implements a non-linear Darcy solver More...

#include <DarcySolverNonLinear.hpp>

Inheritance diagram for DarcySolverNonLinear< MeshType >:

Collaboration diagram for DarcySolverNonLinear< MeshType >:

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

typedef DarcySolverNonLinear< mesh_Type >	darcySolverNonLinear_Type
	Self typedef. More...

typedef DarcySolverLinear< mesh_Type >	darcySolverLinear_Type
	Darcy solver class. More...

typedef darcySolverLinear_Type::data_Type	data_Type
	Typedef for the data type. More...

typedef darcySolverLinear_Type::dataPtr_Type	dataPtr_Type
	Shared pointer for the data type. More...

typedef darcySolverLinear_Type::scalarFctPtr_Type	scalarFctPtr_Type
	Shared pointer to a scalar value function. More...

typedef darcySolverLinear_Type::matrixFctPtr_Type	matrixFctPtr_Type
	Shared pointer to a matrix value function. More...

typedef darcySolverLinear_Type::scalarField_Type	scalarField_Type
	Scalar field. More...

typedef darcySolverLinear_Type::scalarFieldPtr_Type	scalarFieldPtr_Type
	Shared pointer to a scalar field. More...

Constructors & destructor
	DarcySolverNonLinear ()
	Constructor for the class. More...

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

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

virtual void	solve ()
	Solve the problem performing the fixed point scheme. More...

Set methos
void	setPrimalZeroIteration (const scalarFctPtr_Type &primalZeroIteration)
	Initial guess for fixed point iteration. More...

virtual void	setInversePermeability (const matrixFctPtr_Type &invPerm)
	Set the inverse of diffusion tensor,. More...

void	setFixedPointTolerance (const Real &tol)

void	setFixedPointMaxIteration (const UInt &maxit)

Get methods
UInt	fixedPointNumIteration ()

Real	fixedPointResidual ()
	Returns the residual between two iterations of the fixed point scheme. More...

const Real &	fixedPointTolerance () const
	Returns fixed point tolerance. More...

Real &	fixedPointTolerance ()
	Returns fixed point tolerance. More...

const UInt &	fixedPointMaxIteration () const
	Returns maximum number of fixed point iterations allowed. More...

UInt &	fixedPointMaxIteration ()
	Returns maximum number of fixed point iterations allowed. More...

const scalarFieldPtr_Type &	primalPreviousIterationPtr () const
	Returns the pointer of the primal solution field at previous step. More...

scalarFieldPtr_Type &	primalPreviousIterationPtr ()
	Returns the pointer of the primal solution field at previous step. More...

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

void	fixedPoint ()
	Perform the fixed point loop to solve the non-linear problem. More...

void	setupNonLinear ()
	Set up the data for the non-linear solver. More...

Protected Members
scalarFieldPtr_Type	M_primalFieldPreviousIteration
	Primal solution at previous iteration step. More...

Private Constructors
	DarcySolverNonLinear (const darcySolverNonLinear_Type &)
	Inhibited copy constructor. More...

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

Non-linear stuff
UInt	M_fixedPointMaxIteration
	The maximum number of iterations for the fixed point method. More...

UInt	M_fixedPointNumIteration
	The current iterations for the fixed point method. More...

Real	M_fixedPointTolerance
	Tollerance for the stopping criteria for the fixed point method. More...

Real	M_fixedPointResidual
	The residual between two iteration of the fixed point scheme. More...

scalarFctPtr_Type	M_primalFieldZeroIterationFct
	Primal solution at zero time step. More...

Additional Inherited Members
Public Types inherited from DarcySolverLinear< MeshType >
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...

Public Member Functions inherited from DarcySolverLinear< MeshType >
	DarcySolverLinear ()
	Constructor for the class. More...

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

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

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...

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...

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...

Protected Member Functions inherited from DarcySolverLinear< MeshType >
	DarcySolverLinear (const darcySolver_Type &)
	Inhibited copy constructor. More...

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

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...

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

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

Protected Attributes inherited from DarcySolverLinear< MeshType >
displayerPtr_Type	M_displayer
	Displayer for parallel cout. More...

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...

scalarFieldPtr_Type	M_primalField
	Primal solution. More...

scalarFieldPtr_Type	M_dualField
	Dual solution. More...

scalarFieldPtr_Type	M_hybridField
	Hybrid solution. More...

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::DarcySolverNonLinear< MeshType >

implements a non-linear 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

This class implements a non-linear Darcy solver with fixed point scheme to handle the non-linearity.

The classical non-linear Darcy formulation is a couple of differential equations of first order with the 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 flux or the dual unknown, such that

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

The data in the system are:

$\Lambda$ the permeability tensor that depends on ;
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.

