bool ASMs3Dmx::evalSolution (Matrix& sField, const IntegrandBase& integrand,
const RealArray* gpar, bool regular) const
{
sField.resize(0,0);
if (m_basis.empty()) return false;
// Evaluate the basis functions and their derivatives at all points
std::vector<std::vector<Go::BasisDerivs>> splinex(m_basis.size());
if (regular)
{
for (size_t b = 0; b < m_basis.size(); ++b)
m_basis[b]->computeBasisGrid(gpar[0],gpar[1],gpar[2],splinex[b]);
}
else if (gpar[0].size() == gpar[1].size() && gpar[0].size() == gpar[2].size())
{
for (size_t b = 0; b < m_basis.size(); ++b) {
splinex[b].resize(gpar[0].size());
for (size_t i = 0; i < splinex[b].size(); i++)
m_basis[b]->computeBasis(gpar[0][i],gpar[1][i],gpar[2][i],splinex[b][i]);
}
}
std::vector<size_t> elem_sizes;
for (auto& it : m_basis)
elem_sizes.push_back(it->order(0)*it->order(1)*it->order(2));
// Fetch nodal (control point) coordinates
Matrix Xnod, Xtmp;
this->getNodalCoordinates(Xnod);
MxFiniteElement fe(elem_sizes,firstIp);
Vector solPt;
std::vector<Matrix> dNxdu(m_basis.size());
Matrix Jac;
Vec3 X;
// Evaluate the secondary solution field at each point
size_t nPoints = splinex[0].size();
for (size_t i = 0; i < nPoints; i++, fe.iGP++)
{
// Fetch indices of the non-zero basis functions at this point
std::vector<IntVec> ip(m_basis.size());
IntVec ipa;
size_t ofs = 0;
for (size_t b = 0; b < m_basis.size(); ++b) {
scatterInd(m_basis[b]->numCoefs(0),m_basis[b]->numCoefs(1),m_basis[b]->numCoefs(2),
m_basis[b]->order(0),m_basis[b]->order(1),m_basis[b]->order(2),
splinex[b][i].left_idx,ip[b]);
// Fetch associated control point coordinates
if (b == (size_t)geoBasis-1)
utl::gather(ip[geoBasis-1], 3, Xnod, Xtmp);
for (auto& it : ip[b])
it += ofs;
ipa.insert(ipa.end(), ip[b].begin(), ip[b].end());
ofs += nb[b];
}
fe.u = splinex[0][i].param[0];
fe.v = splinex[0][i].param[1];
fe.w = splinex[0][i].param[2];
// Fetch basis function derivatives at current integration point
for (size_t b = 0; b < m_basis.size(); ++b)
SplineUtils::extractBasis(splinex[b][i],fe.basis(b+1),dNxdu[b]);
// Compute Jacobian inverse of the coordinate mapping and
// basis function derivatives w.r.t. Cartesian coordinates
fe.detJxW = utl::Jacobian(Jac,fe.grad(geoBasis),Xtmp,dNxdu[geoBasis-1]);
for (size_t b = 1; b <= m_basis.size(); b++)
if (b != (size_t)geoBasis)
{
if (fe.detJxW == 0.0)
fe.grad(b).clear();
else
fe.grad(b).multiply(dNxdu[b-1],Jac);
}
// Cartesian coordinates of current integration point
X = Xtmp * fe.basis(geoBasis);
// Now evaluate the solution field
if (!integrand.evalSol(solPt,fe,X,ipa,elem_sizes,nb))
return false;
else if (sField.empty())
sField.resize(solPt.size(),nPoints,true);
sField.fillColumn(1+i,solPt);
}
return true;
}
bool ASMs3Dmx::integrate (Integrand& integrand, int lIndex,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (!svol) return true; // silently ignore empty patches
if (m_basis.empty()) return false;
PROFILE2("ASMs3Dmx::integrate(B)");
bool useElmVtx = integrand.getIntegrandType() & Integrand::ELEMENT_CORNERS;
std::map<char,ThreadGroups>::const_iterator tit;
