std::vector<float> sparseVecMult(const SparseMatrix &matrix, std::vector<float> vec, CL::TinyCL &tiny){
if (vec.size() != matrix.dim){
std::cout << "Vector size doesn't match matrix dimensions" << std::endl;
return std::vector<float>();
}
cl::Program program = tiny.loadProgram("../res/sparseMatVec.cl");
cl::Kernel kernel = tiny.loadKernel(program, "sparseMatVec");
int nVals = matrix.elements.size();
int *rows = new int[nVals];
int *cols = new int[nVals];
float *vals = new float[nVals];
matrix.getRaw(rows, cols, vals);
cl::Buffer rowBuf = tiny.buffer(CL::MEM::READ_ONLY, nVals * sizeof(float), rows);
cl::Buffer colBuf = tiny.buffer(CL::MEM::READ_ONLY, nVals * sizeof(float), cols);
cl::Buffer valBuf = tiny.buffer(CL::MEM::READ_ONLY, nVals * sizeof(float), vals);
cl::Buffer vecBuf = tiny.buffer(CL::MEM::READ_ONLY, vec.size() * sizeof(float), &vec[0]);
cl::Buffer resBuf = tiny.buffer(CL::MEM::WRITE_ONLY, vec.size() * sizeof(float));
kernel.setArg(0, sizeof(int), &nVals);
kernel.setArg(1, rowBuf);
kernel.setArg(2, colBuf);
kernel.setArg(3, valBuf);
kernel.setArg(4, vecBuf);
kernel.setArg(5, resBuf);
tiny.runKernel(kernel, cl::NullRange, matrix.dim);
std::vector<float> result;
result.resize(matrix.dim);
tiny.readData(resBuf, matrix.dim * sizeof(float), &result[0], NULL, true);
delete[] rows;
delete[] cols;
delete[] vals;
return result;
}
void Fill( SparseMatrix<T>& A, T alpha )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
A.Resize( m, n );
Zero( A );
if( alpha != T(0) )
{
A.Reserve( m*n );
for( Int i=0; i<m; ++i )
for( Int j=0; j<n; ++j )
A.QueueUpdate( i, j, alpha );
A.ProcessQueues();
}
}
void MatrixMarket( const SparseMatrix<T>& A, string basename="matrix" )
{
EL_DEBUG_CSE
string filename = basename + "." + FileExtension(MATRIX_MARKET);
ofstream file( filename.c_str(), std::ios::binary );
if( !file.is_open() )
RuntimeError("Could not open ",filename);
// Write the header
// ================
{
ostringstream os;
os << "%%MatrixMarket matrix coordinate ";
if( IsComplex<T>::value )
os << "complex ";
else
os << "real ";
os << "general\n";
file << os.str();
}
// Write the size line
// ===================
const Int m = A.Height();
const Int n = A.Width();
const Int numNonzeros = A.NumEntries();
file << BuildString(m," ",n," ",numNonzeros,"\n");
// Write the entries
// =================
for( Int e=0; e<numNonzeros; ++e )
{
const Int i = A.Row(e);
const Int j = A.Col(e);
const T value = A.Value(e);
if( IsComplex<T>::value )
{
file <<
BuildString(i," ",j," ",RealPart(value)," ",ImagPart(value),"\n");
}
else
{
file << BuildString(i," ",j," ",RealPart(value),"\n");
}
}
}
double functionOfW(vector<double>& w, vector<int>& Y, SparseMatrix<double,Eigen::RowMajor>& X)
{
size_t i;
double sum=0.0;
double sum2 = 0.0;
for (i=0; i<w.size(); i++) {
sum+=w.at(i)*w.at(i);
}
sum = sum*0.5;
//cout<<"sum = "<<sum<<endl;
int j;
for (j=0; j<X.outerSize(); j++) {
double dot = 0;
for (SparseMatrix<double,Eigen::RowMajor>::InnerIterator it(X,j); it; ++it) {
dot+=w.at(it.col())*it.value();
}
double temp = exp(-(Y.at(j)*dot));
sum2+= log(1+temp);
//cout<<"sum2 = "<<sum2<<endl;
}
return sum+sum2;
}
void MatrixUtils::bloc_to_sparse_copyDownTopLeftRight(const SparseBlocMatrix<ContiguousBloc<Element, Index> >& A, SparseMatrix<Element>& B)
{
uint32 curr_row_B = B.rowdim() - 1;
for(uint32 i=0; i<A.rowBlocDim (); ++i) //for each row of blocs in A, starting at the last row in B
{
if(A[i].empty ())
{
curr_row_B -= A.bloc_height();
continue;
}
if(A.isFilledWithEmptyBlocs())
check_equal_or_raise_exception(A.FirstBlocsColumIndexes[i], 0);
for(uint32 j=0;j<A[i].size (); ++j) //for each bloc in the row
{
if(A[i][j].empty ())
{
continue;
}
uint32 bloc_idx = A.FirstBlocsColumIndexes[i] + (A.bloc_width() * j);
for(uint16 k=0; k<A.bloc_height () && k <= curr_row_B; ++k) //for each row in the bloc
{
for (uint32 l = 0; l < A[i][j].get_row_size(k); ++l)
{
B[curr_row_B-k].push_back(
typename SparseMatrix<Element>::Row::value_type(
bloc_idx + A[i][j].pos_in_row(k, l),
A[i][j].value_in_row(k, l)));
}
}
}
curr_row_B -= A.bloc_height();
}
}
void makeBoundaryMatrix (SparseMatrix<double>& boundaryMatrix,
const int M,
const int N,
const double h,
const double * viscosityData) {
#ifdef DEBUG
cout << "<Creating " << 3 * M * N - M - N << "x" << 2 * M + 2 * N << " BoundaryMatrix>" << endl;
#endif
vector<Triplet<double> > tripletList;
makeBCLaplacianXBlock (tripletList, 0, 0, M, N, h, viscosityData);
makeBCLaplacianYBlock (tripletList, M * (N - 1), 2 * M, M, N, h, viscosityData);
makeBCDivXBlock (tripletList, 2 * M * N - M - N, 0, M, N, h);
makeBCDivYBlock (tripletList, 2 * M * N - M - N, 2 * M, M, N, h);
boundaryMatrix.setFromTriplets (tripletList.begin(), tripletList.end());
#ifdef DEBUG
cout << endl;
#endif
}
void COctaveInterface::get_real_sparsematrix(SGSparseVector<float64_t>*& matrix, int32_t& num_feat, int32_t& num_vec)
{
const octave_value mat_feat=get_arg_increment();
if (!mat_feat.is_sparse_type() || !(mat_feat.is_double_type()))
SG_ERROR("Expected Sparse Double Matrix as argument %d\n", m_rhs_counter);
SparseMatrix sm = mat_feat.sparse_matrix_value ();
num_vec=sm.cols();
num_feat=sm.rows();
int64_t nnz=sm.nelem();
matrix=new SGSparseVector<float64_t>[num_vec];
int64_t offset=0;
for (int32_t i=0; i<num_vec; i++)
{
int32_t len=sm.cidx(i+1)-sm.cidx(i);
matrix[i].vec_index=i;
matrix[i].num_feat_entries=len;
if (len>0)
{
matrix[i].features=new SGSparseVectorEntry<float64_t>[len];
for (int32_t j=0; j<len; j++)
{
matrix[i].features[j].entry=sm.data(offset);
matrix[i].features[j].feat_index=sm.ridx(offset);
offset++;
}
}
else
matrix[i].features=NULL;
}
ASSERT(offset=nnz);
}
void makeStokesMatrix (SparseMatrix<double>& stokesMatrix,
const int M,
const int N,
const double h,
const double * viscosityData) {
#ifdef DEBUG
cout << "<Creating " << 3 * M * N - M - N << "x" << 3 * M * N - M - N << " stokesMatrix>" << endl;
#endif
vector<Triplet<double> > tripletList;
makeLaplacianXBlock (tripletList, 0, 0, M, N, h, viscosityData);
makeLaplacianYBlock (tripletList, M * (N - 1), M * (N - 1), M, N, h, viscosityData);
makeGradXBlock (tripletList, 0, 2 * M * N - M - N, M, N, h);
makeGradYBlock (tripletList, M * (N - 1), 2 * M * N - M - N, M, N, h);
makeDivXBlock (tripletList, 2 * M * N - M - N, 0, M, N, h);
makeDivYBlock (tripletList, 2 * M * N - M - N, M * (N - 1), M, N, h);
stokesMatrix.setFromTriplets (tripletList.begin(), tripletList.end());
#ifdef DEBUG
cout << endl;
#endif
}
void
Assembly::addCachedJacobian(SparseMatrix<Number> & jacobian)
{
mooseAssert(_cached_jacobian_rows.size() == _cached_jacobian_cols.size(),
"Error: Cached data sizes MUST be the same!");
for(unsigned int i=0; i<_cached_jacobian_rows.size(); i++)
jacobian.add(_cached_jacobian_rows[i], _cached_jacobian_cols[i], _cached_jacobian_values[i]);
if (_max_cached_jacobians < _cached_jacobian_values.size())
_max_cached_jacobians = _cached_jacobian_values.size();
// Try to be more efficient from now on
// The 2 is just a fudge factor to keep us from having to grow the vector during assembly
_cached_jacobian_values.clear();
_cached_jacobian_values.reserve(_max_cached_jacobians*2);
_cached_jacobian_rows.clear();
_cached_jacobian_rows.reserve(_max_cached_jacobians*2);
_cached_jacobian_cols.clear();
_cached_jacobian_cols.reserve(_max_cached_jacobians*2);
}
std::pair<unsigned int, Real>
EigenSparseLinearSolver<T>::adjoint_solve (SparseMatrix<T> &matrix_in,
NumericVector<T> &solution_in,
NumericVector<T> &rhs_in,
const double tol,
const unsigned int m_its)
{
START_LOG("adjoint_solve()", "EigenSparseLinearSolver");
libmesh_experimental();
EigenSparseMatrix<T> mat_trans(this->comm());
matrix_in.get_transpose(mat_trans);
std::pair<unsigned int, Real> retval = this->solve (mat_trans,
solution_in,
rhs_in,
tol,
m_its);
STOP_LOG("adjoint_solve()", "EigenSparseLinearSolver");
return retval;
}
void SymmetricRuizEquil
( SparseMatrix<F>& A,
Matrix<Base<F>>& d,
Int maxIter, bool progress )
{
DEBUG_CSE
typedef Base<F> Real;
const Int n = A.Height();
Ones( d, n, 1 );
Matrix<Real> scales;
const Int indent = PushIndent();
for( Int iter=0; iter<maxIter; ++iter )
{
// Rescale the columns (and rows)
// ------------------------------
ColumnMaxNorms( A, scales );
EntrywiseMap( scales, function<Real(Real)>(DampScaling<Real>) );
EntrywiseMap( scales, function<Real(Real)>(SquareRootScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, d );
SymmetricDiagonalSolve( scales, A );
}
SetIndent( indent );
}
void JordanCholesky( SparseMatrix<T>& A, Int n )
{
DEBUG_ONLY(CSE cse("JordanCholesky"))
Zeros( A, n, n );
A.Reserve( 3*n );
for( Int e=0; e<n; ++e )
{
if( e == 0 )
A.QueueUpdate( e, e, T(1) );
else
A.QueueUpdate( e, e, T(5) );
if( e > 0 )
A.QueueUpdate( e, e-1, T(2) );
if( e < n-1 )
A.QueueUpdate( e, e+1, T(2) );
}
A.ProcessQueues();
}
SparseMatrix<double,0,int> Qinv2(SparseMatrix<double,0,int>& L)
{
int n = L.rows();
SparseMatrix<double,0,int> Sigma;
Sigma.resize(n,n);
Sigma.reserve(L.nonZeros()*50);
int j;
double Lii, val;
for (int i=n-1; i>=0; i--)
{
for(SparseMatrix<double>::ReverseInnerIterator ij(L,i);ij;--ij)
{
j=ij.row();
val = 0;
SparseMatrix<double>::InnerIterator iL(L,i);
SparseMatrix<double>::InnerIterator iS(Sigma,j);
for(; iL; ++iL)
{
if(iL.row() == iL.col()){
Lii = iL.value();
} else {
for(;iS.row() < iL.row(); ++iS){}
if(iS.row() == iL.row())
val += iL.value()*iS.value();
}
}
if(i==j){
Sigma.insert(i,j) = 1/(Lii*Lii) - val/Lii;
} else {
Sigma.insert(i,j) = -val/Lii;
Sigma.insert(j,i) = -val/Lii;
}
}
}
return Sigma;
}
void add_state_unit(const int node_dim, const int node_idx)
{
t_managing_ = clock();
n_nodes_++;
nodes_.push_back(node(node_idx, node_dim, x_incr_.size(), n_nodes_-1));
// Resize accumulated permutations
augment_permutation(acc_node_permutation_, n_nodes_);
// Resize state
x_incr_.conservativeResize(x_incr_.size() + node_dim);
// Resize problem
A_.conservativeResize(A_.rows(), A_.cols() + node_dim);
R_.conservativeResize(R_.cols() + node_dim, R_.cols() + node_dim);
//A_nodes_.conservativeResize(n_measurements, n_nodes); // not necessary
time_managing_ += ((double) clock() - t_managing_) / CLOCKS_PER_SEC;
}
// Solve the symmetric system: At·A·x = At·b
bool nv::LeastSquaresSolver(const SparseMatrix & A, const FullVector & b, FullVector & x, float epsilon/*1e-5f*/)
{
nvDebugCheck(A.width() == x.dimension());
nvDebugCheck(A.height() == b.dimension());
nvDebugCheck(A.height() >= A.width()); // @@ If height == width we could solve it directly...
