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gsVisitorMixedLinearElasticity.h
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/** @file gsVisitorMixedLinearElasticity.h
@brief Visitor class for volumetric integration of the mixed linear elasticity 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):
O. Weeger (2012 - 2015, TU Kaiserslautern),
A.Shamanskiy (2016 - ...., TU Kaiserslautern)
*/
#pragma once
#include <gsElasticity/gsVisitorElUtils.h>
#include <gsElasticity/gsBasePde.h>
#include <gsAssembler/gsQuadrature.h>
#include <gsCore/gsFuncData.h>
namespace gismo
{
template <class T>
class gsVisitorMixedLinearElasticity
{
public:
gsVisitorMixedLinearElasticity(const gsPde<T> & pde_)
: dim(0), N_D(0), pde_ptr(static_cast<const gsBasePde<T>*>(&pde_)) {}
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
T E = options.getReal("YoungsModulus");
T pr = options.getReal("PoissonsRatio");
lambda_inv = ( 1. + pr ) * ( 1. - 2. * pr ) / E / pr ;
mu = E / ( 2. * ( 1. + pr ) );
forceScaling = options.getReal("ForceScaling");
I = gsMatrix<T>::Identity(dim,dim);
// 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 displacement and pressure basis functions active on the element
basisRefs.front().active_into(quNodes.col(0),localIndicesDisp);
N_D = localIndicesDisp.rows();
basisRefs.back().active_into(quNodes.col(0), localIndicesPres);
N_P = localIndicesPres.rows();
// Evaluate displacement basis functions and their derivatives on the element
basisRefs.front().evalAllDers_into(quNodes,1,basisValuesDisp);
// 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_D + N_P, dim*N_D + N_P); // --|-- matrix structure
localRhs.setZero(dim*N_D + N_P,1); // B | C
// elasticity tensor
symmetricIdentityTensor<T>(C,I);
C *= mu;
// 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 basis functions at q as a dim x numActiveFunction matrix
transformGradients(md, q, basisValuesDisp[1], physGradDisp);
// A-matrix: Loop over displacement basis functions
for (index_t i = 0; i < N_D; i++)
{
setB<T>(B_i,I,physGradDisp.col(i));
tempK = B_i.transpose() * C;
// Loop over displacement basis functions
for (index_t j = 0; j < N_D; j++)
{
setB<T>(B_j,I,physGradDisp.col(j));
K = tempK * B_j;
for (short_t di = 0; di < dim; ++di)
for (short_t dj = 0; dj < dim; ++dj)
localMat(di*N_D+i, dj*N_D+j) += weight * K(di,dj);
}
}
// B-matrix
for (short_t d = 0; d < dim; ++d)
{
block = weight*basisValuesPres.col(q)*physGradDisp.row(d);
localMat.block(dim*N_D,d*N_D,N_P,N_D) += block.block(0,0,N_P,N_D);
localMat.block(d*N_D,dim*N_D,N_D,N_P) += block.transpose().block(0,0,N_D,N_P);
}
// C-matrix
if (abs(lambda_inv) > 0)
localMat.block(dim*N_D,dim*N_D,N_P,N_P) -=
(weight*lambda_inv*basisValuesPres.col(q)*basisValuesPres.col(q).transpose()).block(0,0,N_P,N_P);
// rhs contribution
for (short_t d = 0; d < dim; ++d)
localRhs.middleRows(d*N_D,N_D).noalias() += weight * forceScaling * forceValues(d,q) * basisValuesDisp[0].col(q) ;
}
}
inline void localToGlobal(const int patchIndex,
const std::vector<gsMatrix<T> > & eliminatedDofs,
gsSparseSystem<T> & system)
{
// computes global indices for displacement components
for (short_t d = 0; d < dim; ++d)
{
system.mapColIndices(localIndicesDisp,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;
// Lame coefficients and force scaling factor
T lambda_inv, mu, forceScaling;
// 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> localIndicesDisp;
gsMatrix<index_t> localIndicesPres;
// number of displacement and pressure basis functions active at the current element
index_t N_D, N_P;
// values and derivatives of displacement basis functions at quadrature points at the current element
// values are stored as a N_D x numQuadPoints matrix; not sure about derivatives, must be smth like N_D*dim x numQuadPoints
std::vector<gsMatrix<T> > basisValuesDisp;
// 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> C, physGradDisp, B_i, tempK, B_j, K, block, I;
// containers for global indices
std::vector< gsMatrix<index_t> > globalIndices;
gsVector<index_t> blockNumbers;
};
} // namespace gismo