/**
* Returns the function value at x
*/
double BSpline::eval(DenseVector x) const
{
checkInput(x);
// NOTE: casting to DenseVector to allow accessing as res(0)
DenseVector res = coefficients.transpose()*evalBasis(x);
return res(0);
}
bool ASMs2DSpec::evalSolution (Matrix& sField, const IntegrandBase& integrand,
const RealArray*, bool) const
{
sField.resize(0,0);
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;
size_t nPoints = this->getNoNodes();
IntVec check(nPoints,0);
FiniteElement fe(p1*p2);
Vector solPt;
Vectors globSolPt(nPoints);
Matrix dNdu(p1*p2,2), Xnod, Jac;
// Evaluate the secondary solution field at each point
const int nel = this->getNoElms();
for (int iel = 1; iel <= nel; iel++)
{
const IntVec& mnpc = MNPC[iel-1];
this->getElementCoordinates(Xnod,iel);
int i, j, loc = 0;
for (j = 0; j < p2; j++)
for (i = 0; i < p1; i++, loc++)
{
evalBasis(i+1,j+1,p1,p2,D1,D2,fe.N,dNdu);
// Compute the Jacobian inverse
fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu);
// Now evaluate the solution field
if (!integrand.evalSol(solPt,fe,Xnod.getColumn(loc+1),mnpc))
return false;
else if (sField.empty())
sField.resize(solPt.size(),nPoints,true);
if (++check[mnpc[loc]] == 1)
globSolPt[mnpc[loc]] = solPt;
else
globSolPt[mnpc[loc]] += solPt;
}
}
for (size_t i = 0; i < nPoints; i++)
sField.fillColumn(1+i,globSolPt[i] /= check[i]);
return true;
}
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 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;
}
