bool ASMs1D::integrate (Integrand& integrand,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (!curv) 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 the reduced integration quadrature points, if needed
const double* xr = nullptr;
const double* wr = nullptr;
int nRed = integrand.getReducedIntegration(nGauss);
if (nRed > 0)
{
xr = GaussQuadrature::getCoord(nRed);
wr = GaussQuadrature::getWeight(nRed);
if (!xr || !wr) return false;
}
else if (nRed < 0)
nRed = nGauss; // The integrand needs to know nGauss
if (integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES)
if (curv->rational())
{
std::cerr <<" *** ASMs1D::integrate: Second-derivatives of NURBS "
<<" is not implemented yet, sorry..."<< std::endl;
return false;
}
// Compute parameter values of the Gauss points over the whole patch
Matrix gpar, redpar;
this->getGaussPointParameters(gpar,nGauss,xg);
if (xr)
this->getGaussPointParameters(redpar,nRed,xr);
const int p1 = curv->order();
FiniteElement fe(p1);
Matrix dNdu, Jac;
Matrix3D d2Ndu2, Hess;
Vec4 X;
if (nsd > 1 && (integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES))
fe.G.resize(nsd,2); // For storing d{X}/du and d2{X}/du2
// === Assembly loop over all elements in the patch ==========================
for (size_t iel = 0; iel < nel; iel++)
{
fe.iel = MLGE[iel];
if (fe.iel < 1) continue; // zero-length element
// Check that the current element has nonzero length
double dL = this->getParametricLength(1+iel);
if (dL < 0.0) return false; // topology error (probably logic error)
// Set up control point coordinates for current element
if (!this->getElementCoordinates(fe.Xn,1+iel)) return false;
if (integrand.getIntegrandType() & Integrand::ELEMENT_CORNERS)
this->getElementEnds(p1+iel,fe.XC);
if (integrand.getIntegrandType() & Integrand::NODAL_ROTATIONS)
{
this->getElementNodalRotations(fe.Tn,iel);
if (!elmCS.empty()) fe.Te = elmCS[iel];
}
// Initialize element matrices
LocalIntegral* A = integrand.getLocalIntegral(fe.N.size(),fe.iel);
bool ok = integrand.initElement(MNPC[iel],fe,X,nRed,*A);
if (xr)
{
// --- Selective reduced integration loop --------------------------------
for (int i = 0; i < nRed && ok; i++)
{
// Local element coordinates of current integration point
fe.xi = xr[i];
// Parameter values of current integration point
fe.u = redpar(1+i,1+iel);
if (integrand.getIntegrandType() & Integrand::NO_DERIVATIVES)
this->extractBasis(fe.u,fe.N);
else
{
// Fetch basis function derivatives at current point
this->extractBasis(fe.u,fe.N,dNdu);
// Compute Jacobian inverse and derivatives
dNdu.multiply(0.5*dL); // Derivatives w.r.t. xi=[-1,1]
fe.detJxW = utl::Jacobian(Jac,fe.dNdX,fe.Xn,dNdu)*wr[i];
}
// Cartesian coordinates of current integration point
X = fe.Xn * fe.N;
X.t = time.t;
// Compute the reduced integration terms of the integrand
ok = integrand.reducedInt(*A,fe,X);
}
}
// --- Integration loop over all Gauss points in current element -----------
int jp = iel*nGauss;
fe.iGP = firstIp + jp; // Global integration point counter
for (int i = 0; i < nGauss && ok; i++, fe.iGP++)
{
// Local element coordinate of current integration point
fe.xi = xg[i];
// Parameter value of current integration point
fe.u = gpar(1+i,1+iel);
// Compute basis functions and derivatives
if (integrand.getIntegrandType() & Integrand::NO_DERIVATIVES)
this->extractBasis(fe.u,fe.N);
else if (integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES)
this->extractBasis(fe.u,fe.N,dNdu,d2Ndu2);
else
this->extractBasis(fe.u,fe.N,dNdu);
if (!dNdu.empty())
{
// Compute derivatives in terms of physical coordinates
dNdu.multiply(0.5*dL); // Derivatives w.r.t. xi=[-1,1]
fe.detJxW = utl::Jacobian(Jac,fe.dNdX,fe.Xn,dNdu)*wg[i];
if (fe.detJxW == 0.0) continue; // skip singular points
// Compute Hessian of coordinate mapping and 2nd order derivatives
if (integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES)
{
d2Ndu2.multiply(0.25*dL*dL); // 2nd derivatives w.r.t. xi=[-1,1]
if (!utl::Hessian(Hess,fe.d2NdX2,Jac,fe.Xn,d2Ndu2,fe.dNdX))
ok = false;
else if (fe.G.cols() == 2)
{
// Store the first and second derivatives of {X} w.r.t.
