Go::SplineCurve* SplineUtils::project (const Go::SplineCurve* curve,
const FunctionBase& f,
int nComp, Real time)
{
if (!curve || nComp < 1) return nullptr;
const Go::BsplineBasis& basis = curve->basis();
const int nPoints = basis.numCoefs();
Go::Point X;
RealArray gpar(nPoints), fval, fOfX;
fval.reserve(nComp*nPoints);
// Compute parameter values of the function sampling points (Greville points)
// and evaluate the function at these points
for (int i = 0; i < nPoints; i++)
{
gpar[i] = basis.grevilleParameter(i);
curve->point(X,gpar[i]);
fOfX = f.getValue(toVec4(X,time));
fval.insert(fval.end(),fOfX.begin(),fOfX.begin()+nComp);
}
// Get weights for rational spline curves (NURBS)
RealArray weights;
if (curve->rational())
curve->getWeights(weights);
// Project the function onto the spline basis to find control point values
return Go::CurveInterpolator::regularInterpolation(basis,gpar,fval,nComp,
curve->rational(),weights);
}
void SparseTileLayoutData<Dim>::initialize(const Domain_t &bbox,
const PatchList_t &plist,
const ContextMapper<Dim> &cmap)
{
this->blocks_m = Loc<Dim>();
initialize(bbox);
TilePartition<Dim> gpar(plist);
gpar.partition(bbox,this->all_m,cmap);
syncPatch();
}
TEST(TestSplineUtils, ExtractBasisVolume)
{
Go::SphereVolume sphere(1.0, Go::Point(0.0, 0.0, 0.0),
Go::Point(0.0, 0.0, 1.0), Go::Point(1.0, 0.0, 0.0));
Go::SplineVolume* vol = sphere.geometryVolume();
vol->setParameterDomain(0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
std::vector<Go::BasisDerivs> spline;
std::vector<Go::BasisDerivs2> spline2;
Matrix gpar(1, 1);
gpar(1,1) = 0.3;
vol->computeBasisGrid(gpar,gpar,gpar,spline);
vol->raiseOrder(1,1,1);
vol->computeBasisGrid(gpar,gpar,gpar,spline2);
Vector N;
Matrix dNdU;
Matrix3D d2NdU2;
SplineUtils::extractBasis(spline[0],N,dNdU);
CHECK_VECTORS_EQUAL(N, "src/Utility/Test/refdata/ExtractBasis_vol_N.asc");
CHECK_MATRICES_EQUAL(dNdU, "src/Utility/Test/refdata/ExtractBasis_vol_dNdU.asc");
SplineUtils::extractBasis(spline2[0],N,dNdU,d2NdU2);
CHECK_MATRICES3D_EQUAL(d2NdU2, "src/Utility/Test/refdata/ExtractBasis_vol_d2NdU2.asc");
}
TEST(TestSplineUtils, ExtractBasisSurface)
{
Go::Plane plane(Go::Point(0.0, 0.0, 0.0), Go::Point(0.0, 0.0, 1.0),
Go::Point(sqrt(2.0), sqrt(2.0), 0.0));
Go::SplineSurface* srf = plane.createSplineSurface();
srf->setParameterDomain(0.0, 1.0, 0.0, 1.0);
std::vector<Go::BasisDerivsSf> spline;
std::vector<Go::BasisDerivsSf2> spline2;
Matrix gpar(1, 1);
gpar(1,1) = 0.3;
srf->computeBasisGrid(gpar,gpar,spline);
srf->raiseOrder(1,1);
srf->computeBasisGrid(gpar,gpar,spline2);
Vector N;
Matrix dNdU;
Matrix3D d2NdU2;
SplineUtils::extractBasis(spline[0],N,dNdU);
CHECK_VECTORS_EQUAL(N, "src/Utility/Test/refdata/ExtractBasis_srf_N.asc");
CHECK_MATRICES_EQUAL(dNdU, "src/Utility/Test/refdata/ExtractBasis_srf_dNdU.asc");
SplineUtils::extractBasis(spline2[0],N,dNdU,d2NdU2);
CHECK_MATRICES3D_EQUAL(d2NdU2, "src/Utility/Test/refdata/ExtractBasis_srf_d2NdU2.asc");
}
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;
}
int main(int argc, char *argv[])
{
// Initialize POOMA and output stream, using Tester class
Pooma::initialize(argc, argv);
Pooma::Tester tester(argc, argv);
tester.out() << argv[0] << ": MP DynamicArray w/ shared layouts."