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

Introducing the following operator, bilinear forms and the functionals

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

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

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

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 $\Lambda_h \subset \Lambda$

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

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

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

To solve the non-linearity we use a fixed point scheme based on the relative difference between two consecutive iterations of the primal variable. We start from the, user defined, function $ p^0 $ and solve the linearized problem for $n \geq 1$ : find $(\sigma_h^n,\, p_h^n, \, \lambda_h^n) \in Z_h \times V_h \times \Lambda_h$ such that

$\left\{ \begin{array}{l l} a(\sigma_h^n, \tau_h; p_h^{n-1}) + b(p_h^n, \tau_h) + c(\lambda_h^n, \tau_h) = F_v(\tau) \,, & \forall \tau_h \in Z_h \,,\vspace{0.2cm}\\ b(q_h, \sigma_h^n) - d(p_h, q_h)= - F(q_h)\,, & \forall q_h \in V_h \,,\vspace{0.2cm}\\ c(\mu_h, \sigma_h^n) + h(\lambda_h^n, \mu_h) = G(\mu_h) \,, & \forall \mu_h \in \Lambda_h\,. \end{array} \right.$

At each iteration, 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^n $ , $\sigma_K^n$ may be written in function of $\lambda_K^n$ alone. We introduce the following local matrices

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

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, at each iteration, is

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

Or alternatively

$\begin{array}{l l l} \left[ \begin{array}{c c c} A \left( p_K^{n-1} \right) & B & C \vspace{0.2cm} \\ B^T & -D & 0 \vspace{0.2cm} \\ C^T & 0 & H \end{array} \right] \, \cdot & \left[ \begin{array}{c} \sigma_K^n \vspace{0.2cm}\\ p_K^n \vspace{0.2cm}\\ \lambda_K^n \end{array} \right] \, & = \left[ \begin{array}{c} F_v \vspace{0.2cm}\\ -F \vspace{0.2cm}\\ G \end{array} \right]\,. \end{array}$

Introducing the local hybrid matrix and local hybrid right hand side

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

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

$L^n \lambda^n = r \,.$

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

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

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.

Attention! We have the hypothesis that we use P0 elements for the primal unknown. Change this in a future!

Add criteria to ensure convergence of the fixed point method.

Definition at line 247 of file DarcySolverNonLinear.hpp.

Member Typedef Documentation

◆ mesh_Type

typedef MeshType mesh_Type

Typedef for mesh template.

Definition at line 257 of file DarcySolverNonLinear.hpp.

◆ darcySolverNonLinear_Type

typedef DarcySolverNonLinear< mesh_Type > darcySolverNonLinear_Type

Self typedef.

Definition at line 260 of file DarcySolverNonLinear.hpp.

◆ darcySolverLinear_Type

typedef DarcySolverLinear< mesh_Type > darcySolverLinear_Type

Darcy solver class.

Definition at line 263 of file DarcySolverNonLinear.hpp.

◆ data_Type

typedef darcySolverLinear_Type::data_Type data_Type

Typedef for the data type.

Definition at line 266 of file DarcySolverNonLinear.hpp.

◆ dataPtr_Type

typedef darcySolverLinear_Type::dataPtr_Type dataPtr_Type

Shared pointer for the data type.

Definition at line 269 of file DarcySolverNonLinear.hpp.

◆ scalarFctPtr_Type

typedef darcySolverLinear_Type::scalarFctPtr_Type scalarFctPtr_Type

Shared pointer to a scalar value function.

Definition at line 272 of file DarcySolverNonLinear.hpp.

◆ matrixFctPtr_Type

typedef darcySolverLinear_Type::matrixFctPtr_Type matrixFctPtr_Type

Shared pointer to a matrix value function.

Definition at line 275 of file DarcySolverNonLinear.hpp.

◆ scalarField_Type

typedef darcySolverLinear_Type::scalarField_Type scalarField_Type

Scalar field.

Definition at line 278 of file DarcySolverNonLinear.hpp.

◆ scalarFieldPtr_Type

typedef darcySolverLinear_Type::scalarFieldPtr_Type scalarFieldPtr_Type

Shared pointer to a scalar field.

Definition at line 281 of file DarcySolverNonLinear.hpp.

Constructor & Destructor Documentation

◆ DarcySolverNonLinear() [1/2]

DarcySolverNonLinear ( )

Constructor for the class.

Definition at line 567 of file DarcySolverNonLinear.hpp.

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◆ ~DarcySolverNonLinear()

virtual ~DarcySolverNonLinear ( )

inlinevirtual

Virtual destructor.

Definition at line 292 of file DarcySolverNonLinear.hpp.

◆ DarcySolverNonLinear() [2/2]

DarcySolverNonLinear ( const darcySolverNonLinear_Type & )

private

Inhibited copy constructor.