// the parametric coordinate (xi), in the G-matrix
fe.G.fillColumn(1,Jac.ptr());
fe.G.fillColumn(2,Hess.ptr());
}
}
}
// Cartesian coordinates of current integration point
X = fe.Xn * fe.N;
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
if (ok && !integrand.evalInt(*A,fe,time,X))
ok = false;
}
// Finalize the element quantities
if (ok && !integrand.finalizeElement(*A,fe,time,firstIp+jp))
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 ASMs2DLag::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
int nG1 = this->getNoGaussPt(lIndex%10 < 3 ? p1 : p2, true);
int nGP = integrand.getBouIntegrationPoints(nG1);
const double* xg = GaussQuadrature::getCoord(nGP);
const double* wg = GaussQuadrature::getWeight(nGP);
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
// Number of elements in each direction
const int nelx = (nx-1)/(p1-1);
const int nely = (ny-1)/(p2-1);
// Get parametric coordinates of the elements
FiniteElement fe(p1*p2);
RealArray upar, vpar;
if (t1 == 1)
{
fe.u = edgeDir < 0 ? surf->startparam_u() : surf->endparam_u();
this->getGridParameters(vpar,1,1);
}
else if (t1 == 2)
{
this->getGridParameters(upar,0,1);
fe.v = edgeDir < 0 ? surf->startparam_v() : surf->endparam_v();
}
// Extract the Neumann order flag (1 or higher) for the integrand
integrand.setNeumannOrder(1 + lIndex/10);
// Integrate the extraordinary elements?
size_t doXelms = 0;
if (integrand.getIntegrandType() & Integrand::XO_ELEMENTS)
if ((doXelms = nelx*nely)*2 > MNPC.size())
{
std::cerr <<" *** ASMs2DLag::integrate: Too few XO-elements "
<< MNPC.size() - doXelms << std::endl;
return false;
}
std::map<char,size_t>::const_iterator iit = firstBp.find(lIndex%10);
size_t firstp = iit == firstBp.end() ? 0 : iit->second;
Matrix dNdu, 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 nodal point coordinates for current element
if (!this->getElementCoordinates(Xnod,iel)) return false;
// Initialize element quantities
fe.iel = abs(MLGE[doXelms+iel-1]);
LocalIntegral* A = integrand.getLocalIntegral(fe.N.size(),fe.iel,true);
bool ok = integrand.initElementBou(MNPC[doXelms+iel-1],*A);
// --- Integration loop over all Gauss points along the edge -------------
int jp = (t1 == 1 ? i2 : i1)*nGP;
fe.iGP = firstp + jp; // Global integration point counter
for (int i = 0; i < nGP && ok; i++, fe.iGP++)
{
// Local element coordinates of current integration point
xi[t1-1] = edgeDir < 0 ? -1.0 : 1.0;
xi[t2-1] = xg[i];
fe.xi = xi[0];
fe.eta = xi[1];
// Parameter values of current integration point
if (upar.size() > 1)
fe.u = 0.5*(upar[i1]*(1.0-xg[i]) + upar[i1+1]*(1.0+xg[i]));
if (vpar.size() > 1)
fe.v = 0.5*(vpar[i2]*(1.0-xg[i]) + vpar[i2+1]*(1.0+xg[i]));
// Compute the basis functions and their derivatives, using
// tensor product of one-dimensional Lagrange polynomials
if (!Lagrange::computeBasis(fe.N,dNdu,p1,xi[0],p2,xi[1]))
ok = false;
// Compute basis function derivatives and the edge normal
fe.detJxW = utl::Jacobian(Jac,normal,fe.dNdX,Xnod,dNdu,t1,t2);
if (fe.detJxW == 0.0) continue; // skip singular points
if (edgeDir < 0) normal *= -1.0;
// Cartesian coordinates of current integration point
X = Xnod * fe.N;