const uint D = A.width();
SparseMatrix At(A.height(), A.width());
transpose(A, At);
FullVector Atb(D);
//mult(Transposed, A, b, Atb);
mult(At, b, Atb);
SparseMatrix AtA(D);
//mult(Transposed, A, NoTransposed, A, AtA);
mult(At, A, AtA);
return SymmetricSolver(AtA, Atb, x, epsilon);
}
void GetMappedDiagonal
( const SparseMatrix<T>& A,
Matrix<S>& d,
function<S(const T&)> func,
Int offset )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const T* valBuf = A.LockedValueBuffer();
const Int* colBuf = A.LockedTargetBuffer();
const Int iStart = Max(-offset,0);
const Int jStart = Max( offset,0);
const Int diagLength = El::DiagonalLength(m,n,offset);
d.Resize( diagLength, 1 );
Zero( d );
S* dBuf = d.Buffer();
for( Int k=0; k<diagLength; ++k )
{
const Int i = iStart + k;
const Int j = jStart + k;
const Int thisOff = A.RowOffset(i);
const Int nextOff = A.RowOffset(i+1);
auto it = std::lower_bound( colBuf+thisOff, colBuf+nextOff, j );
if( *it == j )
{
const Int e = it-colBuf;
dBuf[Min(i,j)] = func(valBuf[e]);
}
else
dBuf[Min(i,j)] = func(0);
}
}
/*! @param spm Matrix A in Sparse form*/
void SparseMatrix::extractdiagonal(SparseMatrix & spm){
for(int i = 0; i < spm.get_row_size(); i++){
float temp = 1.0/spm.getValue(i,i);
update_matrix(temp,i,i);
}
}
void Simulation::staticSolveNewtonsForces(MatrixXd& TV, MatrixXi& TT, MatrixXd& B, VectorXd& fixed_forces, int ignorePastIndex){
cout<<"----------------Static Solve Newtons, Fix Forces-------------"<<endl;
//Newtons method static solve for minimum Strain E
SparseMatrix<double> forceGradient;
forceGradient.resize(3*TV.rows(), 3*TV.rows());
SparseMatrix<double> forceGradientStaticBlock;
forceGradientStaticBlock.resize(3*ignorePastIndex, 3*ignorePastIndex);
VectorXd f, x;
f.resize(3*TV.rows());
f.setZero();
x.resize(3*TV.rows());
x.setZero();
setTVtoX(x, TV);
cout<<x<<endl;
int NEWTON_MAX = 100, k=0;
for(k=0; k<NEWTON_MAX; k++){
xToTV(x, TV);
calculateForceGradient(TV, forceGradient);
calculateElasticForces(f, TV);
for(unsigned int i=0; i<fixed_forces.rows(); i++){
if(abs(fixed_forces(i))>0.000001){
if(i>3*ignorePastIndex){
cout<<"Problem Check simulation.cpp file"<<endl;
cout<<ignorePastIndex<<endl;
cout<<i<<" - "<<fixed_forces(i)<<endl;
exit(0);
}
f(i) = fixed_forces(i);
}
}
//Block forceGrad and f to exclude the fixed verts
forceGradientStaticBlock = forceGradient.block(0,0, 3*(ignorePastIndex), 3*ignorePastIndex);
VectorXd fblock = f.head(ignorePastIndex*3);
//Sparse QR
// SparseQR<SparseMatrix<double>, COLAMDOrdering<int>> sqr;
// sqr.compute(forceGradientStaticBlock);
// VectorXd deltaX = -1*sqr.solve(fblock);
// Conj Grad
ConjugateGradient<SparseMatrix<double>> cg;
cg.compute(forceGradientStaticBlock);
if(cg.info() == Eigen::NumericalIssue){
cout<<"ConjugateGradient numerical issue"<<endl;
exit(0);
}
VectorXd deltaX = -1*cg.solve(fblock);
// // Sparse Cholesky LL^T
// SimplicialLLT<SparseMatrix<double>> llt;
// llt.compute(forceGradientStaticBlock);
// if(llt.info() == Eigen::NumericalIssue){
// cout<<"Possibly using a non- pos def matrix in the LLT method"<<endl;
// exit(0);
// }
// VectorXd deltaX = -1*llt.solve(fblock);
x.segment(0,3*(ignorePastIndex))+=deltaX;
cout<<" Newton Iter "<<k<<endl;
if(x != x){
cout<<"NAN"<<endl;
exit(0);
}
cout<<"fblock square norm"<<endl;
cout<<fblock.squaredNorm()/fblock.size()<<endl;
double strainE = 0;
for(int i=0; i< M.tets.size(); i++){
strainE += M.tets[i].undeformedVol*M.tets[i].energyDensity;
}
cout<<strainE<<endl;
if (fblock.squaredNorm()/fblock.size() < 0.00001){
break;
}
}
if(k== NEWTON_MAX){
cout<<"ERROR Static Solve: Newton max reached"<<endl;
cout<<k<<endl;
exit(0);
}
double strainE = 0;
for(int i=0; i< M.tets.size(); i++){
strainE += M.tets[i].undeformedVol*M.tets[i].energyDensity;
}
cout<<"strain E"<<strainE<<endl;
cout<<"x[0] "<<x(0)<<endl;
cout<<"x[1] "<<x(1)<<endl;
exit(0);
cout<<"-------------------"<<endl;
}
void SparseMatrix::copy(SparseMatrix & spm){
// cout << spm.get_row_size();
I.set_size(spm.get_row_size() + 1);
J.set_size(spm.get_non_zero_enteries());
Elements.set_size(spm.get_non_zero_enteries());
number_of_rows = spm.get_row_size();
// cout << number_of_rows;
number_of_non_zero = spm.get_non_zero_enteries();
size_of_array = spm.get_size();
for (int i = 0; i < spm.get_row_size() + 1;i++){
// cout << "row";
I[i] = spm.get_I(i);
}
for (int i = 0; i < spm.get_non_zero_enteries();i++){
// cout << "volumn";
J[i] = spm.get_J(i);
}
for (int i = 0; i < spm.get_non_zero_enteries(); i++){
// cout << spm.get_non_zero_Elements(i);
Elements[i] = spm.get_non_zero_Elements(i);
// cout << Elements[i];
}
}
SparseILUPreconditioner::SparseILUPreconditioner(const SparseMatrix& A,
Integer lfil)
: L_(A.size1(),A.size2()),
U_(A.size1(),A.size2()) {
QL_REQUIRE(A.size1() == A.size2(),
"sparse ILU preconditioner works only with square matrices");
for (SparseMatrix::size_type i=0; i < L_.size1(); ++i)
L_(i,i) = 1.0;
const Integer n = A.size1();
std::set<Integer> lBandSet, uBandSet;
compressed_matrix<Integer> levs(n,n);
Integer lfilp = lfil + 1;
for (Integer ii=0; ii<n; ++ii) {
Array w(n);
for(Integer k=0; k<n; ++k) {
w[k] = A(ii,k);
}
std::vector<Integer> levii(n, 0);
for (Integer i=0; i<n; ++i) {
if( w[i] > QL_EPSILON
|| w[i] < -1.0*QL_EPSILON) levii[i] = 1;
}
Integer jj = -1;
while (jj < ii) {
for (Integer k=jj+1; k<n; ++k) {
if(levii[k]) {
jj = k;
break;
}
}
if (jj >= ii) {
break;
}
Integer jlev = levii[jj];
if (jlev <= lfilp) {
std::vector<Integer> nonZeros;
std::vector<Real> nonZeroEntries;
nonZeros.reserve(uBandSet.size()+1);
nonZeroEntries.reserve(uBandSet.size()+1);
const Real entry = U_(jj,jj);
if(entry > QL_EPSILON || entry < -1.0*QL_EPSILON) {
nonZeros.push_back(jj);
nonZeroEntries.push_back(entry);
}
std::set<Integer>::const_iterator iter=uBandSet.begin();
std::set<Integer>::const_iterator end =uBandSet.end();
for (; iter != end; ++iter) {
const Real entry = U_(jj,jj+*iter);
if(entry > QL_EPSILON || entry < -1.0*QL_EPSILON) {
nonZeros.push_back(jj+*iter);
nonZeroEntries.push_back(entry);
}
}
Real fact = w[jj];
if(!nonZeroEntries.empty()) {
fact /= nonZeroEntries[0];
}
for (Size k=0; k<nonZeros.size(); ++k) {
const Integer j = nonZeros[k] ;
const Integer temp = levs(jj,j) + jlev ;
if (levii[j] == 0) {
if (temp <= lfilp) {
w[j] = - fact*nonZeroEntries[k];
levii[j] = temp;
}
}
else {
w[j] -= fact*nonZeroEntries[k];
levii[j] = std::min(levii[j],temp);
}
}
w[jj] = fact;
}
}
std::vector<Integer> wNonZeros;
std::vector<Real> wNonZeroEntries;
wNonZeros.reserve(w.size());
wNonZeroEntries.reserve(w.size());
for (Size i=0; i<w.size(); ++i) {
const Real entry = w[i];
if(entry > QL_EPSILON || entry < -1.0*QL_EPSILON) {
wNonZeros.push_back(i);
wNonZeroEntries.push_back(entry);
}
}
std::vector<Integer> leviiNonZeroEntries;
leviiNonZeroEntries.reserve(levii.size());
for (Size i=0; i<levii.size(); ++i) {
const Integer entry = levii[i];
if(entry > QL_EPSILON || entry < -1.0*QL_EPSILON) {
leviiNonZeroEntries.push_back(entry);
}
}
for (Size k=0; k<wNonZeros.size(); ++k) {
Integer j = wNonZeros[k];
if (j < ii) {
L_(ii,j) = wNonZeroEntries[k];
lBandSet.insert(ii-j);
}
else {
U_(ii,j) = wNonZeroEntries[k];
levs(ii,j) = leviiNonZeroEntries[k];
if(j-ii > 0) {
uBandSet.insert(j-ii);
}
}
}
}
lBands_.resize(lBandSet.size());
uBands_.resize(uBandSet.size());
std::copy(lBandSet.begin(), lBandSet.end(), lBands_.begin());
std::copy(uBandSet.begin(), uBandSet.end(), uBands_.begin());
}
void levelGen<T>::generateRP(const FixedSparseMatrix<T> &A,
FixedSparseMatrix<T> &R,
FixedSparseMatrix<T> &P,
int ni, int nj, int nk)
{
//matlab code(2D):
//m = ceil(M/2);
//n = ceil(N/2);
//R = sparse(zeros(m*n, M*N));
//coef = [1 3 3 1; 3 9 9 3; 3 9 9 3; 1 3 3 1]/16.0;
//for i=0:m-1
// for j=0:n-1
// index = i*n + j +1;
// for ii=0:1
// for jj=0:1
// iii = i*2+ii;
// jjj = j*2+jj;
// if iii<M && jjj<N && iii>=0 && jjj>=0
// index2 = iii*N + jjj +1;
// if A(index2,index2)~=0
// R(index, index2) = 0.25;
// %R(index, index2) = coef(ii+2,jj+2)/4;
// else
// R(index, index2) = 0.0;
// end
// end
// end
// end
// end
//end
//P = 4*R';
int nni = ceil((float)ni/2.0);
int nnj = ceil((float)nj/2.0);
int nnk = ceil((float)nk/2.0);
SparseMatrix<T> r;
SparseMatrix<T> p;
p.resize(ni*nj*nk);
p.zero();
r.resize(nni*nnj*nnk);
r.zero();
for(int k=0;k<nnk;k++)for(int j=0;j<nnj;j++)for (int i=0;i<nni;i++)
{
unsigned int index = (k*nnj +j)*nni + i;
for(int kk=0;kk<=1;kk++)for(int jj=0;jj<=1;jj++)for(int ii=0;ii<=1;ii++)
{
int iii = i*2 + ii;
int jjj = j*2 + jj;
int kkk = k*2 + kk;
if(iii<ni && jjj<nj && kkk<nk)
{
unsigned int index2 = (kkk*nj + jjj)*ni + iii;
r.set_element(index, index2, (T)0.125);
p.set_element(index2,index, 1.0);
}
}
}
R.construct_from_matrix(r);
P.construct_from_matrix(p);
r.clear();
p.clear();
//transposeMat(R,P,(T)8.0);
}
void AssembleMatrixResNS(MultiLevelProblem &ml_prob){
adept::Stack & adeptStack = FemusInit::_adeptStack;
clock_t AssemblyTime=0;
clock_t start_time, end_time;
//pointers and references