if ((tit = threadGroupsFace.find(lIndex)) == threadGroupsFace.end())
{
std::cerr <<" *** ASMs3D::integrate: No thread groups for face "<< lIndex
<< std::endl;
return false;
}
const ThreadGroups& threadGrp = tit->second;
// Get Gaussian quadrature points and weights
const double* xg = GaussQuadrature::getCoord(nGauss);
const double* wg = GaussQuadrature::getWeight(nGauss);
if (!xg || !wg) return false;
// Find the parametric direction of the face normal {-3,-2,-1, 1, 2, 3}
const int faceDir = (lIndex+1)/(lIndex%2 ? -2 : 2);
const int t1 = 1 + abs(faceDir)%3; // first tangent direction
const int t2 = 1 + t1%3; // second tangent direction
// Compute parameter values of the Gauss points over the whole patch face
std::array<Matrix,3> gpar;
for (int d = 0; d < 3; d++)
if (-1-d == faceDir)
{
gpar[d].resize(1,1);
gpar[d].fill(svol->startparam(d));
}
else if (1+d == faceDir)
{
gpar[d].resize(1,1);
gpar[d].fill(svol->endparam(d));
}
else
this->getGaussPointParameters(gpar[d],d,nGauss,xg);
// Evaluate basis function derivatives at all integration points
std::vector<std::vector<Go::BasisDerivs>> splinex(m_basis.size());
#pragma omp parallel for schedule(static)
for (size_t i = 0; i < m_basis.size(); ++i)
m_basis[i]->computeBasisGrid(gpar[0],gpar[1],gpar[2],splinex[i]);
const int n1 = svol->numCoefs(0);
const int n2 = svol->numCoefs(1);
const int p1 = svol->order(0);
const int p2 = svol->order(1);
const int p3 = svol->order(2);
std::vector<size_t> elem_sizes;
for (auto& it : m_basis)
elem_sizes.push_back(it->order(0)*it->order(1)*it->order(2));
const int nel1 = n1 - p1 + 1;
const int nel2 = n2 - p2 + 1;
std::map<char,size_t>::const_iterator iit = firstBp.find(lIndex);
size_t firstp = iit == firstBp.end() ? 0 : iit->second;
// === Assembly loop over all elements on the patch face =====================
bool ok = true;
for (size_t g = 0; g < threadGrp.size() && ok; ++g) {
#pragma omp parallel for schedule(static)
for (size_t t = 0; t < threadGrp[g].size(); ++t) {
MxFiniteElement fe(elem_sizes);
fe.xi = fe.eta = fe.zeta = faceDir < 0 ? -1.0 : 1.0;
fe.u = gpar[0](1,1);
fe.v = gpar[1](1,1);
fe.w = gpar[2](1,1);
std::vector<Matrix> dNxdu(m_basis.size());
Matrix Xnod, Jac;
Vec4 X;
Vec3 normal;
for (size_t l = 0; l < threadGrp[g][t].size() && ok; ++l)
{
int iel = threadGrp[g][t][l];
fe.iel = MLGE[iel];
if (fe.iel < 1) continue; // zero-volume element
int i1 = p1 + iel % nel1;
int i2 = p2 + (iel / nel1) % nel2;
int i3 = p3 + iel / (nel1*nel2);
// Get element face area in the parameter space
double dA = this->getParametricArea(++iel,abs(faceDir));
if (dA < 0.0) // topology error (probably logic error)
{
ok = false;
break;
}
// Set up control point coordinates for current element
if (!this->getElementCoordinates(Xnod,iel))
{
ok = false;
break;
}
if (useElmVtx)
this->getElementCorners(i1-1,i2-1,i3-1,fe.XC);
// Initialize element quantities
LocalIntegral* A = integrand.getLocalIntegral(elem_sizes,fe.iel,true);
if (!integrand.initElementBou(MNPC[iel-1],elem_sizes,nb,*A))
{
A->destruct();
ok = false;
break;
}
// Define some loop control variables depending on which face we are on