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= wg[i];
if (ok && !integrand.evalBou(*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 ASMs1DSpec::integrate (Integrand& integrand,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (!curv) return true; // silently ignore empty patches
// Order of basis (order = degree + 1)
const int p1 = curv->order();
const int n1 = nGauss < 1 ? p1 : nGauss;
// Evaluate integration points and weights
Vector wg1, xg1, points1;
if (!Legendre::GLL(wg1,points1,p1))
return false;
Matrix D1;
if (nGauss < 1)
{
// We are using the nodal points themselves as integration points
if (!Legendre::basisDerivatives(n1,D1))
return false;
}
else
// Using Gauss-Legendre scheme with nGauss points
if (!Legendre::GL(wg1,xg1,n1))
return false;
FiniteElement fe(p1);
Matrix dNdu, Xnod, Jac;
Vec4 X;
// === Assembly loop over all elements in the patch ==========================
const int nel = this->getNoElms();
for (int iel = 1; iel <= nel; iel++)
{
// 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(p1,fe.iel);
if (!integrand.initElement(MNPC[iel-1],*A)) return false;
// --- Integration loop over integration points ----------------------------
for (int i = 0; i < n1; i++)
{
// Compute basis function derivatives at current integration point
if (nGauss < 1)
{
fe.N.fill(0.0);
fe.N(i+1) = 1.0;
dNdu.fillColumn(1,D1.getRow(i+1));
}
else
if (!Lagrange::computeBasis(fe.N,&dNdu,points1,xg1[i]))
return false;
// Compute Jacobian inverse of coordinate mapping and derivatives
fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu);
// Cartesian coordinates of current integration point
X = Xnod*fe.N;
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= wg1[i];
if (!integrand.evalInt(*A,fe,time,X))
return false;
}
// Assembly of global system integral
if (!glInt.assemble(A->ref(),fe.iel))
return false;
A->destruct();
}
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 ASMs2DLag::integrate (Integrand& integrand,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (this->empty()) return true; // silently ignore empty patches
// Get Gaussian quadrature points and weights
std::array<int,2> ng;
std::array<const double*,2> xg, wg;
for (int d = 0; d < 2; d++)
{
ng[d] = this->getNoGaussPt(d == 0 ? p1 : p2);
xg[d] = GaussQuadrature::getCoord(ng[d]);
wg[d] = GaussQuadrature::getWeight(ng[d]);
if (!xg[d] || !wg[d]) return false;
}
// Get the reduced integration quadrature points, if needed
const double* xr = nullptr;
const double* wr = nullptr;
int nRed = integrand.getReducedIntegration(ng[0]);
if (nRed > 0)
{
xr = GaussQuadrature::getCoord(nRed);
wr = GaussQuadrature::getWeight(nRed);
if (!xr || !wr) return false;
}
else if (nRed < 0)
nRed = ng[0]; // The integrand needs to know nGauss
// Get parametric coordinates of the elements
RealArray upar, vpar;
this->getGridParameters(upar,0,1);
this->getGridParameters(vpar,1,1);
// Number of elements in each direction
const int nelx = upar.empty() ? 0 : 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++)
{
FiniteElement fe(p1*p2);
Matrix dNdu, Xnod, Jac;
Vec4 X;
for (size_t i = 0; i < threadGroups[g][t].size() && ok; i++)
{
int iel = threadGroups[g][t][i];
