bool LagrangeFields2D::gradFE (const FiniteElement& fe, Matrix& grad) const
{
grad.resize(nf,2,true);
Vector N;
Matrix dNdu;
if (!Lagrange::computeBasis(N,dNdu,p1,fe.xi,p2,fe.eta))
return false;
const int nel1 = (n1-1)/p1;
div_t divresult = div(fe.iel,nel1);
int iel1 = divresult.rem;
int iel2 = divresult.quot;
const int node1 = p1*iel1-1;
const int node2 = p2*iel2-1;
const int nen = (p1+1)*(p2+1);
Matrix Xnod(2,nen), Vnod(nf,nen);
int locNode = 1;
for (int j = node2; j <= node2+p2; j++)
for (int i = node1; i <= node1+p1; i++, locNode++)
{
int node = (j-1)*n1 + i;
Xnod.fillColumn(locNode,coord.getColumn(node));
Vnod.fillColumn(locNode,values.ptr()+nf*(node-1));
}
Matrix Jac, dNdX;
utl::Jacobian(Jac,dNdX,Xnod,dNdu);
grad.multiply(Vnod,dNdX);
return true;
}
bool LagrangeField3D::gradFE (const FiniteElement& fe, Vector& grad) const
{
grad.resize(3,true);
Vector Vnod;
Matrix dNdu;
if (!Lagrange::computeBasis(Vnod,dNdu,p1,fe.xi,p2,fe.eta,p3,fe.zeta))
return false;
const int nel1 = (n1-1)/p1;
const int nel2 = (n2-1)/p2;
div_t divresult = div(fe.iel,nel1*nel2);
int iel2 = divresult.rem;
int iel3 = divresult.quot;
divresult = div(iel2,nel1);
int iel1 = divresult.rem;
iel2 = divresult.quot;
const int node1 = p1*iel1-1;
const int node2 = p2*iel2-1;
const int node3 = p3*iel3-1;
const int nen = (p1+1)*(p2+1)*(p3+1);
Matrix Xnod(3,nen);
int locNode = 1;
for (int k = node3; k <= node3+p3; k++)
for (int j = node2; j <= node2+p2; j++)
for (int i = node1; i <= node1+p1; i++, locNode++)
{
int node = (k-1)*n1*n2 + (j-1)*n1 + i;
Xnod.fillColumn(locNode,coord.getColumn(node));
Vnod(locNode) = values(node);
}
Matrix Jac, dNdX;
utl::Jacobian(Jac,dNdX,Xnod,dNdu);
return dNdX.multiply(Vnod,grad);
}
bool ASMs3DLag::integrate (Integrand& integrand,
GlobalIntegral& glInt,
const TimeDomain& time)
{
if (!svol) 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
// Get parametric coordinates of the elements
RealArray upar, vpar, wpar;
this->getGridParameters(upar,0,1);
this->getGridParameters(vpar,1,1);
this->getGridParameters(wpar,2,1);
// Number of elements in each direction
const int nel1 = upar.size() - 1;
const int nel2 = vpar.size() - 1;
// 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);
// === 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++)
{
FiniteElement fe(p1*p2*p3);
Matrix dNdu, Xnod, Jac;
Vec4 X;
for (size_t l = 0; l < threadGroupsVol[g][t].size() && ok; l++)
{
int iel = threadGroupsVol[g][t][l];
int i1 = iel % nel1;
int i2 = (iel / nel1) % nel2;
int i3 = iel / (nel1*nel2);
// Set up nodal point coordinates for current element
if (!this->getElementCoordinates(Xnod,++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 <= 3; 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-1];
LocalIntegral* A = integrand.getLocalIntegral(fe.N.size(),fe.iel);
if (!integrand.initElement(MNPC[iel-1],fe,X,nRed*nRed*nRed,*A))
{
A->destruct();
ok = false;
break;
}
if (xr)
{
// --- Selective reduced integration loop ----------------------------
for (int k = 0; k < nRed; k++)
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];
fe.zeta = xr[k];
// Parameter value of current integration point
fe.u = 0.5*(upar[i1]*(1.0-xr[i]) + upar[i1+1]*(1.0+xr[i]));
fe.v = 0.5*(vpar[i2]*(1.0-xr[j]) + vpar[i2+1]*(1.0+xr[j]));
fe.w = 0.5*(wpar[i3]*(1.0-xr[k]) + wpar[i3+1]*(1.0+xr[k]));
// 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],p3,xr[k]))
{
ok = false;
break;
}
// 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]*wr[k];
if (!integrand.reducedInt(*A,fe,X))
ok = false;
}
}
// --- Integration loop over all Gauss points in each direction --------
int jp = ((i3*nel2 + i2)*nel1 + i1)*nGauss*nGauss*nGauss;
fe.iGP = firstIp + jp; // Global integration point counter
for (int k = 0; k < nGauss; k++)
for (int j = 0; j < nGauss; j++)
for (int i = 0; i < nGauss; i++, fe.iGP++)
{
// Local element coordinates of current integration point
fe.xi = xg[i];
fe.eta = xg[j];
fe.zeta = xg[k];
// 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]));
fe.w = 0.5*(wpar[i3]*(1.0-xg[k]) + wpar[i3+1]*(1.0+xg[k]));
// Compute basis function derivatives at current integration point
// using tensor product of one-dimensional Lagrange polynomials
if (!Lagrange::computeBasis(fe.N,dNdu,p1,xg[i],p2,xg[j],p3,xg[k]))
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[i]*wg[j]*wg[k];
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 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;
}