int nf1, j1, j2;
switch (abs(faceDir))
{
case 1: nf1 = nel2; j2 = i3-p3; j1 = i2-p2; break;
case 2: nf1 = nel1; j2 = i3-p3; j1 = i1-p1; break;
case 3: nf1 = nel1; j2 = i2-p2; j1 = i1-p1; break;
default: nf1 = j1 = j2 = 0;
}
// --- Integration loop over all Gauss points in each direction --------
int k1, k2, k3;
int ip = (j2*nGauss*nf1 + j1)*nGauss;
int jp = (j2*nf1 + j1)*nGauss*nGauss;
fe.iGP = firstp + jp; // Global integration point counter
for (int j = 0; j < nGauss; j++, ip += nGauss*(nf1-1))
for (int i = 0; i < nGauss; i++, ip++, fe.iGP++)
{
// Local element coordinates and parameter values
// of current integration point
switch (abs(faceDir))
{
case 1: k2 = i; k3 = j; k1 = 0; break;
case 2: k1 = i; k3 = j; k2 = 0; break;
case 3: k1 = i; k2 = j; k3 = 0; break;
default: k1 = k2 = k3 = 0;
}
if (gpar[0].size() > 1)
{
fe.xi = xg[k1];
fe.u = gpar[0](k1+1,i1-p1+1);
}
if (gpar[1].size() > 1)
{
fe.eta = xg[k2];
fe.v = gpar[1](k2+1,i2-p2+1);
}
if (gpar[2].size() > 1)
{
fe.zeta = xg[k3];
fe.w = gpar[2](k3+1,i3-p3+1);
}
// Fetch basis function derivatives at current integration point
for (size_t b = 0; b < m_basis.size(); ++b)
SplineUtils::extractBasis(splinex[b][ip],fe.basis(b+1),dNxdu[b]);
// Compute Jacobian inverse of the coordinate mapping and
// basis function derivatives w.r.t. Cartesian coordinates
fe.detJxW = utl::Jacobian(Jac,normal,fe.grad(geoBasis),Xnod,dNxdu[geoBasis-1],t1,t2);
if (fe.detJxW == 0.0) continue; // skip singular points
for (size_t b = 0; b < m_basis.size(); ++b)
if (b != (size_t)geoBasis-1)
fe.grad(b+1).multiply(dNxdu[b],Jac);
if (faceDir < 0) normal *= -1.0;
// Cartesian coordinates of current integration point
X = Xnod * fe.basis(geoBasis);
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= 0.25*dA*wg[i]*wg[j];
if (!integrand.evalBouMx(*A,fe,time,X,normal))
ok = false;
}
// Finalize the element quantities
if (ok && !integrand.finalizeElementBou(*A,fe,time))
ok = false;
// Assembly of global system integral
if (ok && !glInt.assemble(A->ref(),fe.iel))
ok = false;
A->destruct();
}
}
}
return ok;
}
bool ASMs3Dmx::integrate (Integrand& integrand,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (!svol) return true; // silently ignore empty patches
if (m_basis.empty()) return false;
PROFILE2("ASMs3Dmx::integrate(I)");
bool use2ndDer = integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES;
bool useElmVtx = integrand.getIntegrandType() & Integrand::ELEMENT_CORNERS;
// Get Gaussian quadrature points and weights
const double* xg = GaussQuadrature::getCoord(nGauss);
const double* wg = GaussQuadrature::getWeight(nGauss);
if (!xg || !wg) return false;
// Compute parameter values of the Gauss points over the whole patch
std::array<Matrix,3> gpar;
for (int d = 0; d < 3; d++)
this->getGaussPointParameters(gpar[d],d,nGauss,xg);
// Evaluate basis function derivatives at all integration points
std::vector<std::vector<Go::BasisDerivs>> splinex(m_basis.size());
std::vector<std::vector<Go::BasisDerivs2>> splinex2(m_basis.size());
if (use2ndDer) {
#pragma omp parallel for schedule(static)