<< std::endl;
tester.out() << "-------------------------------------------" << std::endl;
// Create some Interval objects to create and index into Array's with
tester.out() << "Creating Interval<1> objects ..." << std::endl;
Interval<1> D1(3);
tester.out() << "D1 = " << D1 << std::endl;
// Create MultiPatch dynamic arrays that share a layout.
tester.out() << "Creating MP DynamicArray using domain D1 ... " << std::endl;
Loc<1> blocks(3);
GridPartition<1> gpar(blocks);
LocalMapper<1> cmap(gpar);
DynamicLayout dynlayout(D1,gpar,cmap);
DynamicArray< int, MultiPatch<DynamicTag,Dynamic> > a2(dynlayout);
tester.check("a2 size", a2.domain().size() == D1.size());
tester.check("a2 patches", a2.layout().sizeLocal() == 3);
tester.out() << "Creating MP DynamicArray w/ same layout ..." << std::endl;
DynamicArray< int, MultiPatch<DynamicTag,Dynamic> > b2(a2.layout());
tester.check("b2 size", b2.domain().size() == D1.size());
tester.check("b2 patches", b2.layout().sizeLocal() == 3);
// Test looping over layout nodes
tester.out() << "DynamicArray< MultiPatch<DynamicTag,Dynamic> > layout:\n";
tester.out() << a2.layout() << std::endl;
// Initialize dynamic arrays with scalars.
a2 = 30;
b2 = 40;
Pooma::blockAndEvaluate();
tester.out() << "Initialized MP DynamicArray's to 30, 40:" << std::endl;
tester.out() << "a2 = " << a2 << std::endl;
tester.out() << "b2 = " << b2 << std::endl;
tester.check("a2 initial sum", sum(a2) == (a2.domain().size() * 30));
tester.check("b2 initial sum", sum(b2) == (b2.domain().size() * 40));
// Create elements in the shared-layout MPE arrays
tester.out() << "Creating 2 elements at end of a2 and b2 ..." << std::endl;
a2.create(2);
a2.sync();
a2(3)=a2(4)=-50;
b2(3)=b2(4)=-60;
a2(a2.engine().domain().last()-1)=0;
a2(a2.engine().domain().last())=0;
tester.out() << "a2 = " << a2 << std::endl;
tester.out() << "b2 = " << b2 << std::endl;
tester.check("a2 size after create", a2.domain().size() == (D1.size() + 2));
tester.check("b2 size after create", b2.domain().size() == (D1.size() + 2));
// Delete an element in the shared-layout MPE arrays
tester.out() << "Deleting 2nd element of a2 & b2 w/backfill ..."<<std::endl;
b2.destroy(Interval<1>(1,1), BackFill());
b2.sync();
tester.out() << "a2 = " << a2 << std::endl;
tester.out() << "b2 = " << b2 << std::endl;
tester.check("a2 size after BackFill",a2.domain().size() == (D1.size() + 1));
tester.check("b2 size after BackFill",b2.domain().size() == (D1.size() + 1));
// Copy values from the beginning of a2 and b2 to their end
tester.out() << "Copying first three elements of a2 and b2 ..." << std::endl;
a2.copy(Interval<1>(3));
a2.sync();
tester.out() << "a2 = " << a2 << std::endl;
tester.out() << "b2 = " << b2 << std::endl;
tester.check("a2 size after copy", a2.domain().size() == (D1.size() + 4));
tester.check("b2 size after copy", b2.domain().size() == (D1.size() + 4));
// Return resulting error code and exit; Tester will shut down POOMA.
tester.out() << "-------------------------------------------" << std::endl;
int retval = tester.results("MP DynamicArray w/ shared layouts");
Pooma::finalize();
return retval;
}