int i1 = nelx > 0 ? iel % nelx : 0;
int i2 = nelx > 0 ? iel / nelx : 0;
// Set up nodal point coordinates for current element
if (!this->getElementCoordinates(Xnod,1+iel))
{
ok = false;
break;
}
if (integrand.getIntegrandType() & Integrand::ELEMENT_CENTER)
{
// Compute the element "center" (average of element node coordinates)
X = 0.0;
for (size_t i = 1; i <= nsd; i++)
for (size_t j = 1; j <= Xnod.cols(); j++)
X[i-1] += Xnod(i,j);
X *= 1.0/(double)Xnod.cols();
}
// Initialize element quantities
fe.iel = MLGE[iel];
LocalIntegral* A = integrand.getLocalIntegral(fe.N.size(),fe.iel);
if (!integrand.initElement(MNPC[iel],fe,X,nRed*nRed,*A))
{
A->destruct();
ok = false;
break;
}
if (xr)
{
// --- Selective reduced integration loop ----------------------------
for (int j = 0; j < nRed; j++)
for (int i = 0; i < nRed; i++)
{
// Local element coordinates of current integration point
fe.xi = xr[i];
fe.eta = xr[j];
// Parameter value of current integration point
if (!upar.empty())
fe.u = 0.5*(upar[i1]*(1.0-xr[i]) + upar[i1+1]*(1.0+xr[i]));
if (!vpar.empty())
fe.v = 0.5*(vpar[i2]*(1.0-xr[j]) + vpar[i2+1]*(1.0+xr[j]));
// Compute basis function derivatives at current point
// using tensor product of one-dimensional Lagrange polynomials
if (!Lagrange::computeBasis(fe.N,dNdu,p1,xr[i],p2,xr[j]))
ok = false;
// Compute Jacobian inverse and derivatives
fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu);
// Cartesian coordinates of current integration point
X = Xnod * fe.N;
X.t = time.t;
// Compute the reduced integration terms of the integrand
fe.detJxW *= wr[i]*wr[j];
if (!integrand.reducedInt(*A,fe,X))
ok = false;
}
}
// --- Integration loop over all Gauss points in each direction --------
int jp = iel*ng[0]*ng[1];
fe.iGP = firstIp + jp; // Global integration point counter
for (int j = 0; j < ng[1]; j++)
for (int i = 0; i < ng[0]; i++, fe.iGP++)
{
// Local element coordinates of current integration point
fe.xi = xg[0][i];
fe.eta = xg[1][j];
// Parameter value of current integration point
if (!upar.empty())
fe.u = 0.5*(upar[i1]*(1.0-xg[0][i]) + upar[i1+1]*(1.0+xg[0][i]));
if (!vpar.empty())
fe.v = 0.5*(vpar[i2]*(1.0-xg[1][j]) + vpar[i2+1]*(1.0+xg[1][j]));
// Compute basis function derivatives at current integration point
// using tensor product of one-dimensional Lagrange polynomials
if (!Lagrange::computeBasis(fe.N,dNdu,p1,xg[0][i],p2,xg[1][j]))
ok = false;
// Compute Jacobian inverse of coordinate mapping and derivatives
fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu);
if (fe.detJxW == 0.0) continue; // skip singular points
// Cartesian coordinates of current integration point
X = Xnod * fe.N;
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= wg[0][i]*wg[1][j];
if (!integrand.evalInt(*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 ASMs2DSpec::integrate (Integrand& integrand,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (this->empty()) return true; // silently ignore empty patches
// Evaluate integration points (= nodal points) and weights
Vector wg1,xg1,wg2,xg2;
if (!Legendre::GLL(wg1,xg1,p1)) return false;
if (!Legendre::GLL(wg2,xg2,p2)) return false;
Matrix D1, D2;
if (!Legendre::basisDerivatives(p1,D1)) return false;
