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gsVisitorBiharmonic.h
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/** @file gsVisitorBiharmonic.h
@brief Visitor class for mixed formulation for the biharmonic equation
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>
namespace gismo
{
template <class T>
class gsVisitorBiharmonic
{
public:
gsVisitorBiharmonic(const gsPde<T> & pde_, gsSparseMatrix<T> * elimMatrix = nullptr)
: pde_ptr(static_cast<const gsPoissonPde<T>*>(&pde_)),
N_M(), N_A(), localStiffening(),
elimMat(elimMatrix)
{}
void initialize(const gsBasisRefs<T> & basisRefs,
const index_t patchIndex,
const gsOptionList & options,
gsQuadRule<T> & rule)
{
GISMO_UNUSED(patchIndex);
// a quadrature rule is defined by the basis for the auxiliary variable.
// the same rule is used for the main variable
rule = gsQuadrature::get(basisRefs.back(), options);
// saving necessary info
localStiffening = options.getReal("LocalStiff");
// resize containers for global indices
globalIndices.resize(2);
blockNumbers.resize(2);
}
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 main and auxiliary basis functions active on the element
basisRefs.front().active_into(quNodes.col(0),localIndicesMain);
N_M = localIndicesMain.rows();
basisRefs.back().active_into(quNodes.col(0), localIndicesAux);
N_A = localIndicesAux.rows();
// Evaluate basis functions and their derivatives on the element
basisRefs.front().evalAllDers_into(quNodes,1,basisValuesMain);
basisRefs.back().evalAllDers_into(quNodes,1,basisValuesAux);
// 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 // 0 | B^T = L
localMat.setZero(N_M + N_A, N_M + N_A); // --|-- matrix structure
localRhs.setZero(N_M + N_A,pde_ptr->numRhs()); // B | A = 0
// Loop over the quadrature nodes
for (index_t q = 0; q < quWeights.rows(); ++q)
{
// Multiply quadrature weight by the geometry measure
const T weightMatrix = quWeights[q] * pow(md.measure(q),1-localStiffening);
const T weightRHS = quWeights[q] * md.measure(q);
// Compute physical gradients of the basis functions at q as a 1 x numActiveFunction matrix
transformGradients(md, q, basisValuesAux[1], physGradAux);
transformGradients(md, q, basisValuesMain[1], physGradMain);
// matrix A
block = weightMatrix * basisValuesAux[0].col(q) * basisValuesAux[0].col(q).transpose();
localMat.block(N_M,N_M,N_A,N_A) += block.block(0,0,N_A,N_A);
// matrix B
block = weightMatrix * physGradAux.transpose()*physGradMain; // N_A x N_M
localMat.block(0,N_M,N_M,N_A) += block.block(0,0,N_A,N_M).transpose();
localMat.block(N_M,0,N_A,N_M) += block.block(0,0,N_A,N_M);
// rhs contribution
localRhs.middleRows(0,N_M).noalias() += weightRHS * basisValuesMain[0].col(q) * forceValues.col(q).transpose();
}
}
inline void localToGlobal(const int patchIndex,
const std::vector<gsMatrix<T> > & eliminatedDofs,
gsSparseSystem<T> & system)
{
// compute global indices
system.mapColIndices(localIndicesMain,patchIndex,globalIndices[0],0);
system.mapColIndices(localIndicesAux,patchIndex,globalIndices[1],1);
blockNumbers.at(0) = 0;
blockNumbers.at(1) = 1;
// push to global system
system.pushToRhs(localRhs,globalIndices,blockNumbers);
system.pushToMatrix(localMat,globalIndices,eliminatedDofs,blockNumbers,blockNumbers);
// push to the elimination system
if (elimMat != nullptr)
{
index_t globalI,globalElimJ;
index_t elimSize = 0;
for (short_t dJ = 0; dJ < 2; ++dJ)
{
for (short_t dI = 0; dI < 2; ++dI)
for (index_t i = 0; i < N_M; ++i)
if (system.colMapper(dI).is_free_index(globalIndices[dI].at(i)))
{
system.mapToGlobalRowIndex(localIndicesMain.at(i),patchIndex,globalI,dI);
for (index_t j = 0; j < N_M; ++j)
if (!system.colMapper(dJ).is_free_index(globalIndices[dJ].at(j)))
{
globalElimJ = system.colMapper(dJ).global_to_bindex(globalIndices[dJ].at(j));
elimMat->coeffRef(globalI,elimSize+globalElimJ) += localMat(N_M*dI+i,N_M*dJ+j);
}
}
elimSize += eliminatedDofs[dJ].rows();
}
}
}
protected:
// problem info
const gsPoissonPde<T> * pde_ptr;
// 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> localIndicesMain;
gsMatrix<index_t> localIndicesAux;
// number of main and auxiliary basis functions active at the current element
index_t N_M, N_A;
// values and derivatives of main basis functions at quadrature points at the current element
// values are stored as a N_M x numQuadPoints matrix; not sure about derivatives, must be smth like N_M x numQuadPoints
// same for the auxiliary basis functions
std::vector<gsMatrix<T> > basisValuesMain;
std::vector<gsMatrix<T> > basisValuesAux;
// RHS values at quadrature points at the current element; stored as a 1 x numQuadPoints matrix
gsMatrix<T> forceValues;
// all temporary matrices defined here for efficiency
gsMatrix<T> block, physGradMain, physGradAux;
real_t localStiffening;
// elimination matrix to efficiently change Dirichlet degrees of freedom
gsSparseMatrix<T> * elimMat;
// containers for global indices
std::vector< gsMatrix<index_t> > globalIndices;
gsVector<index_t> blockNumbers;
};
} // namespace gismo