NonLinearImplicitSystem& my_nnlin_impl_sys = ml_prob.get_system<NonLinearImplicitSystem>("Navier-Stokes");
const unsigned level = my_nnlin_impl_sys.GetLevelToAssemble();
const unsigned gridn = my_nnlin_impl_sys.GetLevelMax();
bool assemble_matrix = my_nnlin_impl_sys.GetAssembleMatrix();
MultiLevelSolution* ml_sol = ml_prob._ml_sol;
Solution* mysolution = ml_sol->GetSolutionLevel(level);
LinearEquationSolver* myLinEqSolver = my_nnlin_impl_sys._LinSolver[level];
Mesh *mymsh = ml_prob._ml_msh->GetLevel(level);
elem *myel = mymsh->el;
SparseMatrix *myKK = myLinEqSolver->_KK;
NumericVector *myRES = myLinEqSolver->_RES;
const unsigned dim = mymsh->GetDimension();
const unsigned nabla_dim = 3*(dim-1);
const unsigned max_size = static_cast< unsigned > (ceil(pow(3,dim)));
// local objects
vector<adept::adouble> SolVAR(dim+1);
vector<vector<adept::adouble> > GradSolVAR(dim+1);
vector<vector<adept::adouble> > NablaSolVAR(dim+1);
for(int i=0;i<dim+1;i++){
GradSolVAR[i].resize(dim);
NablaSolVAR[i].resize(nabla_dim);
}
vector <double > phi;
vector <adept::adouble> gradphi;
vector <adept::adouble> nablaphi;
adept::adouble Weight;
phi.reserve(max_size);
gradphi.reserve(max_size*dim);
nablaphi.reserve(max_size*nabla_dim);
vector <double > phi1;
vector <adept::adouble> gradphi1;
vector <adept::adouble> nablaphi1;
adept::adouble Weight1;
phi1.reserve(max_size);
gradphi1.reserve(max_size*dim);
nablaphi1.reserve(max_size*nabla_dim);
vector <vector < adept::adouble> > vx(dim);
vector <vector < adept::adouble> > vx_face(dim);
for(int i=0;i<dim;i++){
vx[i].reserve(max_size);
vx_face[i].resize(9);
}
vector< vector< adept::adouble > > Soli(dim+1);
vector< vector< int > > dofsVAR(dim+1);
for(int i=0;i<dim+1;i++){
Soli[i].reserve(max_size);
dofsVAR[i].reserve(max_size);
}
vector< vector< double > > Rhs(dim+1);
vector< vector< adept::adouble > > aRhs(dim+1);
for(int i=0;i<dim+1;i++){
aRhs[i].reserve(max_size);
Rhs[i].reserve(max_size);
}
vector < int > dofsAll;
dofsAll.reserve(max_size*(dim+1));
vector < double > KKloc;
KKloc.reserve(dim*max_size*(dim+1)*dim*max_size*(dim+1));
vector < double > Jac;
Jac.reserve(dim*max_size*(dim+1)*dim*max_size*(dim+1));
// ------------------------------------------------------------------------
// Physical parameters
double rhof = ml_prob.parameters.get<Fluid>("Fluid").get_density();
double IRe = ml_prob.parameters.get<Fluid>("Fluid").get_IReynolds_number();
double betans = 1.;
// gravity
double _gravity[3]={0.,0.,0.};
double DRe = 1+(counter*counter)*5;
//double DRe=150;
IRe =( DRe*(counter+1) < 10000 )? 1./(DRe*(counter+1)):1./10000.;
cout<<"iteration="<<counter<<" Reynolds Number = "<<1./IRe<<endl;
counter++;
// -----------------------------------------------------------------
// space discretization parameters
unsigned SolType2 = ml_sol->GetSolutionType(ml_sol->GetIndex("U"));
unsigned SolType1 = ml_sol->GetSolutionType(ml_sol->GetIndex("P"));
unsigned SolTypeVx = 2;
// mesh and procs
unsigned nel = mymsh->GetNumberOfElements();
unsigned igrid = mymsh->GetLevel();
unsigned iproc = mymsh->processor_id();
//----------------------------------------------------------------------------------
//variable-name handling
const char varname[4][3] = {"U","V","W","P"};
vector <unsigned> indexVAR(dim+1);
vector <unsigned> indVAR(dim+1);
vector <unsigned> SolType(dim+1);
for(unsigned ivar=0; ivar<dim; ivar++) {
indVAR[ivar]=ml_sol->GetIndex(&varname[ivar][0]);
SolType[ivar]=ml_sol->GetSolutionType(&varname[ivar][0]);
indexVAR[ivar]=my_nnlin_impl_sys.GetSolPdeIndex(&varname[ivar][0]);
}
indVAR[dim]=ml_sol->GetIndex(&varname[3][0]);
SolType[dim]=ml_sol->GetSolutionType(&varname[3][0]);
indexVAR[dim]=my_nnlin_impl_sys.GetSolPdeIndex(&varname[3][0]);
unsigned indLmbd=ml_sol->GetIndex("lmbd");
//----------------------------------------------------------------------------------
start_time=clock();
myKK->zero();
// *** element loop ***
for(int iel=mymsh->IS_Mts2Gmt_elem_offset[iproc]; iel < mymsh->IS_Mts2Gmt_elem_offset[iproc+1]; iel++) {
unsigned kel = mymsh->IS_Mts2Gmt_elem[iel];
short unsigned kelt = myel->GetElementType(kel);
unsigned nve2 = myel->GetElementDofNumber(kel,SolType2);
unsigned nve1 = myel->GetElementDofNumber(kel,SolType1);
unsigned nveVx = myel->GetElementDofNumber(kel,SolTypeVx);
// *******************************************************************************************************
//cout<<SolType1<<" "<<SolType2<<" "<<SolTypeVx<<" "<<nve1<<" "<<nve2<<" "<<nveVx<<endl;
//Rhs
for(int i=0; i<dim; i++) {
dofsVAR[i].resize(nve2);
Soli[indexVAR[i]].resize(nve2);
aRhs[indexVAR[i]].resize(nve2);
Rhs[indexVAR[i]].resize(nve2);
}
dofsVAR[dim].resize(nve1);
Soli[indexVAR[dim]].resize(nve1);
aRhs[indexVAR[dim]].resize(nve1);
Rhs[indexVAR[dim]].resize(nve1);
dofsAll.resize(0);
KKloc.resize((dim*nve2+nve1)*(dim*nve2+nve1));
Jac.resize((dim*nve2+nve1)*(dim*nve2+nve1));
// ----------------------------------------------------------------------------------------
// coordinates
for(int i=0;i<dim;i++){
vx[i].resize(nveVx);
}
for (unsigned i=0;i<nveVx;i++) {
unsigned inode=myel->GetMeshDof(kel,i,SolTypeVx);
unsigned inode_Metis=mymsh->GetMetisDof(inode,SolTypeVx);
for(int j=0; j<dim; j++) {
//coordinates
vx[j][i]= (*mymsh->_coordinate->_Sol[j])(inode_Metis);
}
}
// Velocity
for (unsigned i=0;i<nve2;i++) {
unsigned inode=myel->GetMeshDof(kel,i,SolType2);
unsigned inode_Metis=mymsh->GetMetisDof(inode,SolType2);
for(int j=0; j<dim; j++) {
// velocity dofs
Soli[indexVAR[j]][i] = (*mysolution->_Sol[indVAR[j]])(inode_Metis);
dofsVAR[j][i] = myLinEqSolver->GetKKDof(indVAR[j],indexVAR[j],inode);
aRhs[indexVAR[j]][i] = 0.;
}
}
// Pressure dofs
for (unsigned i=0;i<nve1;i++) {
unsigned inode=myel->GetMeshDof(kel,i,SolType1);
unsigned inode_Metis =mymsh->GetMetisDof(inode,SolType1);
Soli[indexVAR[dim]][i] = (*mysolution->_Sol[indVAR[dim]])(inode_Metis);
dofsVAR[dim][i]=myLinEqSolver->GetKKDof(indVAR[dim],indexVAR[dim],inode);
aRhs[indexVAR[dim]][i] = 0.;
}
// build dof composition
for(int idim=0;idim<dim;idim++){
dofsAll.insert( dofsAll.end(), dofsVAR[idim].begin(), dofsVAR[idim].end() );
}
dofsAll.insert( dofsAll.end(), dofsVAR[dim].begin(), dofsVAR[dim].end() );
if (igrid==gridn || !myel->GetRefinedElementIndex(kel) ) {
adeptStack.new_recording();
// *** Gauss point loop ***
adept::adouble hk;
for (unsigned ig=0;ig < mymsh->_finiteElement[kelt][SolType2]->GetGaussPointNumber(); ig++) {
// *** get Jacobian and test function and test function derivatives in the moving frame***
mymsh->_finiteElement[kelt][SolType2]->Jacobian(vx,ig,Weight,phi,gradphi,nablaphi);
mymsh->_finiteElement[kelt][SolType1]->Jacobian(vx,ig,Weight1,phi1,gradphi1,nablaphi1);
for(int i=0;i<nve1;i++){
for(int j=0;j<nabla_dim;j++){
//cout<<nablaphi[i*nabla_dim+j]<<" ";
}
//cout<<endl;
}
//cout<<endl;
if(ig==0){
double referenceElementArea[6]={8, 1./6., 1., 4., 1., 2.};
double GaussWeight = mymsh->_finiteElement[kelt][SolType2]->GetGaussWeight(ig);
double area=referenceElementArea[kelt]*Weight.value()/GaussWeight;
hk = pow(area,1./dim);
//cout<<hk<<" ";
}
// velocity: solution, gradient and laplace
for(int i=0; i<dim; i++){
SolVAR[i]=0.;
for(int j=0; j<dim; j++) {
GradSolVAR[i][j]=0.;
}
for(int j=0; j<nabla_dim; j++) {
NablaSolVAR[i][j]=0.;
}
for (unsigned inode=0; inode<nve2; inode++) {
adept::adouble soli = Soli[indexVAR[i]][inode];
SolVAR[i]+=phi[inode]*soli;
for(int j=0; j<dim; j++) {
GradSolVAR[i][j]+=gradphi[inode*dim+j]*soli;
}
for(int j=0; j<nabla_dim; j++) {
NablaSolVAR[i][j]+=nablaphi[inode*nabla_dim+j]*soli;
}
}
}
// pressure, solution and gradient
SolVAR[dim]=0.;
for(int j=0; j<dim; j++) {
GradSolVAR[dim][j]=0.;
}
for (unsigned inode=0; inode<nve1; inode++) {
adept::adouble soli = Soli[indexVAR[dim]][inode];
SolVAR[dim]+=phi1[inode]*soli;
for(int j=0; j<dim; j++) {
GradSolVAR[dim][j]+=gradphi1[inode*dim+j]*soli;
}
}
bool Tezduyare=0;
bool FrancaAndFrey=!Tezduyare;
if( Tezduyare ){
//BEGIN TAU_SUPG, TAU_PSPG EVALUATION
// ******** T.E. Tezduyar, S. Mittal, S.E. Ray and R. Shih *****************************
// Computer Methods in Applied Mechanics and Engineering 95 (1992) 221-242 North-Holland
// *************************************************************************************
// velocity
vector < adept::adouble > u(dim);
for(int ivar=0; ivar<dim; ivar++){
u[ivar]=SolVAR[ivar];
}
// speed
adept::adouble uL2Norm=0.;
for(int ivar=0;ivar<dim;ivar++){
uL2Norm += u[ivar]*u[ivar];
}
uL2Norm=sqrt(uL2Norm);
adept::adouble tauSupg=0.;
adept::adouble tauPspg=0.;
if( uL2Norm/(2.*IRe) > 1.0e-10){
// velocity direction s = u/|u|
vector < adept::adouble > s(dim);
for(int ivar=0;ivar<dim;ivar++)
s[ivar]=u[ivar]/uL2Norm;
// element lenght h(s) = 2. ( \sum_i |s . gradphi_i | )^(-1)
adept::adouble h=0.;
for (unsigned i=0; i<nve2; i++) {
adept::adouble sDotGradphi=0.;
for(int ivar=0; ivar<dim; ivar++)
sDotGradphi += s[ivar]*gradphi[i*dim+ivar];
//Start WARNING!!! do not change the following if into h += fabs(sDotGradphi).
//Adept does not like it, and convergence is bad
if( sDotGradphi.value() < 0.)