if (!Legendre::basisDerivatives(p2,D2)) return false;
// === 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++)
{
FiniteElement fe(p1*p2);
Matrix dNdu(p1*p2,2), Xnod, Jac;
Vec4 X;
for (size_t e = 0; e < threadGroups[g][t].size(); e++)
{
int iel = threadGroups[g][t][e]+1;
// 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(fe.N.size(),fe.iel);
if (!integrand.initElement(MNPC[iel-1],*A))
{
A->destruct();
ok = false;
break;
}
// --- Integration loop over all Gauss points in each direction --------
int count = 1;
for (int j = 1; j <= p2; j++)
for (int i = 1; i <= p1; i++, count++)
{
// Evaluate the basis functions and gradients using
// tensor product of one-dimensional Lagrange polynomials
evalBasis(i,j,p1,p2,D1,D2,fe.N,dNdu);
// Compute Jacobian inverse of coordinate mapping and derivatives
fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu);
if (fe.detJxW == 0.0) continue; // skip singular points
// Cartesian coordinates of current integration point
X.x = Xnod(1,count);
X.y = Xnod(2,count);
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= wg1(i)*wg2(j);
if (!integrand.evalInt(*A,fe,time,X))
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 ASMs2DSpec::integrate (Integrand& integrand, int lIndex,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (this->empty()) return true; // silently ignore empty patches
// Find the parametric direction of the edge normal {-2,-1, 1, 2}
int edgeDir = lIndex = (lIndex+1)/((lIndex%2) ? -2 : 2);
const int t1 = abs(edgeDir); // Tangent direction normal to the patch edge
const int t2 = 3-abs(edgeDir); // Tangent direction along the patch edge
// Number of elements in each direction
int n1, n2;
this->getSize(n1,n2);
const int nelx = (n1-1)/(p1-1);
const int nely = (n2-1)/(p2-1);
// Evaluate integration points and weights
std::array<Vector,2> wg, xg;
std::array<Matrix,2> D;
std::array<int,2> p({{p1,p2}});
for (int d = 0; d < 2; d++)
{
if (!Legendre::GLL(wg[d],xg[d],p[d])) return false;
if (!Legendre::basisDerivatives(p[d],D[d])) return false;
}
int nen = p1*p2;
FiniteElement fe(nen);
Matrix dNdu(nen,2), Xnod, Jac;
Vec4 X;
Vec3 normal;
int 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(nen,fe.iel,true);
if (!integrand.initElementBou(MNPC[iel-1],*A)) return false;
// --- Integration loop over all Gauss points along the edge -------------
for (int i = 0; i < p[t2-1]; i++)
{
// "Coordinates" along the edge
xi[t1-1] = edgeDir < 0 ? 1 : p[t1-1];
xi[t2-1] = i+1;
// Evaluate the basis functions and gradients using
// tensor product of one-dimensional Lagrange polynomials
evalBasis(xi[0],xi[1],p1,p2,D[0],D[1],fe.N,dNdu);
// Compute basis function derivatives and the edge normal
fe.detJxW = utl::Jacobian(Jac,normal,fe.dNdX,Xnod,dNdu,t1,t2);
if (fe.detJxW == 0.0) continue; // skip singular points
if (edgeDir < 0) normal *= -1.0;
// Cartesian coordinates of current integration point
X = Xnod * fe.N;
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= wg[t2-1][i];
if (!integrand.evalBou(*A,fe,time,X,normal))
return false;
}
// Finalize the element quantities
if (!integrand.finalizeElementBou(*A,fe,time))
return false;
// Assembly of global system integral
