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gsVisitorStokes.h
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/** @file gsVisitorStokes.h
@brief Visitor class for volumetric integration of the Stokes system.
This file is part of the G+Smo library.
This Source Code Form is subject to the terms of the Mozilla Public
License, v. 2.0. If a copy of the MPL was not distributed with this
file, You can obtain one at http://mozilla.org/MPL/2.0/.
Author(s):
A.Shamanskiy (2016 - ...., TU Kaiserslautern)
*/
#pragma once
#include <gsAssembler/gsQuadrature.h>
#include <gsCore/gsFuncData.h>
#include <gsElasticity/gsBasePde.h>
namespace gismo
{
template <class T>
class gsVisitorStokes
{
public:
gsVisitorStokes(const gsPde<T> & pde_)
: dim(), pde_ptr(static_cast<const gsBasePde<T>*>(&pde_)),
viscosity(), density(), N_V(), N_P()
{}
void initialize(const gsBasisRefs<T> & basisRefs,
const index_t patchIndex,
const gsOptionList & options,
gsQuadRule<T> & rule)
{
GISMO_UNUSED(patchIndex);
// parametric dimension of the first displacement component
dim = basisRefs.front().dim();
// a quadrature rule is defined by the basis for the first velocity component.
// the same rule is used for the presure
rule = gsQuadrature::get(basisRefs.front(), options);
// saving necessary info
viscosity = options.getReal("Viscosity");
density = options.getReal("Density");
// resize containers for global indices
globalIndices.resize(dim+1);
blockNumbers.resize(dim+1);
}
inline void evaluate(const gsBasisRefs<T> & basisRefs,
const gsGeometry<T> & geo,
const gsMatrix<T> & quNodes)
{
// store quadrature points of the element for geometry evaluation
md.points = quNodes;
// NEED_VALUE to get points in the physical domain for evaluation of the RHS
// NEED_MEASURE to get the Jacobian determinant values for integration
// NEED_GRAD_TRANSFORM to get the Jacobian matrix to transform gradient from the parametric to physical domain
md.flags = NEED_VALUE | NEED_MEASURE | NEED_GRAD_TRANSFORM;
// Compute image of the quadrature points plus gradient, jacobian and other necessary data
geo.computeMap(md);
// find local indices of the velocity and pressure basis functions active on the element
basisRefs.front().active_into(quNodes.col(0),localIndicesVel);
N_V = localIndicesVel.rows();
basisRefs.back().active_into(quNodes.col(0), localIndicesPres);
N_P = localIndicesPres.rows();
// Evaluate velocity basis functions and their derivatives on the element
basisRefs.front().evalAllDers_into(quNodes,1,basisValuesVel);
// Evaluate pressure basis functions on the element
basisRefs.back().eval_into(quNodes,basisValuesPres);
// Evaluate right-hand side at the image of the quadrature points
pde_ptr->rhs()->eval_into(md.values[0],forceValues);
}
inline void assemble(gsDomainIterator<T> & element,
const gsVector<T> & quWeights)
{
GISMO_UNUSED(element);
// Initialize local matrix/rhs // A | B^T
localMat.setZero(dim*N_V + N_P, dim*N_V + N_P); // --|-- matrix structure
localRhs.setZero(dim*N_V + N_P,1); // B | 0
// Loop over the quadrature nodes
for (index_t q = 0; q < quWeights.rows(); ++q)
{
// Multiply quadrature weight by the geometry measure
const T weight = quWeights[q] * md.measure(q);
// Compute physical gradients of the velocity basis functions at q as a dim x numActiveFunction matrix
transformGradients(md, q, basisValuesVel[1], physGradVel);
// matrix A
block = weight*viscosity*density * physGradVel.transpose()*physGradVel;
for (short_t d = 0; d < dim; ++d)
localMat.block(d*N_V,d*N_V,N_V,N_V) += block.block(0,0,N_V,N_V);
// matrix B
for (short_t d = 0; d < dim; ++d)
{
block = weight*basisValuesPres.col(q)*physGradVel.row(d);
localMat.block(dim*N_V,d*N_V,N_P,N_V) -= block.block(0,0,N_P,N_V);
localMat.block(d*N_V,dim*N_V,N_V,N_P) -= block.transpose().block(0,0,N_V,N_P);
}
// rhs contribution
for (short_t d = 0; d < dim; ++d)
localRhs.middleRows(d*N_V,N_V).noalias() += weight *density * forceValues(d,q) * basisValuesVel[0].col(q) ;
}
}
inline void localToGlobal(const int patchIndex,
const std::vector<gsMatrix<T> > & eliminatedDofs,
gsSparseSystem<T> & system)
{
// computes global indices for velocity components
for (short_t d = 0; d < dim; ++d)
{
system.mapColIndices(localIndicesVel, patchIndex, globalIndices[d], d);
blockNumbers.at(d) = d;
}
// computes global indices for pressure
system.mapColIndices(localIndicesPres, patchIndex, globalIndices[dim], dim);
blockNumbers.at(dim) = dim;
// push to global system
system.pushToRhs(localRhs,globalIndices,blockNumbers);
system.pushToMatrix(localMat,globalIndices,eliminatedDofs,blockNumbers,blockNumbers);
}
protected:
// problem info
short_t dim;
const gsBasePde<T> * pde_ptr;
T viscosity, density;
// geometry mapping
gsMapData<T> md;
// local components of the global linear system
gsMatrix<T> localMat;
gsMatrix<T> localRhs;
// local indices (at the current patch) of basis functions active at the current element
gsMatrix<index_t> localIndicesVel;
gsMatrix<index_t> localIndicesPres;
// number of velocity and pressure basis functions active at the current element
index_t N_V, N_P;
// values and derivatives of velocity basis functions at quadrature points at the current element
// values are stored as a N_V x numQuadPoints matrix; not sure about derivatives, must be smth like N_V*dim x numQuadPoints
std::vector<gsMatrix<T> > basisValuesVel;
// values of pressure basis functions active at the current element;
// stores as a N_P x numQuadPoints matrix
gsMatrix<T> basisValuesPres;
// RHS values at quadrature points at the current element; stored as a dim x numQuadPoints matrix
gsMatrix<T> forceValues;
// all temporary matrices defined here for efficiency
gsMatrix<T> block, physGradVel;
// containers for global indices
std::vector< gsMatrix<index_t> > globalIndices;
gsVector<index_t> blockNumbers;
};
} // namespace gismo