h -= sDotGradphi;
else
h += sDotGradphi;
//End WARNING
}
h = 2./h;
//tauSupg
adept::adouble Reu = 1./3.*(uL2Norm*h)/(2.*IRe);
adept::adouble zReu = (Reu.value() < 1.)? Reu : 1.;
tauSupg = h / (2.*uL2Norm)*zReu;
uL2Norm=0.01;
h = 2.*hk/sqrt(acos(-1.));
Reu = 1./3.*(uL2Norm*h)/(2.*IRe);
zReu = (Reu.value() < 1.)? Reu : 1.;
tauPspg = h / (2.*uL2Norm)*zReu;
}
//END TAU_SUPG, TAU_PSPG EVALUATION
//BEGIN FLUID ASSEMBLY
{
vector < adept::adouble > Res(dim,0.);
for(unsigned ivar=0; ivar<dim; ivar++) {
Res[ivar] += 0. - GradSolVAR[dim][ivar];
for(unsigned jvar=0; jvar<dim; jvar++) {
unsigned kvar;
if(ivar == jvar) kvar = jvar;
else if (1 == ivar + jvar ) kvar = dim; // xy
else if (2 == ivar + jvar ) kvar = dim+2; // xz
else if (3 == ivar + jvar ) kvar = dim+1; // yz
Res[ivar] += - SolVAR[jvar]*GradSolVAR[ivar][jvar]
+ IRe * ( NablaSolVAR[ivar][jvar] + NablaSolVAR[jvar][kvar] );
}
}
adept::adouble div_vel=0.;
for(int ivar=0; ivar<dim; ivar++) {
div_vel +=GradSolVAR[ivar][ivar];
}
//BEGIN redidual momentum block
for (unsigned i=0; i<nve2; i++){
for(unsigned ivar=0; ivar<dim; ivar++) {
adept::adouble Advection = 0.;
adept::adouble Laplacian = 0.;
adept::adouble phiSupg=0.;
for(unsigned jvar=0; jvar<dim; jvar++) {
unsigned kvar;
if(ivar == jvar) kvar = jvar;
else if (1 == ivar + jvar ) kvar = dim; // xy
else if (2 == ivar + jvar ) kvar = dim+2; // xz
else if (3 == ivar + jvar ) kvar = dim+1; // yz
Advection += SolVAR[jvar]*GradSolVAR[ivar][jvar]*phi[i];
Laplacian += IRe*gradphi[i*dim+jvar]*(GradSolVAR[ivar][jvar]+GradSolVAR[jvar][ivar]);
phiSupg += ( SolVAR[jvar]*gradphi[i*dim+jvar] ) * tauSupg;
}
aRhs[indexVAR[ivar]][i]+= ( - Advection - Laplacian
+ SolVAR[dim] * gradphi[i*dim+ivar]
+ Res[ivar] * phiSupg ) * Weight;
}
}
//END redidual momentum block
//BEGIN continuity block
for (unsigned i=0; i<nve1; i++) {
adept::adouble MinusGradPhi1DotRes = 0.;
for(int ivar=0;ivar<dim;ivar++){
MinusGradPhi1DotRes += -gradphi1[i*dim+ivar] * Res[ivar] * tauPspg;
}
aRhs[indexVAR[dim]][i] += ( - (-div_vel) * phi1[i] + MinusGradPhi1DotRes ) * Weight;
}
//END continuity block
}
//END FLUID ASSEMBLY
}
else if(FrancaAndFrey){
//BEGIN TAU_SUPG EVALUATION
// ********************************* Tau_Supg FRANCA and FREY **************************
// Computer Methods in Applied Mechanics and Engineering 99 (1992) 209-233 North-Holland
// *************************************************************************************
// velocity
// double Ck[6][3]={{1.,1.,1.},{1.,1.,1.},{1.,1.,1.},{0.5, 11./270., 11./270.},{0.,1./42.,1./42.},{1.,1.,1.}};
vector < adept::adouble > a(dim);
for(int ivar=0; ivar<dim; ivar++){
a[ivar]=SolVAR[ivar];
}
// speed
adept::adouble aL2Norm=0.;
for(int ivar=0;ivar<dim;ivar++){
aL2Norm += a[ivar]*a[ivar];
}
aL2Norm=sqrt(aL2Norm);
adept::adouble deltaSupg=0.;
double sqrtlambdak = (*mysolution->_Sol[indLmbd])(iel);
adept::adouble tauSupg=1. / ( sqrtlambdak*sqrtlambdak *4.*IRe);
adept::adouble Rek = aL2Norm / ( 4.*sqrtlambdak*IRe);
/*adept::adouble mk=std::min(1./3., 2.*Ck[kelt][SolType2]);
adept::adouble Rek = mk * aL2Norm * hk / ( 4.*IRe);
adept::adouble tauSupg = (mk*hk*hk/2.) / ( 4.*IRe);
*/
if( Rek > 1.0e-15){
adept::adouble xiRek = ( Rek >= 1. ) ? 1.:Rek;
tauSupg = xiRek/(aL2Norm*sqrtlambdak);
deltaSupg = (xiRek*aL2Norm)/sqrtlambdak;
// tauSupg = hk / (2.*aL2Norm)*xiRek;
// double lambda=1.;
// deltaSupg = lambda*aL2Norm*hk*xiRek;
}
//END TAU_SUPG EVALUATION ============
//BEGIN FLUID ASSEMBLY ============
{
vector < adept::adouble > Res(dim,0.);
for(unsigned ivar=0; ivar<dim; ivar++) {
Res[ivar] += 0. - GradSolVAR[dim][ivar];
for(unsigned jvar=0; jvar<dim; jvar++) {
unsigned kvar;
if(ivar == jvar) kvar = jvar;
else if (1 == ivar + jvar ) kvar = dim; // xy
else if (2 == ivar + jvar ) kvar = dim+2; // xz
else if (3 == ivar + jvar ) kvar = dim+1; // yz
Res[ivar] += - SolVAR[jvar]*GradSolVAR[ivar][jvar]
+ IRe * ( NablaSolVAR[ivar][jvar] + NablaSolVAR[jvar][kvar] );
}
}
adept::adouble div_vel=0.;
for(int ivar=0; ivar<dim; ivar++) {
div_vel +=GradSolVAR[ivar][ivar];
}
//BEGIN redidual momentum block
for (unsigned i=0; i<nve2; i++){
for(unsigned ivar=0; ivar<dim; ivar++) {
adept::adouble Advection = 0.;
adept::adouble Laplacian = 0.;
adept::adouble phiSupg=0.;
for(unsigned jvar=0; jvar<dim; jvar++) {
unsigned kvar;
if(ivar == jvar) kvar = jvar;
else if (1 == ivar + jvar ) kvar = dim; // xy
else if (2 == ivar + jvar ) kvar = dim+2; // xz
else if (3 == ivar + jvar ) kvar = dim+1; // yz
Advection += SolVAR[jvar]*GradSolVAR[ivar][jvar]*phi[i];
Laplacian += IRe*gradphi[i*dim+jvar]*(GradSolVAR[ivar][jvar]+GradSolVAR[jvar][ivar]);
phiSupg += ( SolVAR[jvar]*gradphi[i*dim+jvar] ) * tauSupg;
aRhs[indexVAR[ivar]][i] += Res[ivar] * (-IRe * nablaphi[i*nabla_dim+jvar])* tauSupg * Weight;
aRhs[indexVAR[jvar]][i] += Res[ivar] * (-IRe * nablaphi[i*nabla_dim+kvar])* tauSupg * Weight;
}
aRhs[indexVAR[ivar]][i]+= ( - Advection - Laplacian
+ ( SolVAR[dim] - deltaSupg * div_vel) * gradphi[i*dim+ivar]
+ Res[ivar] * phiSupg ) * Weight;
}
}
//END redidual momentum block
//BEGIN continuity block
for (unsigned i=0; i<nve1; i++) {
adept::adouble MinusGradPhi1DotRes = 0.;
for(int ivar=0;ivar<dim;ivar++){
MinusGradPhi1DotRes += -gradphi1[i*dim+ivar] * Res[ivar] * tauSupg;
}
aRhs[indexVAR[dim]][i] += ( - (-div_vel) * phi1[i] + MinusGradPhi1DotRes ) * Weight;
}
//END continuity block ===========================
}
//END FLUID ASSEMBLY ============
}
}
}
//BEGIN local to global assembly
//copy adouble aRhs into double Rhs
for (unsigned i=0;i<dim;i++) {
for(int j=0; j<nve2; j++) {
Rhs[indexVAR[i]][j] = aRhs[indexVAR[i]][j].value();
}
}
for (unsigned j=0;j<nve1;j++) {
Rhs[indexVAR[dim]][j] = aRhs[indexVAR[dim]][j].value();
}
for(int i=0; i<dim+1; i++) {
myRES->add_vector_blocked(Rhs[indexVAR[i]],dofsVAR[i]);
}
//Store equations
for(int i=0; i<dim; i++) {
adeptStack.dependent(&aRhs[indexVAR[i]][0], nve2);
adeptStack.independent(&Soli[indexVAR[i]][0], nve2);
}
adeptStack.dependent(&aRhs[indexVAR[dim]][0], nve1);
adeptStack.independent(&Soli[indexVAR[dim]][0], nve1);
adeptStack.jacobian(&Jac[0]);
unsigned nveAll=(dim*nve2+nve1);
for (int inode=0;inode<nveAll;inode++){
for (int jnode=0;jnode<nveAll;jnode++){
KKloc[inode*nveAll+jnode]=-Jac[jnode*nveAll+inode];
}
}
myKK->add_matrix_blocked(KKloc,dofsAll,dofsAll);
adeptStack.clear_independents();
adeptStack.clear_dependents();
//END local to global assembly
} //end list of elements loop
myKK->close();
myRES->close();
// *************************************
end_time=clock();
AssemblyTime+=(end_time-start_time);
// ***************** END ASSEMBLY RESIDUAL + MATRIX *******************
}
void AssembleBoussinesqAppoximation_AD(MultiLevelProblem& ml_prob) {
// ml_prob is the global object from/to where get/set all the data
// level is the level of the PDE system to be assembled
// levelMax is the Maximum level of the MultiLevelProblem
// assembleMatrix is a flag that tells if only the residual or also the matrix should be assembled
// call the adept stack object
adept::Stack& s = FemusInit::_adeptStack;
// extract pointers to the several objects that we are going to use
NonLinearImplicitSystem* mlPdeSys = &ml_prob.get_system<NonLinearImplicitSystem> ("NS"); // pointer to the linear implicit system named "Poisson"
const unsigned level = mlPdeSys->GetLevelToAssemble();
const unsigned levelMax = mlPdeSys->GetLevelMax();
const bool assembleMatrix = mlPdeSys->GetAssembleMatrix();
Mesh* msh = ml_prob._ml_msh->GetLevel(level); // pointer to the mesh (level) object
elem* el = msh->el; // pointer to the elem object in msh (level)
MultiLevelSolution* mlSol = ml_prob._ml_sol; // pointer to the multilevel solution object
Solution* sol = ml_prob._ml_sol->GetSolutionLevel(level); // pointer to the solution (level) object
LinearEquationSolver* pdeSys = mlPdeSys->_LinSolver[level]; // pointer to the equation (level) object
SparseMatrix* KK = pdeSys->_KK; // pointer to the global stifness matrix object in pdeSys (level)
NumericVector* RES = pdeSys->_RES; // pointer to the global residual vector object in pdeSys (level)
const unsigned dim = msh->GetDimension(); // get the domain dimension of the problem
unsigned dim2 = (3 * (dim - 1) + !(dim - 1)); // dim2 is the number of second order partial derivatives (1,3,6 depending on the dimension)
unsigned iproc = msh->processor_id(); // get the process_id (for parallel computation)
// reserve memory for the local standar vectors
const unsigned maxSize = static_cast< unsigned >(ceil(pow(3, dim))); // conservative: based on line3, quad9, hex27
//solution variable
vector < unsigned > solVIndex(dim);
solVIndex[0] = mlSol->GetIndex("U"); // get the position of "U" in the ml_sol object
solVIndex[1] = mlSol->GetIndex("V"); // get the position of "V" in the ml_sol object
if (dim == 3) solVIndex[2] = mlSol->GetIndex("W"); // get the position of "V" in the ml_sol object
unsigned solVType = mlSol->GetSolutionType(solVIndex[0]); // get the finite element type for "u"
unsigned solPIndex;
solPIndex = mlSol->GetIndex("P"); // get the position of "P" in the ml_sol object
unsigned solPType = mlSol->GetSolutionType(solPIndex); // get the finite element type for "u"
vector < unsigned > solVPdeIndex(dim);
solVPdeIndex[0] = mlPdeSys->GetSolPdeIndex("U"); // get the position of "U" in the pdeSys object
solVPdeIndex[1] = mlPdeSys->GetSolPdeIndex("V"); // get the position of "V" in the pdeSys object
if (dim == 3) solVPdeIndex[2] = mlPdeSys->GetSolPdeIndex("W");
unsigned solPPdeIndex;
solPPdeIndex = mlPdeSys->GetSolPdeIndex("P"); // get the position of "P" in the pdeSys object
vector < vector < adept::adouble > > solV(dim); // local solution
vector < adept::adouble > solP; // local solution
vector< vector < adept::adouble > > aResV(dim); // local redidual vector
vector< adept::adouble > aResP; // local redidual vector
vector < vector < double > > coordX(dim); // local coordinates
unsigned coordXType = 2; // get the finite element type for "x", it is always 2 (LAGRANGE QUADRATIC)
for (unsigned k = 0; k < dim; k++) {
solV[k].reserve(maxSize);
aResV[k].reserve(maxSize);
coordX[k].reserve(maxSize);
}
solP.reserve(maxSize);
aResP.reserve(maxSize);
vector <double> phiV; // local test function
vector <double> phiV_x; // local test function first order partial derivatives
vector <double> phiV_xx; // local test function second order partial derivatives
phiV.reserve(maxSize);
phiV_x.reserve(maxSize * dim);
phiV_xx.reserve(maxSize * dim2);
double* phiP;
double weight; // gauss point weight
vector< int > KKDof; // local to global pdeSys dofs
KKDof.reserve((dim + 1) *maxSize);
vector< double > Res; // local redidual vector
Res.reserve((dim + 1) *maxSize);
vector < double > Jac;
Jac.reserve((dim + 1) *maxSize * (dim + 1) *maxSize);
if (assembleMatrix)
KK->zero(); // Set to zero all the entries of the Global Matrix
// element loop: each process loops only on the elements that owns
for (int iel = msh->IS_Mts2Gmt_elem_offset[iproc]; iel < msh->IS_Mts2Gmt_elem_offset[iproc + 1]; iel++) {