for (size_t i=0;i<m_basis.size();++i)
m_basis[i]->computeBasisGrid(gpar[0],gpar[1],gpar[2],splinex2[i]);
} else {
#pragma omp parallel for schedule(static)
for (size_t i=0;i<m_basis.size();++i)
m_basis[i]->computeBasisGrid(gpar[0],gpar[1],gpar[2],splinex[i]);
}
std::vector<size_t> elem_sizes;
for (auto& it : m_basis)
elem_sizes.push_back(it->order(0)*it->order(1)*it->order(2));
const int p1 = svol->order(0);
const int p2 = svol->order(1);
const int p3 = svol->order(2);
const int n1 = svol->numCoefs(0);
const int n2 = svol->numCoefs(1);
const int n3 = svol->numCoefs(2);
const int nel1 = n1 - p1 + 1;
const int nel2 = n2 - p2 + 1;
const int nel3 = n3 - p3 + 1;
// === Assembly loop over all elements in the patch ==========================
bool ok=true;
for (size_t g=0;g<threadGroupsVol.size() && ok;++g) {
#pragma omp parallel for schedule(static)
for (size_t t=0;t<threadGroupsVol[g].size();++t) {
MxFiniteElement fe(elem_sizes);
std::vector<Matrix> dNxdu(m_basis.size());
std::vector<Matrix3D> d2Nxdu2(m_basis.size());
Matrix3D Hess;
double dXidu[3];
Matrix Xnod, Jac;
Vec4 X;
for (size_t l = 0; l < threadGroupsVol[g][t].size() && ok; ++l)
{
int iel = threadGroupsVol[g][t][l];
fe.iel = MLGE[iel];
if (fe.iel < 1) continue; // zero-volume element
int i1 = p1 + iel % nel1;
int i2 = p2 + (iel / nel1) % nel3;
int i3 = p3 + iel / (nel1*nel2);
// Get element volume in the parameter space
double dV = this->getParametricVolume(++iel);
if (dV < 0.0) // topology error (probably logic error)
{
ok = false;
break;
}
// Set up control point (nodal) coordinates for current element
if (!this->getElementCoordinates(Xnod,iel))
{
ok = false;
break;
}
if (useElmVtx)
this->getElementCorners(i1-1,i2-1,i3-1,fe.XC);
if (integrand.getIntegrandType() & Integrand::G_MATRIX)
{
// Element size in parametric space
dXidu[0] = svol->knotSpan(0,i1-1);
dXidu[1] = svol->knotSpan(1,i2-1);
dXidu[2] = svol->knotSpan(2,i3-1);
}
// Initialize element quantities
LocalIntegral* A = integrand.getLocalIntegral(elem_sizes,fe.iel,false);
if (!integrand.initElement(MNPC[iel-1],elem_sizes,nb,*A))
{
A->destruct();
ok = false;
break;
}
// --- Integration loop over all Gauss points in each direction --------
int ip = (((i3-p3)*nGauss*nel2 + i2-p2)*nGauss*nel1 + i1-p1)*nGauss;
int jp = (((i3-p3)*nel2 + i2-p2*nel1 + i1-p1))*nGauss*nGauss*nGauss;
fe.iGP = firstIp + jp; // Global integration point counter
for (int k = 0; k < nGauss; k++, ip += nGauss*(nel2-1)*nGauss*nel1)
for (int j = 0; j < nGauss; j++, ip += nGauss*(nel1-1))
for (int i = 0; i < nGauss; i++, ip++, fe.iGP++)
{
// Local element coordinates of current integration point
fe.xi = xg[i];
fe.eta = xg[j];
fe.zeta = xg[k];
// Parameter values of current integration point
fe.u = gpar[0](i+1,i1-p1+1);
fe.v = gpar[1](j+1,i2-p2+1);
fe.w = gpar[2](k+1,i3-p3+1);
// Fetch basis function derivatives at current integration point
if (use2ndDer) {
for (size_t b = 0; b < m_basis.size(); ++b)
SplineUtils::extractBasis(splinex2[b][ip],fe.basis(b+1),dNxdu[b], d2Nxdu2[b]);
} else {
for (size_t b = 0; b < m_basis.size(); ++b)