Member Function Documentation

◆ setup()

void setup ( )

virtual

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

Reimplemented from DarcySolverLinear< MeshType >.

Reimplemented in DarcySolverTransientNonLinear< MeshType >.

Definition at line 586 of file DarcySolverNonLinear.hpp.

◆ solve()

virtual void solve ( )

inlinevirtual

Solve the problem performing the fixed point scheme.

Reimplemented from DarcySolverLinear< MeshType >.

Reimplemented in DarcySolverTransientNonLinear< MeshType >.

Definition at line 303 of file DarcySolverNonLinear.hpp.

◆ setPrimalZeroIteration()

void setPrimalZeroIteration ( const scalarFctPtr_Type & primalZeroIteration )

Initial guess for fixed point iteration.

Set the function for the first iteration for the fixed point method.

Parameters

primalZeroIteration The function for the first iteration.

Definition at line 681 of file DarcySolverNonLinear.hpp.

◆ setInversePermeability()

virtual void setInversePermeability ( const matrixFctPtr_Type & invPerm )

inlinevirtual

Set the inverse of diffusion tensor,.

The non linearity of the solver is in the diffusion or permeability tensor. To handle this type of non linearity we use an iterative scheme and we write the tensor depending on the solution at previuos step. The non linear tensor now has as an additional scalar field, the last one, the solution of the problem at previuos step. This scalar field is automatically updated each iteration of the non linear solver.
The user should take into account that the value of the primal variable is the last field set, by the user, plus one. So the inverse of permeability can access to the primal variable, for example, with

// Inverse of permeability matrix
typedef RegionMesh < LinearTriangle > regionMesh_Type;
class inversePermeability : public FEFunction < regionMesh_Type, MapEpetra, Matrix >
{
public:
virtual Matrix eval ( const UInt& iElem, const Vector3D& P, const Real& time = 0. ) const;
};

Its implementation is

Matrix inversePermeability::eval ( const UInt& iElem, const Vector3D& P, const Real& time ) const
{
Matrix invK ( 2, 2 );
Real unkown_n = scalarField(0).eval( iElem, P, time );
// Fill in of the inversePermeabilityMatrix
invK ( 0, 0 ) = 1;
invK ( 0, 1 ) = 0;
invK ( 1, 0 ) = 0;
invK ( 1, 1 ) = 1. / ( unkown_n * unkown_n + 1. );
return invK;
}

obtaining a tensor with the non linearity in the position $ (1,1) $ the function $\left[K^{-1}\right]_{1,1} = u^2 + 1$ .
In the previous example we have supposed that the permeability has not others scalar fields. If the user has set $ m $ scalar fields prior to calling setInversePermeability, then the code should be

const Real unkown_n = scalarField(m).eval( iElem, P, time );

to access the primal at previous step.

Note: For an example of the usage see darcy_nonlinear and twophase_impes

Parameters

invPerm Inverse of the permeability tensor for the problem.

Reimplemented from DarcySolverLinear< MeshType >.

Reimplemented in DarcySolverTransientNonLinear< MeshType >.

Definition at line 375 of file DarcySolverNonLinear.hpp.

◆ setFixedPointTolerance()

void setFixedPointTolerance ( const Real & tol )

inline

Set fixed point tolerance

Parameters

tol	requested tolerance

Definition at line 392 of file DarcySolverNonLinear.hpp.

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◆ setFixedPointMaxIteration()

void setFixedPointMaxIteration ( const UInt & maxit )

inline

Set maximum number of fixed point iterations permitted

Parameters

maxit requested maximum

Definition at line 401 of file DarcySolverNonLinear.hpp.

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◆ fixedPointNumIteration()

UInt fixedPointNumIteration ( )

inline

Returns the number of iteration of the fixed point scheme.

Returns: Final number of iterations of the fixed point method as a constant UInt.

Definition at line 415 of file DarcySolverNonLinear.hpp.

◆ fixedPointResidual()

Real fixedPointResidual ( )

inline

Returns the residual between two iterations of the fixed point scheme.

Returns: Final residual of the fixed point method as a constant Real.

Definition at line 424 of file DarcySolverNonLinear.hpp.

◆ fixedPointTolerance() [1/2]

const Real& fixedPointTolerance ( ) const

inline

Returns fixed point tolerance.

Returns: M_fixedPointTolerance

Definition at line 433 of file DarcySolverNonLinear.hpp.

◆ fixedPointTolerance() [2/2]

Real& fixedPointTolerance ( )

inline

Returns fixed point tolerance.

Returns: M_fixedPointTolerance

Definition at line 442 of file DarcySolverNonLinear.hpp.

◆ fixedPointMaxIteration() [1/2]

const UInt& fixedPointMaxIteration ( ) const

inline

Returns maximum number of fixed point iterations allowed.

