimalAndDual()

void computePrimalAndDual ( )

Compute primal and dual variables from the hybrid variable as a post process.

Loop on all the volume elements.

End of loop on the volume elements.

Definition at line 982 of file DarcySolverLinear.hpp.

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◆ solve()

void solve ( )

virtual

Solve the Darcy problem grouping other public methods.

Reimplemented in DarcySolverTransient< MeshType >, DarcySolverTransientNonLinear< MeshType >, and DarcySolverNonLinear< MeshType >.

Definition at line 1104 of file DarcySolverLinear.hpp.

◆ setData()

void setData ( dataPtr_Type & data )

inline

Set the data.

Parameters

data	Data for the problem.

Definition at line 374 of file DarcySolverLinear.hpp.

◆ setBoundaryConditions()

void setBoundaryConditions ( bcHandlerPtr_Type & bcHandler )

inline

Set the boundary conditions.

Parameters

bcHandler Boundary condition handler for the problem.

Definition at line 383 of file DarcySolverLinear.hpp.

◆ setScalarSource()

void setScalarSource ( const scalarFctPtr_Type & scalarSourceFct )

inline

Set scalar source term.

Parameters

scalarSourceFct Vector source term for the problem.

Definition at line 392 of file DarcySolverLinear.hpp.

◆ setVectorSource()

void setVectorSource ( const vectorFctPtr_Type & vectorSourceFct )

inline

Set vector source term.

Parameters

vectorSourceFct Vector source term for the problem.

Definition at line 401 of file DarcySolverLinear.hpp.

◆ setInversePermeability()

virtual void setInversePermeability ( const matrixFctPtr_Type & invPermFct )

inlinevirtual

Set inverse diffusion tensor.

Set the inverse of diffusion tensor, the default inverse of permeability is the identity matrix.

Parameters

invPermFct Inverse of the permeability tensor for the problem.

Reimplemented in DarcySolverNonLinear< MeshType >, and DarcySolverTransientNonLinear< MeshType >.

Definition at line 411 of file DarcySolverLinear.hpp.

◆ setReactionTerm()

void setReactionTerm ( const scalarFctPtr_Type & reactionTermFct )

inline

Set the coefficient for the reaction term.

Parameters

reactionTermFct Reaction term for the problem.

Note: Useful also for time discretization term.

Definition at line 421 of file DarcySolverLinear.hpp.

◆ setHybridField()

void setHybridField ( const scalarFieldPtr_Type & hybridField )

inline

Set the hybrid field vector.

Parameters

hybrid Constant scalarFieldPtr_Type reference of the hybrid vector.

Definition at line 430 of file DarcySolverLinear.hpp.

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◆ setPrimalField()

void setPrimalField ( const scalarFieldPtr_Type & primalField )

inline

Set the primal field vector.

Parameters

primalField Constant scalarFieldPtr_Type reference of the primal solution.

Definition at line 439 of file DarcySolverLinear.hpp.

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◆ setDualField()

void setDualField ( const scalarFieldPtr_Type & dualField )

inline

Set the dual field vector.

Parameters

dualField Constant scalarFieldPtr_Type reference of the dual solution.

Definition at line 448 of file DarcySolverLinear.hpp.

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◆ setFields()

void setFields	(	const scalarFieldPtr_Type &	dualField,
		const scalarFieldPtr_Type &	primalField,
		const scalarFieldPtr_Type &	hybridField
	)

inline

Set the fields.

Parameters

dualField	Constant scalarFieldPtr_Type reference of the dual solution.
primalField	Constant scalarFieldPtr_Type reference of the primal solution.
hybrid	Constant scalarFieldPtr_Type reference of the hybrid vector.

Definition at line 459 of file DarcySolverLinear.hpp.

◆ setDisplayer()

void setDisplayer ( const displayerPtr_Type & displayer )

inline

Set the displayer and, implicitly, the communicator.

Parameters

displayer Constant displayerPtr_Type reference of the displayer.

Definition at line 477 of file DarcySolverLinear.hpp.

◆ setCommunicator()

void setCommunicator ( const commPtr_Type & comm )

inline

Set the communicator and, implicitly, the displayer.

Parameters

comm	Constant commPtr_Type reference of the communicator.

Definition at line 486 of file DarcySolverLinear.hpp.

◆ hybridFieldPtr() [1/2]

const scalarFieldPtr_Type& hybridFieldPtr ( ) const

inline

Returns pointer to the hybrid solution field.