unsigned kel = msh->IS_Mts2Gmt_elem[iel]; // mapping between paralell dof and mesh dof
short unsigned kelGeom = el->GetElementType(kel); // element geometry type
unsigned nDofsV = el->GetElementDofNumber(kel, solVType); // number of solution element dofs
unsigned nDofsP = el->GetElementDofNumber(kel, solPType); // number of solution element dofs
unsigned nDofsX = el->GetElementDofNumber(kel, coordXType); // number of coordinate element dofs
unsigned nDofsVP = dim * nDofsV + nDofsP;
// resize local arrays
KKDof.resize(nDofsVP);
for (unsigned k = 0; k < dim; k++) {
solV[k].resize(nDofsV);
coordX[k].resize(nDofsX);
}
solP.resize(nDofsP);
for (unsigned k = 0; k < dim; k++) {
aResV[k].resize(nDofsV); //resize
std::fill(aResV[k].begin(), aResV[k].end(), 0); //set aRes to zero
}
aResP.resize(nDofsP); //resize
std::fill(aResP.begin(), aResP.end(), 0); //set aRes to zero
// local storage of global mapping and solution
for (unsigned i = 0; i < nDofsV; i++) {
unsigned iNode = el->GetMeshDof(kel, i, solVType); // local to global solution node
unsigned solVDof = msh->GetMetisDof(iNode, solVType); // global to global mapping between solution node and solution dof
for (unsigned k = 0; k < dim; k++) {
solV[k][i] = (*sol->_Sol[solVIndex[k]])(solVDof); // global extraction and local storage for the solution
KKDof[i + k * nDofsV] = pdeSys->GetKKDof(solVIndex[k], solVPdeIndex[k], iNode); // global to global mapping between solution node and pdeSys dof
}
}
for (unsigned i = 0; i < nDofsP; i++) {
unsigned iNode = el->GetMeshDof(kel, i, solPType); // local to global solution node
unsigned solPDof = msh->GetMetisDof(iNode, solPType); // global to global mapping between solution node and solution dof
solP[i] = (*sol->_Sol[solPIndex])(solPDof); // global extraction and local storage for the solution
KKDof[i + dim * nDofsV] = pdeSys->GetKKDof(solPIndex, solPPdeIndex, iNode); // global to global mapping between solution node and pdeSys dof
}
// local storage of coordinates
for (unsigned i = 0; i < nDofsX; i++) {
unsigned iNode = el->GetMeshDof(kel, i, coordXType); // local to global coordinates node
unsigned coordXDof = msh->GetMetisDof(iNode, coordXType); // global to global mapping between coordinates node and coordinate dof
for (unsigned k = 0; k < dim; k++) {
coordX[k][i] = (*msh->_coordinate->_Sol[k])(coordXDof); // global extraction and local storage for the element coordinates
}
}
if (level == levelMax || !el->GetRefinedElementIndex(kel)) { // do not care about this if now (it is used for the AMR)
// start a new recording of all the operations involving adept::adouble variables
s.new_recording();
// *** Gauss point loop ***
for (unsigned ig = 0; ig < msh->_finiteElement[kelGeom][solVType]->GetGaussPointNumber(); ig++) {
// *** get gauss point weight, test function and test function partial derivatives ***
msh->_finiteElement[kelGeom][solVType]->Jacobian(coordX, ig, weight, phiV, phiV_x, phiV_xx);
phiP = msh->_finiteElement[kelGeom][solPType]->GetPhi(ig);
vector < adept::adouble > solV_gss(dim, 0);
vector < vector < adept::adouble > > gradSolV_gss(dim);
for (unsigned k = 0; k < dim; k++) {
gradSolV_gss[k].resize(dim);
std::fill(gradSolV_gss[k].begin(), gradSolV_gss[k].end(), 0);
}
for (unsigned i = 0; i < nDofsV; i++) {
for (unsigned k = 0; k < dim; k++) {
solV_gss[k] += phiV[i] * solV[k][i];
}
for (unsigned j = 0; j < dim; j++) {
for (unsigned k = 0; k < dim; k++) {
gradSolV_gss[k][j] += phiV_x[i * dim + j] * solV[k][i];
}
}
}
adept::adouble solP_gss = 0;
for (unsigned i = 0; i < nDofsP; i++) {
solP_gss += phiP[i] * solP[i];
}
double nu = 1.;
// *** phiV_i loop ***
for (unsigned i = 0; i < nDofsV; i++) {
vector < adept::adouble > NSV(dim, 0.);
for (unsigned j = 0; j < dim; j++) {
for (unsigned k = 0; k < dim; k++) {
NSV[k] += nu * phiV_x[i * dim + j] * (gradSolV_gss[k][j] + gradSolV_gss[j][k]);
NSV[k] += phiV[i] * (solV_gss[j] * gradSolV_gss[k][j]);
}
}
for (unsigned k = 0; k < dim; k++) {
NSV[k] += -solP_gss * phiV_x[i * dim + k];
}
for (unsigned k = 0; k < dim; k++) {
aResV[k][i] += - NSV[k] * weight;
}
} // end phiV_i loop
// *** phiP_i loop ***
for (unsigned i = 0; i < nDofsP; i++) {
for (int k = 0; k < dim; k++) {
aResP[i] += - (gradSolV_gss[k][k]) * phiP[i] * weight;
}
} // end phiP_i loop
} // end gauss point loop
} // endif single element not refined or fine grid loop
//--------------------------------------------------------------------------------------------------------
// Add the local Matrix/Vector into the global Matrix/Vector
//copy the value of the adept::adoube aRes in double Res and store them in RES
Res.resize(nDofsVP); //resize
for (int i = 0; i < nDofsV; i++) {
for (unsigned k = 0; k < dim; k++) {
Res[ i + k * nDofsV ] = -aResV[k][i].value();
}
}
for (int i = 0; i < nDofsP; i++) {
Res[ i + dim * nDofsV ] = -aResP[i].value();
}
RES->add_vector_blocked(Res, KKDof);
//Extarct and store the Jacobian
if (assembleMatrix) {
Jac.resize(nDofsVP * nDofsVP);
// define the dependent variables
for (unsigned k = 0; k < dim; k++) {
s.dependent(&aResV[k][0], nDofsV);
}
s.dependent(&aResP[0], nDofsP);
// define the independent variables
for (unsigned k = 0; k < dim; k++) {
s.independent(&solV[k][0], nDofsV);
}
s.independent(&solP[0], nDofsP);
// get the and store jacobian matrix (row-major)
s.jacobian(&Jac[0] , true);
KK->add_matrix_blocked(Jac, KKDof, KKDof);
s.clear_independents();
s.clear_dependents();
}
} //end element loop for each process
RES->close();
if (assembleMatrix) KK->close();
// ***************** END ASSEMBLY *******************
}
void AssemblePoisson_AD (MultiLevelProblem& ml_prob) {
// ml_prob is the global object from/to where get/set all the data
// level is the level of the PDE system to be assembled
// levelMax is the Maximum level of the MultiLevelProblem
// assembleMatrix is a flag that tells if only the residual or also the matrix should be assembled
// call the adept stack object
adept::Stack& s = FemusInit::_adeptStack;
// extract pointers to the several objects that we are going to use
NonLinearImplicitSystem* mlPdeSys = &ml_prob.get_system<NonLinearImplicitSystem> ("Poisson"); // pointer to the linear implicit system named "Poisson"
const unsigned level = mlPdeSys->GetLevelToAssemble();
Mesh* msh = ml_prob._ml_msh->GetLevel (level); // pointer to the mesh (level) object
elem* el = msh->el; // pointer to the elem object in msh (level)
MultiLevelSolution* mlSol = ml_prob._ml_sol; // pointer to the multilevel solution object
Solution* sol = ml_prob._ml_sol->GetSolutionLevel (level); // pointer to the solution (level) object
LinearEquationSolver* pdeSys = mlPdeSys->_LinSolver[level]; // pointer to the equation (level) object
SparseMatrix* KK = pdeSys->_KK; // pointer to the global stifness matrix object in pdeSys (level)
NumericVector* RES = pdeSys->_RES; // pointer to the global residual vector object in pdeSys (level)
const unsigned dim = msh->GetDimension(); // get the domain dimension of the problem
unsigned dim2 = (3 * (dim - 1) + ! (dim - 1)); // dim2 is the number of second order partial derivatives (1,3,6 depending on the dimension)
unsigned iproc = msh->processor_id(); // get the process_id (for parallel computation)
// reserve memory for the local standar vectors
const unsigned maxSize = static_cast< unsigned > (ceil (pow (3, dim))); // conservative: based on line3, quad9, hex27
//solution variable
unsigned solUIndex;
solUIndex = mlSol->GetIndex ("U"); // get the position of "U" in the ml_sol object = 0
unsigned solUType = mlSol->GetSolutionType (solUIndex); // get the finite element type for "T"
unsigned solUPdeIndex;
solUPdeIndex = mlPdeSys->GetSolPdeIndex ("U"); // get the position of "U" in the pdeSys object = 0
vector < adept::adouble > solU; // local solution
vector< adept::adouble > aResU; // local redidual vector
unsigned solVIndex;
solVIndex = mlSol->GetIndex ("V");
unsigned solVType = mlSol->GetSolutionType (solVIndex);
unsigned solVPdeIndex;
solVPdeIndex = mlPdeSys->GetSolPdeIndex ("V");
vector < adept::adouble > solV; // local solution
vector< adept::adouble > aResV; // local redidual vector
vector < vector < double > > crdX (dim); // local coordinates
unsigned crdXType = 2; // get the finite element type for "x", it is always 2 (LAGRANGE QUADRATIC)
solU.reserve (maxSize);
aResU.reserve (maxSize);
solV.reserve (maxSize);
aResV.reserve (maxSize);
for (unsigned k = 0; k < dim; k++) {
crdX[k].reserve (maxSize);
}
vector <double> phi; // local test function
vector <double> phi_x; // local test function first order partial derivatives
vector <double> phi_xx; // local test function second order partial derivatives
phi.reserve (maxSize);
phi_x.reserve (maxSize * dim);
phi_xx.reserve (maxSize * dim2);
vector <double> phiV; // local test function
vector <double> phiV_x; // local test function first order partial derivatives
vector <double> phiV_xx; // local test function second order partial derivatives
phiV.reserve (maxSize);
phiV_x.reserve (maxSize * dim);
phiV_xx.reserve (maxSize * dim2);
double weight; // gauss point weight
vector< int > sysDof; // local to global pdeSys dofs
sysDof.reserve (2 * maxSize);
vector< double > Res; // local residual vector
Res.reserve (2 * maxSize);
vector < double > Jac;
Jac.reserve (4 * maxSize * maxSize);
KK->zero(); // Set to zero all the entries of the Global Matrix
// element loop: each process loops only on the elements that owns
for (int iel = msh->_elementOffset[iproc]; iel < msh->_elementOffset[iproc + 1]; iel++) {
short unsigned ielGeom = msh->GetElementType (iel); // element geometry type
unsigned nDofsU = msh->GetElementDofNumber (iel, solUType); // number of solution element dofs
unsigned nDofsV = msh->GetElementDofNumber (iel, solVType);
unsigned nDofsX = msh->GetElementDofNumber (iel, crdXType); // number of solution element dofs
// resize local arrays
sysDof.resize (nDofsU + nDofsV);
solU.resize (nDofsU);
solV.resize (nDofsV);
for (unsigned k = 0; k < dim; k++) {
crdX[k].resize (nDofsX);
}
aResU.assign (nDofsU, 0);
aResV.assign (nDofsV, 0);
// local storage of global mapping and solution
for (unsigned i = 0; i < nDofsU; i++) {
unsigned solUDof = msh->GetSolutionDof (i, iel, solUType); // local to global mapping of the solution U
solU[i] = (*sol->_Sol[solUIndex]) (solUDof); // value of the solution U in the dofs
sysDof[i] = pdeSys->GetSystemDof (solUIndex, solUPdeIndex, i, iel); // local to global mapping between solution U and system
}
for (unsigned i = 0; i < nDofsV; i++) {
unsigned solVDof = msh->GetSolutionDof (i, iel, solVType);
solV[i] = (*sol->_Sol[solVIndex]) (solVDof);
sysDof[i + nDofsU] = pdeSys->GetSystemDof (solVIndex, solVPdeIndex, i, iel);
}
// local storage of coordinates
for (unsigned i = 0; i < nDofsX; i++) {
unsigned coordXDof = msh->GetSolutionDof (i, iel, crdXType); // local to global mapping of the coordinate X[dim]
for (unsigned k = 0; k < dim; k++) {
crdX[k][i] = (*msh->_topology->_Sol[k]) (coordXDof); // value of the solution X[dim]
}
}
s.new_recording();
// *** Gauss point loop *** //