Returns: max possible number of fixed point iterations

Definition at line 451 of file DarcySolverNonLinear.hpp.

◆ fixedPointMaxIteration() [2/2]

UInt& fixedPointMaxIteration ( )

inline

Returns maximum number of fixed point iterations allowed.

Returns: max possible number of fixed point iterations

Definition at line 460 of file DarcySolverNonLinear.hpp.

◆ primalPreviousIterationPtr() [1/2]

const scalarFieldPtr_Type& primalPreviousIterationPtr ( ) const

inline

Returns the pointer of the primal solution field at previous step.

Returns: Constant scalarFieldPtr_Type reference of the primal solution field at previous step.

Definition at line 469 of file DarcySolverNonLinear.hpp.

◆ primalPreviousIterationPtr() [2/2]

scalarFieldPtr_Type& primalPreviousIterationPtr ( )

inline

Returns the pointer of the primal solution field at previous step.

Returns: Constant scalarFieldPtr_Type reference of the primal solution field at previous step.

Definition at line 478 of file DarcySolverNonLinear.hpp.

◆ 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.

Reimplemented from DarcySolverLinear< MeshType >.

Reimplemented in DarcySolverTransientNonLinear< MeshType >.

Definition at line 700 of file DarcySolverNonLinear.hpp.

◆ fixedPoint()

void fixedPoint ( )

protected

Perform the fixed point loop to solve the non-linear problem.

Definition at line 623 of file DarcySolverNonLinear.hpp.

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◆ setupNonLinear()

void setupNonLinear ( )

protected

Set up the data for the non-linear solver.

Definition at line 601 of file DarcySolverNonLinear.hpp.

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◆ operator=()

darcySolverNonLinear_Type& operator= ( const darcySolverNonLinear_Type & )

private

Inhibited assign operator.

Field Documentation

◆ M_primalFieldPreviousIteration

scalarFieldPtr_Type M_primalFieldPreviousIteration

protected

Primal solution at previous iteration step.

Definition at line 511 of file DarcySolverNonLinear.hpp.

◆ M_fixedPointMaxIteration

UInt M_fixedPointMaxIteration

private

The maximum number of iterations for the fixed point method.

Definition at line 538 of file DarcySolverNonLinear.hpp.

◆ M_fixedPointNumIteration

UInt M_fixedPointNumIteration

private

The current iterations for the fixed point method.

Definition at line 541 of file DarcySolverNonLinear.hpp.

◆ M_fixedPointTolerance

Real M_fixedPointTolerance

private

Tollerance for the stopping criteria for the fixed point method.

Definition at line 544 of file DarcySolverNonLinear.hpp.

◆ M_fixedPointResidual

Real M_fixedPointResidual

private

The residual between two iteration of the fixed point scheme.

Definition at line 547 of file DarcySolverNonLinear.hpp.

◆ M_primalFieldZeroIterationFct

scalarFctPtr_Type M_primalFieldZeroIterationFct

private

Primal solution at zero time step.

Definition at line 550 of file DarcySolverNonLinear.hpp.

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

DarcySolverNonLinear.hpp

Public Types

Constructors & destructor

Methods

Set methos

Get methods

Protected Methods

Protected Members

Private Constructors

Private Operators

Non-linear stuff

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

◆ mesh_Type

◆ darcySolverNonLinear_Type

◆ darcySolverLinear_Type

◆ data_Type

◆ dataPtr_Type

◆ scalarFctPtr_Type

◆ matrixFctPtr_Type

◆ scalarField_Type

◆ scalarFieldPtr_Type

Constructor & Destructor Documentation

◆ DarcySolverNonLinear() [1/2]

◆ ~DarcySolverNonLinear()

◆ DarcySolverNonLinear() [2/2]

Member Function Documentation

◆ setup()

◆ solve()

◆ setPrimalZeroIteration()

◆ setInversePermeability()

◆ setFixedPointTolerance()

◆ setFixedPointMaxIteration()

◆ fixedPointNumIteration()

◆ fixedPointResidual()

◆ fixedPointTolerance() [1/2]

◆ fixedPointTolerance() [2/2]

◆ fixedPointMaxIteration() [1/2]

◆ fixedPointMaxIteration() [2/2]

◆ primalPreviousIterationPtr() [1/2]

◆ primalPreviousIterationPtr() [2/2]

◆ resetVariables()

◆ fixedPoint()

◆ setupNonLinear()

◆ operator=()

Field Documentation

◆ M_primalFieldPreviousIteration

◆ M_fixedPointMaxIteration

◆ M_fixedPointNumIteration

◆ M_fixedPointTolerance

◆ M_fixedPointResidual

◆ M_primalFieldZeroIterationFct

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