Returns: Constant scalarFieldPtr_Type reference of the hybrid field.

Definition at line 500 of file DarcySolverLinear.hpp.

◆ hybridFieldPtr() [2/2]

scalarFieldPtr_Type& hybridFieldPtr ( )

inline

Returns pointer to the hybrid solution field.

Returns: scalarFieldPtr_Type reference of the hybrid solution field.

Definition at line 509 of file DarcySolverLinear.hpp.

◆ primalFieldPtr() [1/2]

const scalarFieldPtr_Type& primalFieldPtr ( ) const

inline

Returns pointer to the primal solution field.

Returns: Constant scalarFieldPtr_Type reference of the primal solution field.

Definition at line 518 of file DarcySolverLinear.hpp.

◆ primalFieldPtr() [2/2]

scalarFieldPtr_Type& primalFieldPtr ( )

inline

Returns pointer to the primal solution field.

Returns: scalarFieldPtr_Type reference of the primal solution field.

Definition at line 527 of file DarcySolverLinear.hpp.

◆ dualFieldPtr() [1/2]

const scalarFieldPtr_Type& dualFieldPtr ( ) const

inline

Returns pointer to the dual solution field.

Returns: Constant scalarFieldPtr_Type reference of the dual solution field.

Definition at line 536 of file DarcySolverLinear.hpp.

◆ dualFieldPtr() [2/2]

scalarFieldPtr_Type& dualFieldPtr ( )

inline

Returns pointer to the dual solution field.

Returns: scalarFieldPtr_Type reference of the dual solution field.

Definition at line 545 of file DarcySolverLinear.hpp.

◆ residualPtr() [1/2]

const vectorPtr_Type& residualPtr ( ) const

inline

Returns the pointer of the residual vector.

Returns: Constant vectorPtr_Type reference of the residual.

Definition at line 554 of file DarcySolverLinear.hpp.

◆ residualPtr() [2/2]

vectorPtr_Type& residualPtr ( )

inline

Returns the pointer of the residual vector.

Returns: vectorPtr_Type reference of the residual.

Definition at line 563 of file DarcySolverLinear.hpp.

◆ boundaryConditionHandlerPtr() [1/2]

const bcHandlerPtr_Type& boundaryConditionHandlerPtr ( ) const

inline

Returns boundary conditions handler.

Returns: Constant reference of boundary conditions handler.

Definition at line 572 of file DarcySolverLinear.hpp.

◆ boundaryConditionHandlerPtr() [2/2]

bcHandlerPtr_Type& boundaryConditionHandlerPtr ( )

inline

Returns boundary conditions handler.

Returns: Reference of boundary conditions handler.

Definition at line 581 of file DarcySolverLinear.hpp.

◆ getMap()

const map_Type& getMap ( ) const

inline

Returns Epetra local map.

Returns: Constant MapEpetra reference of the problem.

Definition at line 590 of file DarcySolverLinear.hpp.

◆ getCommPtr()

const commPtr_Type& getCommPtr ( ) const

inline

Returns Epetra communicator.

Returns: Reference of the shared pointer of the communicator of the problem.

Definition at line 599 of file DarcySolverLinear.hpp.

◆ operator=()

darcySolver_Type& operator= ( const darcySolver_Type & )

protected

Inhibited assign operator.

◆ preLoopElementsComputation()

virtual void preLoopElementsComputation ( )

inlineprotectedvirtual

Perform all the operations before doing the loop on volume elements.

Computes the element independent matrices, clean all the fields and all the algebraich stuff. Useful for extentions in child classes.

Definition at line 632 of file DarcySolverLinear.hpp.

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◆ computeConstantMatrices()

void computeConstantMatrices ( MatrixElemental & elmatMix )

protected

Pre-computes local (element independant) matrices.

Compute all the local matrices that are independant from the geometrical element.

Parameters

elmatMix The local matrix in mixed form.

Definition at line 1125 of file DarcySolverLinear.hpp.

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◆ localMatrixComputation()

void localMatrixComputation	(	const UInt &	iElem,
		MatrixElemental &	elmatMix,
		MatrixElemental &	elmatReactionTerm
	)

protectedvirtual

Computes local (element dependent) matrices.

Locally update the current finite element for the dual finite element space, then compute the Hdiv mass matrix.

Parameters

iElem	Id of the current geometrical element.
elmatMix	The local matrix in mixed form.
elmatReactionTerm	The local matrix for the reaction term.