for (unsigned ig = 0; ig < msh->_finiteElement[ielGeom][solUType]->GetGaussPointNumber(); ig++) {
// *** get gauss point weight, test function and test function partial derivatives ***
msh->_finiteElement[ielGeom][solUType]->Jacobian (crdX, ig, weight, phi, phi_x, phi_xx);
msh->_finiteElement[ielGeom][solVType]->Jacobian (crdX, ig, weight, phiV, phiV_x, phiV_xx);
adept::adouble solUig = 0; // solution U in the gauss point
vector < adept::adouble > gradSolUig (dim, 0.); // gradient of solution U in the gauss point
for (unsigned i = 0; i < nDofsU; i++) {
solUig += phi[i] * solU[i];
for (unsigned j = 0; j < dim; j++) {
gradSolUig[j] += phi_x[i * dim + j] * solU[i];
}
}
adept::adouble solVig = 0; // solution V in the gauss point
vector < adept::adouble > gradSolVig (dim, 0.); // gradient of solution U in the gauss point
for (unsigned i = 0; i < nDofsV; i++) {
solVig += phiV[i] * solV[i];
for (unsigned j = 0; j < dim; j++) {
gradSolVig[j] += phiV_x[i * dim + j] * solV[i];
}
}
double nu = 1.;
// *** phiU_i loop ***
for (unsigned i = 0; i < nDofsU; i++) {
adept::adouble LaplaceU = 0.;
for (unsigned j = 0; j < dim; j++) {
LaplaceU -= nu * phi_x[i * dim + j] * gradSolUig[j];
}
aResU[i] += (phi[i] - LaplaceU) * weight;
} // end phiU_i loop
for (unsigned i = 0; i < nDofsV; i++) {
adept::adouble LaplaceV = 0.;
for (unsigned j = 0; j < dim; j++) {
LaplaceV -= nu * phiV_x[i * dim + j] * gradSolVig[j];
}
aResV[i] += (phiV[i] * solUig - LaplaceV) * weight;
} // end phiV_i loop
} // end gauss point loop
// } // endif single element not refined or fine grid loop
//--------------------------------------------------------------------------------------------------------
// Add the local Matrix/Vector into the global Matrix/Vector
//copy the value of the adept::adoube aRes in double Res and store them in RES
Res.resize (nDofsU + nDofsV); //resize
for (int i = 0; i < nDofsU; i++) {
Res[i] = -aResU[i].value();
}
for (int i = 0; i < nDofsV; i++) {
Res[i + nDofsU] = -aResV[i].value();
}
RES->add_vector_blocked (Res, sysDof);
//Extarct and store the Jacobian
Jac.resize ( (nDofsU + nDofsV) * (nDofsU + nDofsV));
// define the dependent variables
s.dependent (&aResU[0], nDofsU);
s.dependent (&aResV[0], nDofsV);
// define the independent variables
s.independent (&solU[0], nDofsU);
s.independent (&solV[0], nDofsV);
// get the and store jacobian matrix (row-major)
s.jacobian (&Jac[0] , true);
KK->add_matrix_blocked (Jac, sysDof, sysDof);
s.clear_independents();
s.clear_dependents();
} //end element loop for each process
RES->close();
KK->close();
// ***************** END ASSEMBLY *******************
}
void AssembleBilaplaceProblem_AD(MultiLevelProblem& ml_prob) {
// ml_prob is the global object from/to where get/set all the data
// level is the level of the PDE system to be assembled
// call the adept stack object
adept::Stack& s = FemusInit::_adeptStack;
// extract pointers to the several objects that we are going to use
NonLinearImplicitSystem* mlPdeSys = &ml_prob.get_system<NonLinearImplicitSystem> ("Poisson"); // pointer to the linear implicit system named "Poisson"
const unsigned level = mlPdeSys->GetLevelToAssemble();
Mesh* msh = ml_prob._ml_msh->GetLevel(level); // pointer to the mesh (level) object
elem* el = msh->el; // pointer to the elem object in msh (level)
MultiLevelSolution* mlSol = ml_prob._ml_sol; // pointer to the multilevel solution object
Solution* sol = ml_prob._ml_sol->GetSolutionLevel(level); // pointer to the solution (level) object
LinearEquationSolver* pdeSys = mlPdeSys->_LinSolver[level]; // pointer to the equation (level) object
SparseMatrix* KK = pdeSys->_KK; // pointer to the global stifness matrix object in pdeSys (level)
NumericVector* RES = pdeSys->_RES; // pointer to the global residual vector object in pdeSys (level)
const unsigned dim = msh->GetDimension(); // get the domain dimension of the problem
unsigned iproc = msh->processor_id(); // get the process_id (for parallel computation)
//solution variable
unsigned soluIndex;
soluIndex = mlSol->GetIndex("u"); // get the position of "u" in the ml_sol object
unsigned soluType = mlSol->GetSolutionType(soluIndex); // get the finite element type for "u"
unsigned soluPdeIndex;
soluPdeIndex = mlPdeSys->GetSolPdeIndex("u"); // get the position of "u" in the pdeSys object
vector < adept::adouble > solu; // local solution
unsigned solvIndex;
solvIndex = mlSol->GetIndex("v"); // get the position of "v" in the ml_sol object
unsigned solvType = mlSol->GetSolutionType(solvIndex); // get the finite element type for "v"
unsigned solvPdeIndex;
solvPdeIndex = mlPdeSys->GetSolPdeIndex("v"); // get the position of "v" in the pdeSys object
vector < adept::adouble > solv; // local solution
vector < vector < double > > x(dim); // local coordinates
unsigned xType = 2; // get the finite element type for "x", it is always 2 (LAGRANGE QUADRATIC)
vector< int > sysDof; // local to global pdeSys dofs
vector <double> phi; // local test function
vector <double> phi_x; // local test function first order partial derivatives
vector <double> phi_xx; // local test function second order partial derivatives
double weight; // gauss point weight
vector< double > Res; // local redidual vector
vector< adept::adouble > aResu; // local redidual vector
vector< adept::adouble > aResv; // local redidual vector
// reserve memory for the local standar vectors
const unsigned maxSize = static_cast< unsigned >(ceil(pow(3, dim))); // conservative: based on line3, quad9, hex27
solu.reserve(maxSize);
solv.reserve(maxSize);
for (unsigned i = 0; i < dim; i++)
x[i].reserve(maxSize);
sysDof.reserve(2 * maxSize);
phi.reserve(maxSize);
phi_x.reserve(maxSize * dim);
unsigned dim2 = (3 * (dim - 1) + !(dim - 1)); // dim2 is the number of second order partial derivatives (1,3,6 depending on the dimension)
phi_xx.reserve(maxSize * dim2);
Res.reserve(2 * maxSize);
aResu.reserve(maxSize);
aResv.reserve(maxSize);
vector < double > Jac; // local Jacobian matrix (ordered by column, adept)
Jac.reserve(4 * maxSize * maxSize);
KK->zero(); // Set to zero all the entries of the Global Matrix
// element loop: each process loops only on the elements that owns
for (int iel = msh->_elementOffset[iproc]; iel < msh->_elementOffset[iproc + 1]; iel++) {
short unsigned ielGeom = msh->GetElementType(iel);
unsigned nDofs = msh->GetElementDofNumber(iel, soluType); // number of solution element dofs
unsigned nDofs2 = msh->GetElementDofNumber(iel, xType); // number of coordinate element dofs
// resize local arrays
sysDof.resize(2 * nDofs);
solu.resize(nDofs);
solv.resize(nDofs);
for (int i = 0; i < dim; i++) {
x[i].resize(nDofs2);
}
aResu.assign(nDofs, 0.); //resize
aResv.assign(nDofs, 0.); //resize
// local storage of global mapping and solution
for (unsigned i = 0; i < nDofs; i++) {
unsigned solDof = msh->GetSolutionDof(i, iel, soluType); // global to global mapping between solution node and solution dof
solu[i] = (*sol->_Sol[soluIndex])(solDof); // global extraction and local storage for the solution
solv[i] = (*sol->_Sol[solvIndex])(solDof); // global extraction and local storage for the solution
sysDof[i] = pdeSys->GetSystemDof(soluIndex, soluPdeIndex, i, iel); // global to global mapping between solution node and pdeSys dof
sysDof[nDofs + i] = pdeSys->GetSystemDof(solvIndex, solvPdeIndex, i, iel); // global to global mapping between solution node and pdeSys dof
}
// local storage of coordinates
for (unsigned i = 0; i < nDofs2; i++) {
unsigned xDof = msh->GetSolutionDof(i, iel, xType); // global to global mapping between coordinates node and coordinate dof
for (unsigned jdim = 0; jdim < dim; jdim++) {
x[jdim][i] = (*msh->_topology->_Sol[jdim])(xDof); // global extraction and local storage for the element coordinates
}
}
// start a new recording of all the operations involving adept::adouble variables
s.new_recording();
// *** Gauss point loop ***
for (unsigned ig = 0; ig < msh->_finiteElement[ielGeom][soluType]->GetGaussPointNumber(); ig++) {
// *** get gauss point weight, test function and test function partial derivatives ***
msh->_finiteElement[ielGeom][soluType]->Jacobian(x, ig, weight, phi, phi_x, phi_xx);
// evaluate the solution, the solution derivatives and the coordinates in the gauss point
adept::adouble soluGauss = 0;
vector < adept::adouble > soluGauss_x(dim, 0.);
adept::adouble solvGauss = 0;
vector < adept::adouble > solvGauss_x(dim, 0.);
vector < double > xGauss(dim, 0.);
for (unsigned i = 0; i < nDofs; i++) {
soluGauss += phi[i] * solu[i];
solvGauss += phi[i] * solv[i];
for (unsigned jdim = 0; jdim < dim; jdim++) {
soluGauss_x[jdim] += phi_x[i * dim + jdim] * solu[i];
solvGauss_x[jdim] += phi_x[i * dim + jdim] * solv[i];
xGauss[jdim] += x[jdim][i] * phi[i];
}
}
// *** phi_i loop ***
for (unsigned i = 0; i < nDofs; i++) {
adept::adouble Laplace_u = 0.;
adept::adouble Laplace_v = 0.;
for (unsigned jdim = 0; jdim < dim; jdim++) {
Laplace_u += - phi_x[i * dim + jdim] * soluGauss_x[jdim];
Laplace_v += - phi_x[i * dim + jdim] * solvGauss_x[jdim];
}
double exactSolValue = GetExactSolutionValue(xGauss);
double pi = acos(-1.);
aResv[i] += (solvGauss * phi[i] - Laplace_u) * weight;
aResu[i] += (4.*pi * pi * pi * pi * exactSolValue * phi[i] - Laplace_v) * weight;
} // end phi_i loop
} // end gauss point loop
// Add the local Matrix/Vector into the global Matrix/Vector
//copy the value of the adept::adoube aRes in double Res and store
Res.resize(2 * nDofs);
for (int i = 0; i < nDofs; i++) {
Res[i] = -aResu[i].value();
Res[nDofs + i] = -aResv[i].value();
}
RES->add_vector_blocked(Res, sysDof);
Jac.resize( 4 * nDofs * nDofs );
// define the dependent variables
s.dependent(&aResu[0], nDofs);
s.dependent(&aResv[0], nDofs);
// define the independent variables
s.independent(&solu[0], nDofs);
s.independent(&solv[0], nDofs);
// get the jacobian matrix (ordered by column)
s.jacobian(&Jac[0], true);
KK->add_matrix_blocked(Jac, sysDof, sysDof);
s.clear_independents();
s.clear_dependents();
} //end element loop for each process
RES->close();
KK->close();
// ***************** END ASSEMBLY *******************
}
//------------------------------------------------------------------------------------------------------------
void AssembleMatrixResT(MultiLevelProblem &ml_prob){
//pointers and references
LinearImplicitSystem& mylin_impl_sys = ml_prob.get_system<LinearImplicitSystem>("Temperature");
const unsigned level = mylin_impl_sys.GetLevelToAssemble();
const unsigned gridn = mylin_impl_sys.GetLevelMax();
bool assemble_matrix = mylin_impl_sys.GetAssembleMatrix();
Solution* mysolution = ml_prob._ml_sol->GetSolutionLevel(level);
LinearEquationSolver* mylsyspde = mylin_impl_sys._LinSolver[level];
Mesh* mymsh = ml_prob._ml_msh->GetLevel(level);
elem* myel = mymsh->el;
SparseMatrix* myKK = mylsyspde->_KK;
NumericVector* myRES = mylsyspde->_RES;
MultiLevelSolution* ml_sol = ml_prob._ml_sol;
//data
const unsigned dim = mymsh->GetDimension();
unsigned nel = mymsh->GetNumberOfElements();
unsigned igrid = mymsh->GetLevel();
unsigned iproc = mymsh->processor_id();