SplineUtils::extractBasis(splinex[b][ip],fe.basis(b+1),dNxdu[b]);
}
// Compute Jacobian inverse of the coordinate mapping and
// basis function derivatives w.r.t. Cartesian coordinates
fe.detJxW = utl::Jacobian(Jac,fe.grad(geoBasis),Xnod,
dNxdu[geoBasis-1]);
if (fe.detJxW == 0.0) continue; // skip singular points
for (size_t b = 0; b < m_basis.size(); ++b)
if (b != (size_t)geoBasis-1)
fe.grad(b+1).multiply(dNxdu[b],Jac);
// Compute Hessian of coordinate mapping and 2nd order derivatives
if (use2ndDer) {
if (!utl::Hessian(Hess,fe.hess(geoBasis),Jac,Xnod,
d2Nxdu2[geoBasis-1],fe.grad(geoBasis),true))
ok = false;
for (size_t b = 0; b < m_basis.size() && ok; ++b)
if ((int)b != geoBasis)
if (!utl::Hessian(Hess,fe.hess(b+1),Jac,Xnod,
d2Nxdu2[b],fe.grad(b+1),false))
ok = false;
}
// Compute G-matrix
if (integrand.getIntegrandType() & Integrand::G_MATRIX)
utl::getGmat(Jac,dXidu,fe.G);
// Cartesian coordinates of current integration point
X = Xnod * fe.basis(geoBasis);
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= 0.125*dV*wg[i]*wg[j]*wg[k];
if (!integrand.evalIntMx(*A,fe,time,X))
ok = false;
}
// Finalize the element quantities
if (ok && !integrand.finalizeElement(*A,time,firstIp+jp))
ok = false;
// Assembly of global system integral
if (ok && !glInt.assemble(A->ref(),fe.iel))
ok = false;
A->destruct();
}
}
}
return ok;
}
bool ASMs2DmxLag::evalSolution (Matrix& sField, const IntegrandBase& integrand,
const RealArray*, bool) const
{
sField.resize(0,0);
double incx = 2.0/double(p1-1);
double incy = 2.0/double(p2-1);
size_t nPoints = nb[0];
IntVec check(nPoints,0);
MxFiniteElement fe(elem_size);
Vector solPt;
Vectors globSolPt(nPoints);
Matrices dNxdu(nxx.size());
Matrix Xnod, Jac;
// Evaluate the secondary solution field at each point
for (size_t iel = 1; iel <= nel; iel++)
{
IntVec::const_iterator f2start = geoBasis == 1? MNPC[iel-1].begin() :
MNPC[iel-1].begin() +
std::accumulate(elem_size.begin()+geoBasis-2,
elem_size.begin()+geoBasis-1, 0);
IntVec::const_iterator f2end = f2start + elem_size[geoBasis-1];
IntVec mnpc1(f2start,f2end);
this->getElementCoordinates(Xnod,iel);
int i, j, loc = 0;
for (j = 0; j < p2; j++)
for (i = 0; i < p1; i++, loc++)
{
double xi = -1.0 + i*incx;
double eta = -1.0 + j*incy;
for (size_t b = 0; b < nxx.size(); ++b)
if (!Lagrange::computeBasis(fe.basis(b+1),dNxdu[b],elem_sizes[b][0],xi,
elem_sizes[b][1],eta))
return false;
// Compute the Jacobian inverse
fe.detJxW = utl::Jacobian(Jac,fe.grad(geoBasis),Xnod,dNxdu[geoBasis-1]);
for (size_t b = 1; b <= nxx.size(); b++)
if (b != (size_t)geoBasis)
{
if (fe.detJxW == 0.0)
fe.grad(b).clear();
else
fe.grad(b).multiply(dNxdu[b-1],Jac);
}
// Now evaluate the solution field
if (!integrand.evalSol(solPt,fe,Xnod*fe.basis(geoBasis),MNPC[iel-1],elem_size,nb))
return false;
else if (sField.empty())
sField.resize(solPt.size(),nPoints,true);
if (++check[mnpc1[loc]] == 1)
globSolPt[mnpc1[loc]] = solPt;
else
globSolPt[mnpc1[loc]] += solPt;
}
}
for (size_t i = 0; i < nPoints; i++)
sField.fillColumn(1+i,globSolPt[i] /= check[i]);
return true;
}
