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::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;
}