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 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;
}