bool ASMs2DmxLag::integrate (Integrand& integrand, int lIndex,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (this->empty()) return true; // silently ignore empty patches
// Get Gaussian quadrature points and weights
const double* xg = GaussQuadrature::getCoord(nGauss);
const double* wg = GaussQuadrature::getWeight(nGauss);
if (!xg || !wg) return false;
// Find the parametric direction of the edge normal {-2,-1, 1, 2}
const int edgeDir = (lIndex%10+1)/((lIndex%2) ? -2 : 2);
const int t1 = abs(edgeDir); // tangent direction normal to the patch edge
const int t2 = 3-t1; // tangent direction along the patch edge
// Extract the Neumann order flag (1 or higher) for the integrand
integrand.setNeumannOrder(1 + lIndex/10);
// Number of elements in each direction
const int nelx = (nxx[geoBasis-1]-1)/(elem_sizes[geoBasis-1][0]-1);
const int nely = (nyx[geoBasis-1]-1)/(elem_sizes[geoBasis-1][1]-1);
std::map<char,size_t>::const_iterator iit = firstBp.find(lIndex%10);
size_t firstp = iit == firstBp.end() ? 0 : iit->second;
MxFiniteElement fe(elem_size);
Matrices dNxdu(nxx.size());
Matrix Xnod, Jac;
Vec4 X;
Vec3 normal;
double xi[2];
// === Assembly loop over all elements on the patch edge =====================
int iel = 1;
for (int i2 = 0; i2 < nely; i2++)
for (int i1 = 0; i1 < nelx; i1++, iel++)
{
// Skip elements that are not on current boundary edge
bool skipMe = false;
switch (edgeDir)
{
case -1: if (i1 > 0) skipMe = true; break;
case 1: if (i1 < nelx-1) skipMe = true; break;
case -2: if (i2 > 0) skipMe = true; break;
case 2: if (i2 < nely-1) skipMe = true; break;
}
if (skipMe) continue;
// Set up control point coordinates for current element
if (!this->getElementCoordinates(Xnod,iel)) return false;
// Initialize element quantities
fe.iel = MLGE[iel-1];
LocalIntegral* A = integrand.getLocalIntegral(elem_size,fe.iel,true);
bool ok = integrand.initElementBou(MNPC[iel-1],elem_size,nb,*A);
// --- Integration loop over all Gauss points along the edge -------------
int jp = (t1 == 1 ? i2 : i1)*nGauss;
fe.iGP = firstp + jp; // Global integration point counter
for (int i = 0; i < nGauss && ok; i++, fe.iGP++)
{
// Gauss point coordinates along the edge
xi[t1-1] = edgeDir < 0 ? -1.0 : 1.0;
xi[t2-1] = xg[i];
// Compute the basis functions and their derivatives, using
// tensor product of one-dimensional Lagrange polynomials
for (size_t b = 0; b < nxx.size(); ++b)
if (!Lagrange::computeBasis(fe.basis(b+1),dNxdu[b],elem_sizes[b][0],xi[0],
elem_sizes[b][1],xi[1]))
ok = false;
// Compute basis function derivatives and the edge normal
fe.detJxW = utl::Jacobian(Jac,normal,fe.grad(geoBasis),Xnod,dNxdu[geoBasis-1],t1,t2);
if (fe.detJxW == 0.0) continue; // skip singular points
for (size_t b = 0; b < nxx.size(); ++b)
if (b != (size_t)geoBasis-1)
fe.grad(b+1).multiply(dNxdu[b],Jac);
if (edgeDir < 0) normal *= -1.0;
// Cartesian coordinates of current integration point
X = Xnod * fe.basis(geoBasis);
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= wg[i];
if (ok && !integrand.evalBouMx(*A,fe,time,X,normal))
ok = false;
}
// Finalize the element quantities