if (!glInt.assemble(A->ref(),fe.iel))
return false;
A->destruct();
}
return true;
}
bool ASMs3DSpec::integrateEdge (Integrand& integrand, int lEdge,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (!svol) return true; // silently ignore empty patches
// Parametric direction of the edge {0, 1, 2}
const int lDir = (lEdge-1)/4;
// Order of basis in the three parametric directions (order = degree + 1)
const int p1 = svol->order(0);
const int p2 = svol->order(1);
const int p3 = svol->order(2);
const int pe = svol->order(lDir);
// Number of elements in each direction
int n1, n2, n3;
this->getSize(n1,n2,n3);
const int nelx = (n1-1)/(p1-1);
const int nely = (n2-1)/(p2-1);
const int nelz = (n3-1)/(p3-1);
// Evaluate integration points (=nodal points) and weights
std::array<Vector,3> wg, xg;
if (!Legendre::GLL(wg[0],xg[0],p1)) return false;
if (!Legendre::GLL(wg[1],xg[1],p2)) return false;
if (!Legendre::GLL(wg[2],xg[2],p3)) return false;
Matrix D1, D2, D3;
if (!Legendre::basisDerivatives(p1,D1)) return false;
if (!Legendre::basisDerivatives(p2,D2)) return false;
if (!Legendre::basisDerivatives(p3,D3)) return false;
const int nen = p1*p2*p3;
FiniteElement fe(nen);
Matrix dNdu(nen,3), Xnod, Jac;
Vec4 X;
Vec3 tangent;
int xi[3];
switch (lEdge)
{
case 1: xi[1] = 1; xi[2] = 1; break;
case 2: xi[1] = p2; xi[2] = 1; break;
case 3: xi[1] = 1; xi[2] = p3; break;
case 4: xi[1] = p2; xi[2] = p3; break;
case 5: xi[0] = 1; xi[2] = 1; break;
case 6: xi[0] = p1; xi[2] = 1; break;
case 7: xi[0] = 1; xi[2] = p3; break;
case 8: xi[0] = p1; xi[2] = p3; break;
case 9: xi[0] = 1; xi[1] = 1; break;
case 10: xi[0] = p1; xi[1] = 1; break;
case 11: xi[0] = 1; xi[1] = p2; break;
case 12: xi[0] = p1; xi[1] = p2; break;
}
// === Assembly loop over all elements on the patch edge =====================
int iel = 1;
for (int i3 = 0; i3 < nelz; i3++)
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 (lEdge)
{
case 1: if (i2 > 0 || i3 > 0) skipMe = true; break;
case 2: if (i2 < nely-1 || i3 > 0) skipMe = true; break;
case 3: if (i2 > 0 || i3 < nelz-1) skipMe = true; break;
case 4: if (i2 < nely-1 || i3 < nelz-1) skipMe = true; break;
case 5: if (i1 > 0 || i3 > 0) skipMe = true; break;
case 6: if (i1 < nelx-1 || i3 > 0) skipMe = true; break;
case 7: if (i1 > 0 || i3 < nelz-1) skipMe = true; break;
case 8: if (i1 < nelx-1 || i3 < nelz-1) skipMe = true; break;
case 9: if (i1 > 0 || i2 > 0) skipMe = true; break;
case 10: if (i1 < nelx-1 || i2 > 0) skipMe = true; break;
case 11: if (i1 > 0 || i2 < nely-1) skipMe = true; break;
case 12: if (i1 < nelx-1 || i2 < nely-1) skipMe = true; break;
}
if (skipMe) continue;
// Set up nodal point coordinates for current element
if (!this->getElementCoordinates(Xnod,iel)) return false;
// Initialize element quantities
fe.iel = MLGE[iel-1];
LocalIntegral* A = integrand.getLocalIntegral(nen,fe.iel,true);
if (!integrand.initElementBou(MNPC[iel-1],*A)) return false;
// --- Integration loop over all Gauss points along the edge -----------
for (int i = 0; i < pe; i++)
{
// "Coordinate" on the edge
xi[lDir] = i+1;
// Compute the basis functions and their derivatives, using