Reimplemented in DarcySolverTransientNonLinear< MeshType >, and DarcySolverTransient< MeshType >.

Definition at line 1174 of file DarcySolverLinear.hpp.

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◆ localVectorComputation()

void localVectorComputation	(	const UInt &	iElem,
		VectorElemental &	elvecMix
	)

protectedvirtual

Computes local (element dependent) vectors.

Locally update the current finite element for the primal and dual finite element space, then compute the Hdiv and L2 source vectors.

Parameters

iElem	Id of the current geometrical element.
elvecMix	The local vector in mixed form.

Reimplemented in DarcySolverTransientNonLinear< MeshType >, and DarcySolverTransient< MeshType >.

Definition at line 1225 of file DarcySolverLinear.hpp.

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◆ staticCondensation()

void staticCondensation	(	MatrixElemental &	localMatrixHybrid,
		VectorElemental &	localVectorHybrid,
		MatrixElemental &	elmatMix,
		MatrixElemental &	elmatReactionTerm,
		VectorElemental &	elvecMix
	)

protected

Performs static condensation.

Locally eliminate pressure and velocity DOFs, create the local hybrid matrix and local hybrid right hand side.

Parameters

localMatrixHybrid	The matrix which will store the hybrid local matrix.
localVectorHybrid	The vector which will store the hybrid local vector.
elmatMix	The local matrix in mixed form.
elmatReactionTerm	The local matrix for the reaction term.
elvecMix	The local vector in mixed form.

Matrix operations.

End of matrix operations.

Vector operations.

End of vector operations.

Definition at line 1268 of file DarcySolverLinear.hpp.

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◆ localComputePrimalAndDual()

void localComputePrimalAndDual	(	VectorElemental &	localSolution,
		MatrixElemental &	elmatMix,
		MatrixElemental &	elmatReactionTerm,
		VectorElemental &	elvecMix
	)

protected

Compute locally, as a post process, the primal and dual variable given the hybrid.

Parameters

localSolution	A vector which stores the dual, primal and hybrid local solution.
elmatMix	The local matrix in mixed form.
elmatReactionTerm	The local matrix for the reaction term.
elvecMix	The local vector in mixed form.

End of matrix operations.

Vector operations, computation of primal and dual variable.

Computation of the primal variable

Computation of the dual variable.

End of vector computation.

Definition at line 1451 of file DarcySolverLinear.hpp.

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◆ postComputePrimalAndDual()

virtual void postComputePrimalAndDual ( )

inlineprotectedvirtual

Do some computation after the calculation of the primal and dual variable.

The function is empty while it is useful in derived classes, i.e. DarcySolverTransient.

Reimplemented in DarcySolverTransient< MeshType >.

Definition at line 701 of file DarcySolverLinear.hpp.

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◆ resetVariables()

void resetVariables ( )

protectedvirtual

Update all problem variables.

Update all the variables of the problem before the construction of the global hybrid matrix, e.g. reset the global hybrid matrix. It is principally used for a time dependent derived class, in fact we want to clear each time step all the variables.

Reimplemented in DarcySolverNonLinear< MeshType >, and DarcySolverTransientNonLinear< MeshType >.

Definition at line 1630 of file DarcySolverLinear.hpp.

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◆ applyBoundaryConditions()

void applyBoundaryConditions ( )

protected

Apply the boundary condition.

Definition at line 1659 of file DarcySolverLinear.hpp.

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◆ symmetrizeMatrix()

void symmetrizeMatrix	(	Int	N,
		MatrixType &	A
	)

protected

Make matrix symmetric.

Transform a symmetric matrix that is stored only in the lower triangular part in a full symmetric matrix.

Parameters

N	The size of the matrix A.

Template Parameters

A	The matrix to be reordered.

Definition at line 1693 of file DarcySolverLinear.hpp.

Field Documentation

◆ M_displayer

displayerPtr_Type M_displayer

protected

Displayer for parallel cout.

Definition at line 734 of file DarcySolverLinear.hpp.

◆ M_data

dataPtr_Type M_data

protected

Data for Darcy solvers.

Definition at line 743 of file DarcySolverLinear.hpp.

◆ M_scalarSourceFct

scalarFctPtr_Type M_scalarSourceFct

protected

Source function.

Definition at line 746 of file DarcySolverLinear.hpp.

◆ M_vectorSourceFct

vectorFctPtr_Type M_vectorSourceFct

protected

Vector source function.

Definition at line 749 of file DarcySolverLinear.hpp.