double IPe = 1./(ml_prob.parameters.get<Fluid>("Fluid").get_Peclet_number());
//solution variable
unsigned SolIndex;
unsigned SolPdeIndex;
SolIndex=ml_sol->GetIndex("T");
SolPdeIndex=mylin_impl_sys.GetSolPdeIndex("T");
//solution order
unsigned order_ind = ml_sol->GetSolutionType(SolIndex);
//coordinates
vector< vector < double> > coordinates(dim);
//const char coordinate_name[3][2] = {"X","Y","Z"};
//vector < unsigned > coordinate_Index(dim);
// for(unsigned ivar=0; ivar<dim; ivar++) {
// coordinate_Index[ivar]=ivar;//ml_prob.GetIndex(coordinate_name[ivar]);
// }
// declare
vector< int > metis_node;
vector< int > KK_dof;
vector <double> phi;
vector <double> gradphi;
vector <double> nablaphi;
double weight;
vector< double > F;
vector< double > B;
// reserve
const unsigned max_size = static_cast< unsigned > (ceil(pow(3,dim)));
metis_node.reserve(max_size);
KK_dof.reserve(max_size);
for(int i=0;i<dim;i++)
coordinates[i].reserve(max_size);
phi.reserve(max_size);
gradphi.reserve(max_size*dim);
nablaphi.reserve(max_size*(3*(dim-1)) );
F.reserve(max_size);
B.reserve(max_size*max_size);
// Set to zeto all the entries of the Global Matrix
if(assemble_matrix) myKK->zero();
// *** element loop ***
for (int iel=mymsh->IS_Mts2Gmt_elem_offset[iproc]; iel < mymsh->IS_Mts2Gmt_elem_offset[iproc+1]; iel++) {
unsigned kel = mymsh->IS_Mts2Gmt_elem[iel];
short unsigned kelt=myel->GetElementType(kel);
unsigned nve=myel->GetElementDofNumber(kel,order_ind);
// resize
metis_node.resize(nve);
KK_dof.resize(nve);
phi.resize(nve);
gradphi.resize(nve*dim);
nablaphi.resize( nve*(3*(dim-1)) );
for(int i=0;i<dim;i++){
coordinates[i].resize(nve);
}
// set to zero all the entries of the FE matrices
F.resize(nve);
memset(&F[0],0,nve*sizeof(double));
if(assemble_matrix){
B.resize(nve*nve);
memset(&B[0],0,nve*nve*sizeof(double));
}
// get local to global mappings
for( unsigned i=0;i<nve;i++){
unsigned inode=myel->GetElementVertexIndex(kel,i)-1u;
unsigned inode_metis=mymsh->GetMetisDof(inode,2);
metis_node[i]=inode_metis;
for(unsigned ivar=0; ivar<dim; ivar++) {
coordinates[ivar][i]=(*mymsh->_coordinate->_Sol[ivar])(inode_metis);
}
KK_dof[i]=mylsyspde->GetKKDof(SolIndex,SolPdeIndex,inode);
}
if(igrid==gridn || !myel->GetRefinedElementIndex(kel)) {
// *** Gauss poit loop ***
for(unsigned ig=0;ig < ml_prob._ml_msh->_finiteElement[kelt][order_ind]->GetGaussPointNumber(); ig++) {
// *** get Jacobian and test function and test function derivatives ***
ml_prob._ml_msh->_finiteElement[kelt][order_ind]->Jacobian(coordinates,ig,weight,phi,gradphi,nablaphi);
//Temperature and velocity current solution
double SolT=0;
vector < double > gradSolT(dim,0.);
for(unsigned ivar=0; ivar<dim; ivar++){
gradSolT[ivar]=0;
}
vector < double > SolU(dim,0.);
vector < unsigned > SolIndexU(dim);
SolIndexU[0]=ml_sol->GetIndex("U");
SolIndexU[1]=ml_sol->GetIndex("V");
if(dim==3) SolIndexU[2]=ml_sol->GetIndex("W");
unsigned SolType=ml_sol->GetSolutionType("T");
for(unsigned i=0; i<nve; i++) {
double soli = (*mysolution->_Sol[SolIndex])(metis_node[i]);
SolT+=phi[i]*soli;
for(unsigned ivar2=0; ivar2<dim; ivar2++) gradSolT[ivar2] += gradphi[i*dim+ivar2]*soli;
for(int j=0;j<dim;j++) {
SolU[j]+=phi[i]*(*mysolution->_Sol[SolIndexU[j]])(metis_node[i]);
}
}
// *** phi_i loop ***
for(unsigned i=0; i<nve; i++){
//BEGIN RESIDUALS A block ===========================
double Adv_rhs=0;
double Lap_rhs=0;
for(unsigned ivar=0; ivar<dim; ivar++) {
Lap_rhs += gradphi[i*dim+ivar]*gradSolT[ivar];
Adv_rhs += SolU[ivar]*gradSolT[ivar];
}
F[i]+= (-IPe*Lap_rhs-Adv_rhs*phi[i])*weight;
//END RESIDUALS A block ===========================
if(assemble_matrix){
// *** phi_j loop ***
for(unsigned j=0; j<nve; j++) {
double Lap=0;
double Adv1=0;
for(unsigned ivar=0; ivar<dim; ivar++) {
// Laplacian
Lap += gradphi[i*dim+ivar]*gradphi[j*dim+ivar]*weight;
// advection term I
Adv1 += SolU[ivar]*gradphi[j*dim+ivar]*phi[i]*weight;
}
B[i*nve+j] += IPe*Lap + Adv1;
} // end phij loop
} // end phii loop
} // endif assemble_matrix
} // end gauss point loop
} // endif single element not refined or fine grid loop
//--------------------------------------------------------------------------------------------------------
//Sum the local matrices/vectors into the global Matrix/vector
myRES->add_vector_blocked(F,KK_dof);
if(assemble_matrix) myKK->add_matrix_blocked(B,KK_dof,KK_dof);
} //end list of elements loop for each subdomain
myRES->close();
if(assemble_matrix) myKK->close();
// ***************** END ASSEMBLY *******************
}
void AssembleMatrixResNS(MultiLevelProblem &ml_prob){
//pointers
NonLinearImplicitSystem& my_nnlin_impl_sys = ml_prob.get_system<NonLinearImplicitSystem>("Navier-Stokes");
const unsigned level = my_nnlin_impl_sys.GetLevelToAssemble();
const unsigned gridn = my_nnlin_impl_sys.GetLevelMax();
bool assemble_matrix = my_nnlin_impl_sys.GetAssembleMatrix();
Solution* mysolution = ml_prob._ml_sol->GetSolutionLevel(level);
LinearEquationSolver* mylsyspde = my_nnlin_impl_sys._LinSolver[level];
const char* pdename = my_nnlin_impl_sys.name().c_str();
MultiLevelSolution* ml_sol=ml_prob._ml_sol;
Mesh* mymsh = ml_prob._ml_msh->GetLevel(level);
elem* myel = mymsh->el;
SparseMatrix* myKK = mylsyspde->_KK;
NumericVector* myRES = mylsyspde->_RES;
//data
const unsigned dim = mymsh->GetDimension();
unsigned nel= mymsh->GetNumberOfElements();
unsigned igrid= mymsh->GetLevel();
unsigned iproc = mymsh->processor_id();
double ILambda= 0;
double IRe = ml_prob.parameters.get<Fluid>("Fluid").get_IReynolds_number();
bool penalty = true; //mylsyspde->GetStabilization();
const bool symm_mat = false;//mylsyspde->GetMatrixProperties();
const bool NavierStokes = true;
unsigned nwtn_alg = 2;
bool newton = (nwtn_alg==0) ? 0:1;
// solution and coordinate variables
const char Solname[4][2] = {"U","V","W","P"};
vector < unsigned > SolPdeIndex(dim+1);
vector < unsigned > SolIndex(dim+1);
//const char coordinate_name[3][2] = {"X","Y","Z"};
//vector < unsigned > coordinate_Index(dim);
vector< vector < double> > coordinates(dim);
for(unsigned ivar=0; ivar<dim; ivar++) {
SolPdeIndex[ivar]=my_nnlin_impl_sys.GetSolPdeIndex(&Solname[ivar][0]);
SolIndex[ivar]=ml_sol->GetIndex(&Solname[ivar][0]);
//coordinate_Index[ivar]=ivar;//ml_prob.GetIndex(&coordinate_name[ivar][0]);
}
SolPdeIndex[dim]=my_nnlin_impl_sys.GetSolPdeIndex(&Solname[3][0]);
SolIndex[dim]=ml_sol->GetIndex(&Solname[3][0]);
//solution order
unsigned order_ind2 = ml_sol->GetSolutionType(SolIndex[0]);
unsigned order_ind1 = ml_sol->GetSolutionType(SolIndex[dim]);
// declare
vector < int > metis_node2;
vector < int > node1;
vector< vector< int > > KK_dof(dim+1);
vector <double> phi2;
vector <double> gradphi2;
vector <double> nablaphi2;
const double *phi1;
double Weight2;
double normal[3];
vector< vector< double > > F(dim+1);
vector< vector< vector< double > > > B(dim+1);
// reserve
const unsigned max_size = static_cast< unsigned > (ceil(pow(3,dim)));
metis_node2.reserve(max_size);
node1.reserve( static_cast< unsigned > (ceil(pow(2,dim))));
for(int i=0;i<dim;i++) {
coordinates[i].reserve(max_size);
}
phi2.reserve(max_size);
gradphi2.reserve(max_size*dim);
nablaphi2.reserve(max_size*(3*(dim-1)) );
for(int i=0;i<dim;i++) {
KK_dof[i].reserve(max_size);
}
for(int i=0;i<dim+1;i++) F[i].reserve(max_size);
if(assemble_matrix){
for(int i=0;i<dim+1;i++){
B[i].resize(dim+1);
for(int j=0;j<dim+1;j++){
B[i][j].reserve(max_size*max_size);
}
}
}
vector < double > SolVAR(dim+1);
vector < vector < double > > gradSolVAR(dim);
for(int i=0;i<dim;i++) {
gradSolVAR[i].resize(dim);
}
// Set to zeto all the entries of the matrix
if(assemble_matrix) myKK->zero();
// *** element loop ***
for (int iel=mymsh->IS_Mts2Gmt_elem_offset[iproc]; iel < mymsh->IS_Mts2Gmt_elem_offset[iproc+1]; iel++) {
unsigned kel = mymsh->IS_Mts2Gmt_elem[iel];
short unsigned kelt=myel->GetElementType(kel);
unsigned nve2=myel->GetElementDofNumber(kel,order_ind2);
unsigned nve1=myel->GetElementDofNumber(kel,order_ind1);
//set to zero all the entries of the FE matrices
metis_node2.resize(nve2);
node1.resize(nve1);
phi2.resize(nve2);
gradphi2.resize(nve2*dim);
nablaphi2.resize(nve2*(3*(dim-1)) );
for(int ivar=0; ivar<dim; ivar++) {
coordinates[ivar].resize(nve2);
KK_dof[ivar].resize(nve2);
F[SolPdeIndex[ivar]].resize(nve2);
memset(&F[SolPdeIndex[ivar]][0],0,nve2*sizeof(double));
if(assemble_matrix){
B[SolPdeIndex[ivar]][SolPdeIndex[ivar]].resize(nve2*nve2);
B[SolPdeIndex[ivar]][SolPdeIndex[dim]].resize(nve2*nve1);
B[SolPdeIndex[dim]][SolPdeIndex[ivar]].resize(nve1*nve2);
memset(&B[SolPdeIndex[ivar]][SolPdeIndex[ivar]][0],0,nve2*nve2*sizeof(double));
memset(&B[SolPdeIndex[ivar]][SolPdeIndex[dim]][0],0,nve2*nve1*sizeof(double));
memset(&B[SolPdeIndex[dim]][SolPdeIndex[ivar]][0],0,nve1*nve2*sizeof(double));
}
}
KK_dof[dim].resize(nve1);
F[SolPdeIndex[dim]].resize(nve1);
memset(&F[SolPdeIndex[dim]][0],0,nve1*sizeof(double));
if(assemble_matrix*nwtn_alg==2){
for(int ivar=0; ivar<dim; ivar++) {
for(int ivar2=1; ivar2<dim; ivar2++) {
B[SolPdeIndex[ivar]][SolPdeIndex[(ivar+ivar2)%dim]].resize(nve2*nve2);
memset(&B[SolPdeIndex[ivar]][SolPdeIndex[(ivar+ivar2)%dim]][0],0,nve2*nve2*sizeof(double));
}
}
}
if(assemble_matrix*penalty){
B[SolPdeIndex[dim]][SolPdeIndex[dim]].resize(nve1*nve1,0.);
memset(&B[SolPdeIndex[dim]][SolPdeIndex[dim]][0],0,nve1*nve1*sizeof(double));
}
for( unsigned i=0;i<nve2;i++){
unsigned inode=myel->GetElementVertexIndex(kel,i)-1u;
unsigned inode_metis=mymsh->GetMetisDof(inode,2);
metis_node2[i]=inode_metis;
for(unsigned ivar=0; ivar<dim; ivar++) {
coordinates[ivar][i]=(*mymsh->_coordinate->_Sol[ivar])(inode_metis);
KK_dof[ivar][i]=mylsyspde->GetKKDof(SolIndex[ivar],SolPdeIndex[ivar],inode);
}
}
for(unsigned i=0;i<nve1;i++) {
unsigned inode=(order_ind1<3)?(myel->GetElementVertexIndex(kel,i)-1u):(kel+i*nel);
node1[i]=inode;
KK_dof[dim][i]=mylsyspde->GetKKDof(SolIndex[dim],SolPdeIndex[dim],inode);
}
if(igrid==gridn || !myel->GetRefinedElementIndex(kel)) {
// *** Gauss poit loop ***
for(unsigned ig=0;ig < ml_prob._ml_msh->_finiteElement[kelt][order_ind2]->GetGaussPointNumber(); ig++) {
// *** get Jacobian and test function and test function derivatives ***
ml_prob._ml_msh->_finiteElement[kelt][order_ind2]->Jacobian(coordinates,ig,Weight2,phi2,gradphi2,nablaphi2);
phi1=ml_prob._ml_msh->_finiteElement[kelt][order_ind1]->GetPhi(ig);
//velocity variable
for(unsigned ivar=0; ivar<dim; ivar++) {
SolVAR[ivar]=0;
for(unsigned ivar2=0; ivar2<dim; ivar2++){
gradSolVAR[ivar][ivar2]=0;
}
unsigned SolIndex=ml_sol->GetIndex(&Solname[ivar][0]);
unsigned SolType=ml_sol->GetSolutionType(&Solname[ivar][0]);
for(unsigned i=0; i<nve2; i++) {
double soli = (*mysolution->_Sol[SolIndex])(metis_node2[i]);
SolVAR[ivar]+=phi2[i]*soli;
for(unsigned ivar2=0; ivar2<dim; ivar2++){
gradSolVAR[ivar][ivar2] += gradphi2[i*dim+ivar2]*soli;
}
}
}
//pressure variable
SolVAR[dim]=0;
unsigned SolIndex=ml_sol->GetIndex(&Solname[3][0]);
unsigned SolType=ml_sol->GetSolutionType(&Solname[3][0]);
for(unsigned i=0; i<nve1; i++){