// tensor product of one-dimensional Lagrange polynomials
evalBasis(xi[0],xi[1],xi[2],p1,p2,p3,D1,D2,D3,fe.N,dNdu);
// Compute basis function derivatives and the edge tangent
fe.detJxW = utl::Jacobian(Jac,tangent,fe.dNdX,Xnod,dNdu,1+lDir);
if (fe.detJxW == 0.0) continue; // skip singular points
// Cartesian coordinates of current integration point
X = Xnod * fe.N;
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= wg[lDir][i];
if (!integrand.evalBou(*A,fe,time,X,tangent))
return false;
}
// Finalize the element quantities
if (!integrand.finalizeElementBou(*A,fe,time))
return false;
// Assembly of global system integral
if (!glInt.assemble(A->ref(),fe.iel))
return false;
}
return true;
}
bool ASMs3DSpec::integrate (Integrand& integrand, int lIndex,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (!svol) return true; // silently ignore empty patches
std::map<char,ThreadGroups>::const_iterator tit;
if ((tit = threadGroupsFace.find(lIndex)) == threadGroupsFace.end())
{
std::cerr <<" *** ASMs3DSpec::integrate: No thread groups for face "<<lIndex
<< std::endl;
return false;
}
const ThreadGroups& threadGrp = tit->second;
// 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 t0 = abs(faceDir); // unsigned normal direction of the face
const int t1 = 1 + t0%3; // first tangent direction of the face
const int t2 = 1 + t1%3; // second tangent direction of the face
// Order of basis in the three parametric directions (order = degree + 1)
int p[3];
p[0] = svol->order(0);
p[1] = svol->order(1);
p[2] = svol->order(2);
// Evaluate integration points (=nodal points) and weights
std::array<Vector,3> xg, wg;
std::array<Matrix,3> D;
for (int d = 0; d < 3; d++)
{
if (!Legendre::GLL(wg[d],xg[d],p[d])) return false;
if (!Legendre::basisDerivatives(p[d],D[d])) return false;
}
int nen = p[0]*p[1]*p[2];
// === 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++)
{
FiniteElement fe(nen);
Matrix dNdu(nen,3), Xnod, Jac;
Vec4 X;
Vec3 normal;
int xi[3];
for (size_t l = 0; l < threadGrp[g][t].size(); l++)
{
int iel = threadGrp[g][t][l];
// Set up nodal 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(nen,fe.iel,true);
if (!integrand.initElementBou(MNPC[iel-1],*A))
{
A->destruct();
ok = false;
break;
}
// --- Integration loop over all Gauss points in each direction --------
for (int j = 0; j < p[t2-1]; j++)
for (int i = 0; i < p[t1-1]; i++)
{
// "Coordinates" on the face
xi[t0-1] = faceDir < 0 ? 1 : p[t0-1];
xi[t1-1] = i+1;
xi[t2-1] = j+1;
// Compute the basis functions and their derivatives, using
// tensor product of one-dimensional Lagrange polynomials
evalBasis(xi[0],xi[1],xi[2],p[0],p[1],p[2],D[0],D[1],D[2],fe.N,dNdu);
// Compute basis function derivatives and the face normal
fe.detJxW = utl::Jacobian(Jac,normal,fe.dNdX,Xnod,dNdu,t1,t2);
if (fe.detJxW == 0.0) continue; // skip singular points
if (faceDir < 0) normal *= -1.0;
// Cartesian coordinates of current integration point
X = Xnod * fe.N;
X.t = time.t;
// Evaluate the integrand and accumulate element contributions
fe.detJxW *= wg[t1-1][i]*wg[t2-1][j];
if (!integrand.evalBou(*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 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;
}