◆ M_reactionTermFct

scalarFctPtr_Type M_reactionTermFct

protected

Reaction term function.

Definition at line 752 of file DarcySolverLinear.hpp.

◆ M_inversePermeabilityFct

matrixFctPtr_Type M_inversePermeabilityFct

protected

Inverse of the permeability tensor.

Definition at line 755 of file DarcySolverLinear.hpp.

◆ M_boundaryConditionHandler

bcHandlerPtr_Type M_boundaryConditionHandler

protected

Bondary conditions handler.

Definition at line 758 of file DarcySolverLinear.hpp.

◆ M_primalField

scalarFieldPtr_Type M_primalField

protected

Primal solution.

Definition at line 767 of file DarcySolverLinear.hpp.

◆ M_dualField

scalarFieldPtr_Type M_dualField

protected

Dual solution.

Definition at line 770 of file DarcySolverLinear.hpp.

◆ M_hybridField

scalarFieldPtr_Type M_hybridField

protected

Hybrid solution.

Definition at line 773 of file DarcySolverLinear.hpp.

◆ M_matrHybrid

matrixPtr_Type M_matrHybrid

protected

Hybrid matrix.

Definition at line 782 of file DarcySolverLinear.hpp.

◆ M_rhs

vectorPtr_Type M_rhs

protected

Right hand side.

Definition at line 785 of file DarcySolverLinear.hpp.

◆ M_residual

vectorPtr_Type M_residual

protected

Residual.

Definition at line 788 of file DarcySolverLinear.hpp.

◆ M_linearSolver

solver_Type M_linearSolver

protected

Linear solver.

Definition at line 791 of file DarcySolverLinear.hpp.

◆ M_prec

preconditionerPtr_Type M_prec

protected

Epetra preconditioner for the linear system.

Definition at line 794 of file DarcySolverLinear.hpp.

The documentation for this class was generated from the following file:

DarcySolverLinear.hpp

Public Types

Constructors and destructor

Methods

Set Methods

Get Methods

Private Constructors

Private Operators

Protected Methods

Parallel stuff

Data of the problem

Solution fields stuff

Algebraic stuff

Detailed Description

template<typename MeshType> class LifeV::DarcySolverLinear< MeshType >

Member Typedef Documentation

◆ mesh_Type

◆ solver_Type

◆ darcySolver_Type

◆ data_Type

◆ dataPtr_Type

◆ bcHandler_Type

◆ bcHandlerPtr_Type

◆ commPtr_Type

◆ map_Type

◆ displayerPtr_Type

◆ fESpace_Type

◆ fESpacePtr_Type

◆ scalarField_Type

◆ scalarFieldPtr_Type

◆ vectorField_Type

◆ vectorFieldPtr_Type

◆ scalarFct_Type

◆ scalarFctPtr_Type

◆ vectorFct_Type

◆ vectorFctPtr_Type

◆ matrixFct_Type

◆ matrixFctPtr_Type

◆ matrix_Type

◆ matrixPtr_Type

◆ vector_Type

◆ vectorPtr_Type

◆ preconditionerPtr_Type

Constructor & Destructor Documentation

◆ DarcySolverLinear() [1/2]

◆ ~DarcySolverLinear()

◆ DarcySolverLinear() [2/2]

Member Function Documentation

◆ buildSystem()

◆ setup()

◆ solveLinearSystem()

◆ computePrimalAndDual()

◆ solve()

◆ setData()

◆ setBoundaryConditions()

◆ setScalarSource()

◆ setVectorSource()

◆ setInversePermeability()

◆ setReactionTerm()

◆ setHybridField()

◆ setPrimalField()

◆ setDualField()

◆ setFields()

◆ setDisplayer()

◆ setCommunicator()

◆ hybridFieldPtr() [1/2]

◆ hybridFieldPtr() [2/2]

◆ primalFieldPtr() [1/2]

◆ primalFieldPtr() [2/2]

◆ dualFieldPtr() [1/2]

◆ dualFieldPtr() [2/2]

◆ residualPtr() [1/2]

◆ residualPtr() [2/2]

◆ boundaryConditionHandlerPtr() [1/2]

◆ boundaryConditionHandlerPtr() [2/2]

◆ getMap()

◆ getCommPtr()

◆ operator=()

◆ preLoopElementsComputation()

◆ computeConstantMatrices()

◆ localMatrixComputation()

template<typename MeshType>
class LifeV::DarcySolverLinear< MeshType >