if (ok && !integrand.finalizeElementBou(*A,fe,time))
ok = false;
// Assembly of global system integral
if (ok && !glInt.assemble(A->ref(),fe.iel))
ok = false;
A->destruct();
if (!ok) return false;
}
return true;
}
bool ASMs2DmxLag::integrate (Integrand& integrand,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (this->empty()) return true; // silently ignore empty patches
// Get Gaussian quadrature points and weights
const double* xg = GaussQuadrature::getCoord(nGauss);
const double* wg = GaussQuadrature::getWeight(nGauss);
if (!xg || !wg) return false;
// Get parametric coordinates of the elements
RealArray upar, vpar;
this->getGridParameters(upar,0,1);
this->getGridParameters(vpar,1,1);
const int nelx = upar.size() - 1;
// === Assembly loop over all elements in the patch ==========================
bool ok = true;
for (size_t g = 0; g < threadGroups.size() && ok; g++)
{
#pragma omp parallel for schedule(static)
for (size_t t = 0; t < threadGroups[g].size(); t++)
{
MxFiniteElement fe(elem_size);
Matrices dNxdu(nxx.size());
Matrix Xnod, Jac;
Vec4 X;
for (size_t i = 0; i < threadGroups[g][t].size() && ok; ++i)
{
int iel = threadGroups[g][t][i];
int i1 = iel % nelx;
int i2 = iel / nelx;
// Set up control point coordinates for current element
if (!this->getElementCoordinates(Xnod,++iel))
{
ok = false;
break;
}
// Initialize element quantities
fe.iel = MLGE[iel-1];
LocalIntegral* A = integrand.getLocalIntegral(elem_size,fe.iel,false);
if (!integrand.initElement(MNPC[iel-1],elem_size,nb,*A))
{
A->destruct();
ok = false;
break;
}
// --- Integration loop over all Gauss points in each direction --------
int jp = (i2*nelx + i1)*nGauss*nGauss;
fe.iGP = firstIp + jp; // Global integration point counter
for (int j = 0; j < nGauss; j++)
for (int i = 0; i < nGauss; i++, fe.iGP++)
{
// Parameter value of current integration point
fe.u = 0.5*(upar[i1]*(1.0-xg[i]) + upar[i1+1]*(1.0+xg[i]));
fe.v = 0.5*(vpar[i2]*(1.0-xg[j]) + vpar[i2+1]*(1.0+xg[j]));
// Local coordinates of current integration point
fe.xi = xg[i];
fe.eta = xg[j];
// Compute basis function derivatives at current integration point
// using tensor product of one-dimensional Lagrange polynomials
for (size_t b = 0; b < nxx.size(); ++b)
if (!Lagrange::computeBasis(fe.basis(b+1),dNxdu[b],elem_sizes[b][0],xg[i],
elem_sizes[b][1],xg[j]))
ok = false;
// Compute Jacobian inverse of coordinate mapping and derivatives
fe.detJxW = utl::Jacobian(Jac,fe.grad(geoBasis),Xnod,dNxdu[geoBasis-1]);
if (fe.detJxW == 0.0) continue; // skip singular points
for (size_t b = 0; b < nxx.size(); ++b)
if (b != (size_t)geoBasis-1)
fe.grad(b+1).multiply(dNxdu[b],Jac);
// Cartesian coordinates of current integration point
X = Xnod * fe.basis(geoBasis);
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= wg[i]*wg[j];
if (!integrand.evalIntMx(*A,fe,time,X))
ok = false;
}
// Finalize the element quantities
if (ok && !integrand.finalizeElement(*A,time,firstIp+jp))
ok = false;
// Assembly of global system integral
if (ok && !glInt.assemble(A->ref(),fe.iel))
ok = false;
A->destruct();
}
}
}
return ok;
}