unsigned sol_dof = mymsh->GetMetisDof(node1[i],SolType);
double soli = (*mysolution->_Sol[SolIndex])(sol_dof);
SolVAR[dim]+=phi1[i]*soli;
}
// *** phi_i loop ***
for(unsigned i=0; i<nve2; i++){
//BEGIN RESIDUALS A block ===========================
for(unsigned ivar=0; ivar<dim; ivar++) {
double Adv_rhs=0;
double Lap_rhs=0;
for(unsigned ivar2=0; ivar2<dim; ivar2++) {
Lap_rhs += gradphi2[i*dim+ivar2]*gradSolVAR[ivar][ivar2];
Adv_rhs += SolVAR[ivar2]*gradSolVAR[ivar][ivar2];
}
F[SolPdeIndex[ivar]][i]+= (-IRe*Lap_rhs-NavierStokes*Adv_rhs*phi2[i]+SolVAR[dim]*gradphi2[i*dim+ivar])*Weight2;
}
//END RESIDUALS A block ===========================
if(assemble_matrix){
// *** phi_j loop ***
for(unsigned j=0; j<nve2; j++) {
double Lap=0;
double Adv1=0;
double Adv2 = phi2[i]*phi2[j]*Weight2;
for(unsigned ivar=0; ivar<dim; ivar++) {
// Laplacian
Lap += gradphi2[i*dim+ivar]*gradphi2[j*dim+ivar]*Weight2;
// advection term I
Adv1 += SolVAR[ivar]*gradphi2[j*dim+ivar]*phi2[i]*Weight2;
}
for(unsigned ivar=0; ivar<dim; ivar++) {
B[SolPdeIndex[ivar]][SolPdeIndex[ivar]][i*nve2+j] += IRe*Lap+ NavierStokes*newton*Adv1;
if(nwtn_alg==2){
// Advection term II
B[SolPdeIndex[ivar]][SolPdeIndex[ivar]][i*nve2+j] += Adv2*gradSolVAR[ivar][ivar];
for(unsigned ivar2=1; ivar2<dim; ivar2++) {
B[SolPdeIndex[ivar]][SolPdeIndex[(ivar+ivar2)%dim]][i*nve2+j] += Adv2*gradSolVAR[ivar][(ivar+ivar2)%dim];
}
}
}
} //end phij loop
// *** phi1_j loop ***
for(unsigned j=0; j<nve1; j++){
for(unsigned ivar=0; ivar<dim; ivar++) {
B[SolPdeIndex[ivar]][SolPdeIndex[dim]][i*nve1+j] -= gradphi2[i*dim+ivar]*phi1[j]*Weight2;
}
} //end phi1_j loop
} // endif assemble_matrix
} //end phii loop
// *** phi1_i loop ***
for(unsigned i=0; i<nve1; i++){
//BEGIN RESIDUALS B block ===========================
double div = 0;
for(unsigned ivar=0; ivar<dim; ivar++) {
div += gradSolVAR[ivar][ivar];
}
F[SolPdeIndex[dim]][i]+= (phi1[i]*div +penalty*ILambda*phi1[i]*SolVAR[dim])*Weight2;
//END RESIDUALS B block ===========================
if(assemble_matrix){
// *** phi_j loop ***
for(unsigned j=0; j<nve2; j++) {
for(unsigned ivar=0; ivar<dim; ivar++) {
B[SolPdeIndex[dim]][SolPdeIndex[ivar]][i*nve2+j]-= phi1[i]*gradphi2[j*dim+ivar]*Weight2;
}
} //end phij loop
} // endif assemble_matrix
} //end phi1_i loop
if(assemble_matrix * penalty){ //block nve1 nve1
// *** phi_i loop ***
for(unsigned i=0; i<nve1; i++){
// *** phi_j loop ***
for(unsigned j=0; j<nve1; j++){
B[SolPdeIndex[dim]][SolPdeIndex[dim]][i*nve1+j]-= ILambda*phi1[i]*phi1[j]*Weight2;
}
}
} //end if penalty
} // end gauss point loop
//--------------------------------------------------------------------------------------------------------
// Boundary Integral --> to be addded
//number of faces for each type of element
// if (igrid==gridn || !myel->GetRefinedElementIndex(kel) ) {
//
// unsigned nfaces = myel->GetElementFaceNumber(kel);
//
// // loop on faces
// for(unsigned jface=0;jface<nfaces;jface++){
//
// // look for boundary faces
// if(myel->GetFaceElementIndex(kel,jface)<0){
// for(unsigned ivar=0; ivar<dim; ivar++) {
// ml_prob.ComputeBdIntegral(pdename, &Solname[ivar][0], kel, jface, level, ivar);
// }
// }
// }
// }
//--------------------------------------------------------------------------------------------------------
} // endif single element not refined or fine grid loop
//--------------------------------------------------------------------------------------------------------
//Sum the local matrices/vectors into the Global Matrix/Vector
for(unsigned ivar=0; ivar<dim; ivar++) {
myRES->add_vector_blocked(F[SolPdeIndex[ivar]],KK_dof[ivar]);
if(assemble_matrix){
myKK->add_matrix_blocked(B[SolPdeIndex[ivar]][SolPdeIndex[ivar]],KK_dof[ivar],KK_dof[ivar]);
myKK->add_matrix_blocked(B[SolPdeIndex[ivar]][SolPdeIndex[dim]],KK_dof[ivar],KK_dof[dim]);
myKK->add_matrix_blocked(B[SolPdeIndex[dim]][SolPdeIndex[ivar]],KK_dof[dim],KK_dof[ivar]);
if(nwtn_alg==2){
for(unsigned ivar2=1; ivar2<dim; ivar2++) {
myKK->add_matrix_blocked(B[SolPdeIndex[ivar]][SolPdeIndex[(ivar+ivar2)%dim]],KK_dof[ivar],KK_dof[(ivar+ivar2)%dim]);
}
}
}
}
//Penalty
if(assemble_matrix*penalty) myKK->add_matrix_blocked(B[SolPdeIndex[dim]][SolPdeIndex[dim]],KK_dof[dim],KK_dof[dim]);
myRES->add_vector_blocked(F[SolPdeIndex[dim]],KK_dof[dim]);
//--------------------------------------------------------------------------------------------------------
} //end list of elements loop for each subdomain
if(assemble_matrix) myKK->close();
myRES->close();
// ***************** END ASSEMBLY *******************
}
int lanczos (int flag, SparseMatrix const &mat, int max_nstep, double &gsEnergy,
vector<MatType> &z)
{ /*
* In each step of the Lanczos algorithm the values of a[]
* and b[] are computed.
* then a tridiagonal matrix T[j] is formed from the matrix
* T[j-1] as
*
* | a[0] b[0] |
* | b[0] a[1] b[1] |
* T(j) = | b[1] . . |
* | . . a[j-2] b[j-2] |
* | . . b[j-2] a[j-1] |
*/
// Set flag = 1 for the ground state
// Set flag = 0 for the maximum eigenvalue
int i, j;
long int seed;
double s, enew, eold, atmp, btmp, ctmp, eps = 0.001;
vector<double> a,b,c;
vector<MatType> x,y;
MatType tmp,tmp2;
vector<double> nullVector;
if (nullVector.size()>0) {
std::cerr<<"nullVector has size greater than zero\n";
exit(1);
}
seed= rand();
for (i = 0; i < max_nstep; i++) {
a.push_back(0.0);
b.push_back(0.0);
c.push_back(0.0);
}
srand48 (seed);
s = 0.0;
z.clear();
for (i = 0; i < mat.getSize(); i++) {
tmp2 = MatType(0,0);
z.push_back(tmp2);
tmp2 = MatType(0,0);
x.push_back(tmp2);
tmp2 = MatType(drand48 () - 0.5, drand48 () - 0.5);
y.push_back(tmp2);
s += real (y[i] * conj (y[i]));
}
s = 1.0 / sqrt (s);
for (i = 0; i < mat.getSize(); i++)
y[i] *= s;
if (max_nstep > mat.getSize())
max_nstep = mat.getSize();
eold = 100.;
//cout<<"iter\t< 0 | H | 0 >\n";
for (j = 0; j < max_nstep; j++) {
mat.sparse_mult (x, y);
atmp = 0.0;
for (i = 0; i < mat.getSize(); i++)
atmp += real (y[i] * conj (x[i]));
btmp = 0.0;
for (i = 0; i < mat.getSize(); i++) {
x[i] -= atmp * y[i];
btmp += real (x[i] * conj (x[i]));
}
a[j] = atmp;
b[j] = (btmp = sqrt (btmp));
enew = ground (flag,j+1, a, b,nullVector);
// cout<<j<<":\t"<<enew<<" "<<nullVector.size()<<endl;
if (fabs ((enew - eold)/enew) < eps)
break;
eold = enew;
for (i = 0; i < mat.getSize(); i++) {
tmp = y[i];
y[i] = x[i] / btmp;
x[i] = -btmp * tmp;
}
}
if (j < max_nstep)
max_nstep = j + 1;
gsEnergy = ground (flag,max_nstep, a, b, c);
srand48 (seed);
for (i = 0; i < mat.getSize(); i++) {
x[i] = MatType(0,0);
y[i] = s * MatType((drand48 () - 0.5), (drand48 () - 0.5)) ;
z[i] = MatType(0,0);
}
for (j = 0; j < max_nstep; j++) {
mat.sparse_mult (x, y);
atmp = a[j];
btmp = b[j];
ctmp = c[j];
for (i = 0; i < mat.getSize(); i++) {
z[i] += ctmp * y[i];
x[i] -= atmp * y[i];
tmp = y[i];
y[i] = x[i] / btmp;
x[i] = -btmp * tmp;
}
}
return 0;
}
IGL_INLINE bool igl::bbw(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedEle> & Ele,
const Eigen::PlainObjectBase<Derivedb> & b,
const Eigen::PlainObjectBase<Derivedbc> & bc,
igl::BBWData & data,
Eigen::PlainObjectBase<DerivedW> & W
)
{
using namespace igl;
using namespace std;
using namespace Eigen;
// number of domain vertices
int n = V.rows();
// number of handles
int m = bc.cols();
SparseMatrix<typename DerivedW::Scalar> L;
cotmatrix(V,Ele,L);
MassMatrixType mmtype = MASSMATRIX_VORONOI;
if(Ele.cols() == 4)
{
mmtype = MASSMATRIX_BARYCENTRIC;
}
SparseMatrix<typename DerivedW::Scalar> M;
SparseMatrix<typename DerivedW::Scalar> Mi;
massmatrix(V,Ele,mmtype,M);
invert_diag(M,Mi);
// Biharmonic operator
SparseMatrix<typename DerivedW::Scalar> Q = L.transpose() * Mi * L;
W.derived().resize(n,m);
if(data.partition_unity)
{
// Not yet implemented
assert(false);
}else
{
// No linear terms
VectorXd c = VectorXd::Zero(n);
// No linear constraints
SparseMatrix<typename DerivedW::Scalar> A(0,n),Aeq(0,n),Aieq(0,n);
VectorXd uc(0,1),Beq(0,1),Bieq(0,1),lc(0,1);
// Upper and lower box constraints (Constant bounds)
VectorXd ux = VectorXd::Ones(n);
VectorXd lx = VectorXd::Zero(n);
active_set_params eff_params = data.active_set_params;
switch(data.qp_solver)
{
case QP_SOLVER_IGL_ACTIVE_SET:
{
//if(data.verbosity >= 1)
//{
cout<<"BBW: max_iter: "<<eff_params.max_iter<<endl;
//}
if(data.verbosity >= 1)
{
cout<<"BBW: Computing initial weights for "<<m<<" handle"<<
(m!=1?"s":"")<<"."<<endl;
}
min_quad_with_fixed_data<typename DerivedW::Scalar > mqwf;
min_quad_with_fixed_precompute(Q,b,Aeq,true,mqwf);
min_quad_with_fixed_solve(mqwf,c,bc,Beq,W);
// decrement
eff_params.max_iter--;
bool error = false;
// Loop over handles
#pragma omp parallel for
for(int i = 0;i<m;i++)
{
// Quicker exit for openmp
if(error)
{
continue;
}
if(data.verbosity >= 1)
{
#pragma omp critical
cout<<"BBW: Computing weight for handle "<<i+1<<" out of "<<m<<
"."<<endl;
}
VectorXd bci = bc.col(i);
VectorXd Wi;
// use initial guess
Wi = W.col(i);
SolverStatus ret = active_set(
Q,c,b,bci,Aeq,Beq,Aieq,Bieq,lx,ux,eff_params,Wi);
switch(ret)
{
case SOLVER_STATUS_CONVERGED:
break;
case SOLVER_STATUS_MAX_ITER:
cerr<<"active_set: max iter without convergence."<<endl;
break;
case SOLVER_STATUS_ERROR:
default:
cerr<<"active_set error."<<endl;
error = true;
}
W.col(i) = Wi;
}
if(error)
{
return false;
}
break;
}
case QP_SOLVER_MOSEK:
{
#ifdef IGL_NO_MOSEK
assert(false && "Use another QPSolver. Recompile without IGL_NO_MOSEK defined.");
cerr<<"Use another QPSolver. Recompile without IGL_NO_MOSEK defined."<<endl;
return false;
#else
// Loop over handles
for(int i = 0;i<m;i++)
{
if(data.verbosity >= 1)
{
cout<<"BBW: Computing weight for handle "<<i+1<<" out of "<<m<<
"."<<endl;
}
VectorXd bci = bc.col(i);
VectorXd Wi;
// impose boundary conditions via bounds
slice_into(bci,b,ux);
slice_into(bci,b,lx);
bool r = mosek_quadprog(Q,c,0,A,lc,uc,lx,ux,data.mosek_data,Wi);
if(!r)
{
return false;
}
W.col(i) = Wi;
}
#endif
break;
}
default:
{
assert(false && "Unknown qp_solver");
return false;
}
}
#ifndef NDEBUG
const double min_rowsum = W.rowwise().sum().array().abs().minCoeff();
if(min_rowsum < 0.1)
{
cerr<<"bbw.cpp: Warning, minimum row sum is very low. Consider more "
"active set iterations or enforcing partition of unity."<<endl;
}
#endif
}
return true;
}
int SparseFromFile(SparseMatrix &mat, char *filename)
{
int i, j, k;
double eps = 1.e-15;
MatType Aij;
int tmp;
ifstream fin(filename);
if (!fin || fin.bad()) {
cerr<<"new_sparse: can't open file "<<filename<<endl;
return -1;
}
fin>>tmp;
mat.setSize(tmp);
mat.initRow(mat.getSize()+1);
k = 0;
for (i = 0; i < mat.getSize(); i++) {
mat.setRow(i,k);
for (j = 0; j < mat.getSize(); j++) {
fin>>Aij;
if (abs (Aij) > eps)
k++;
}
}
mat.setRow(mat.getSize(),k); /* # of non-zero elements */
mat.initCol(k);
mat.initValues(k);
fin.close();
fin.open(filename);
if (!fin || fin.bad()) {
cerr<<"new_sparse: can't open file "<<filename<<endl;
return -1;
}
fin>>tmp;
mat.setSize(tmp);
k = 0;
for (i = 0; i < mat.getSize(); i++)
for (j = 0; j < mat.getSize(); j++) {
fin>>Aij;
if (abs (Aij) > eps) {
mat.setCol(k,j);
mat.setValues(k,Aij);
k++;
}
}
fin.close();
return mat.getSize();
}