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mfem/fem/fe/fe_nurbs.cpp
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// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
// LICENSE and NOTICE for details. LLNL-CODE-806117.
//
// This file is part of the MFEM library. For more information and source code
// availability visit https://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the BSD-3 license. We welcome feedback and contributions, see file
// CONTRIBUTING.md for details.
// H1 Finite Element classes utilizing the Bernstein basis
#include "fe_nurbs.hpp"
#include "../../mesh/nurbs.hpp"
namespace mfem
{
using namespace std;
void NURBS1DFiniteElement::SetOrder() const
{
order = kv[0]->GetOrder();
dof = order + 1;
weights.SetSize(dof);
shape_x.SetSize(dof);
}
void NURBS1DFiniteElement::CalcShape(const IntegrationPoint &ip,
Vector &shape) const
{
kv[0]->CalcShape(shape, ijk[0], ip.x);
real_t sum = 0.0;
for (int i = 0; i <= order; i++)
{
sum += (shape(i) *= weights(i));
}
shape /= sum;
}
void NURBS1DFiniteElement::CalcDShape(const IntegrationPoint &ip,
DenseMatrix &dshape) const
{
Vector grad(dshape.Data(), dof);
kv[0]->CalcShape (shape_x, ijk[0], ip.x);
kv[0]->CalcDShape(grad, ijk[0], ip.x);
real_t sum = 0.0, dsum = 0.0;
for (int i = 0; i <= order; i++)
{
sum += (shape_x(i) *= weights(i));
dsum += ( grad(i) *= weights(i));
}
sum = 1.0/sum;
add(sum, grad, -dsum*sum*sum, shape_x, grad);
}
void NURBS1DFiniteElement::CalcHessian (const IntegrationPoint &ip,
DenseMatrix &hessian) const
{
Vector grad(dof);
Vector hess(hessian.Data(), dof);
kv[0]->CalcShape (shape_x, ijk[0], ip.x);
kv[0]->CalcDShape(grad, ijk[0], ip.x);
kv[0]->CalcD2Shape(hess, ijk[0], ip.x);
real_t sum = 0.0, dsum = 0.0, d2sum = 0.0;
for (int i = 0; i <= order; i++)
{
sum += (shape_x(i) *= weights(i));
dsum += ( grad(i) *= weights(i));
d2sum += ( hess(i) *= weights(i));
}
sum = 1.0/sum;
add(sum, hess, -2*dsum*sum*sum, grad, hess);
add(1.0, hess, (-d2sum + 2*dsum*dsum*sum)*sum*sum, shape_x, hess);
}
void NURBS1DFiniteElement::Project(Coefficient &coeff,
ElementTransformation &Trans,
Vector &dofs) const
{
IntegrationPoint ip;
for (int i = 0; i <= order; i++)
{
real_t kx = kv[0]->GetBotella(ijk[0] + i);
if (!kv[0]->inSpan(kx, ijk[0]+order)) { continue; }
ip.x = kv[0]->GetRefPoint(kx, ijk[0]+order);
Trans.SetIntPoint(&ip);
dofs(i) = coeff.Eval(Trans, ip);
}
}
void NURBS1DFiniteElement::Project(VectorCoefficient &vc,
ElementTransformation &Trans,
Vector &dofs) const
{
MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
Vector x(vc.GetVDim());
IntegrationPoint ip;
for (int i = 0; i <= order; i++)
{
real_t kx = kv[0]->GetBotella(ijk[0] + i);
if (!kv[0]->inSpan(kx, ijk[0]+order)) { continue; }
ip.x = kv[0]->GetRefPoint(kx, ijk[0]+order);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
for (int j = 0; j < x.Size(); j++)
{
dofs(dof*j+i) = x(j);
}
}
}
void NURBS2DFiniteElement::SetOrder() const
{
orders[0] = kv[0]->GetOrder();
orders[1] = kv[1]->GetOrder();
shape_x.SetSize(orders[0]+1);
shape_y.SetSize(orders[1]+1);
dshape_x.SetSize(orders[0]+1);
dshape_y.SetSize(orders[1]+1);
d2shape_x.SetSize(orders[0]+1);
d2shape_y.SetSize(orders[1]+1);
order = max(orders[0], orders[1]);
dof = (orders[0] + 1)*(orders[1] + 1);
u.SetSize(dof);
du.SetSize(dof);
weights.SetSize(dof);
}
void NURBS2DFiniteElement::CalcShape(const IntegrationPoint &ip,
Vector &shape) const
{
kv[0]->CalcShape(shape_x, ijk[0], ip.x);
kv[1]->CalcShape(shape_y, ijk[1], ip.y);
real_t sum = 0.0;
for (int o = 0, j = 0; j <= orders[1]; j++)
{
const real_t sy = shape_y(j);
for (int i = 0; i <= orders[0]; i++, o++)
{
sum += ( shape(o) = shape_x(i)*sy*weights(o) );
}
}
shape /= sum;
}
void NURBS2DFiniteElement::CalcDShape(const IntegrationPoint &ip,
DenseMatrix &dshape) const
{
real_t sum, dsum[2];
kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
kv[0]->CalcDShape(dshape_x, ijk[0], ip.x);
kv[1]->CalcDShape(dshape_y, ijk[1], ip.y);
sum = dsum[0] = dsum[1] = 0.0;
for (int o = 0, j = 0; j <= orders[1]; j++)
{
const real_t sy = shape_y(j), dsy = dshape_y(j);
for (int i = 0; i <= orders[0]; i++, o++)
{
sum += ( u(o) = shape_x(i)*sy*weights(o) );
dsum[0] += ( dshape(o,0) = dshape_x(i)*sy *weights(o) );
dsum[1] += ( dshape(o,1) = shape_x(i)*dsy*weights(o) );
}
}
sum = 1.0/sum;
dsum[0] *= sum*sum;
dsum[1] *= sum*sum;
for (int o = 0; o < dof; o++)
{
dshape(o,0) = dshape(o,0)*sum - u(o)*dsum[0];
dshape(o,1) = dshape(o,1)*sum - u(o)*dsum[1];
}
}
void NURBS2DFiniteElement::CalcHessian (const IntegrationPoint &ip,
DenseMatrix &hessian) const
{
real_t sum, dsum[2], d2sum[3];
kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
kv[0]->CalcDShape(dshape_x, ijk[0], ip.x);
kv[1]->CalcDShape(dshape_y, ijk[1], ip.y);
kv[0]->CalcD2Shape(d2shape_x, ijk[0], ip.x);
kv[1]->CalcD2Shape(d2shape_y, ijk[1], ip.y);
sum = dsum[0] = dsum[1] = 0.0;
d2sum[0] = d2sum[1] = d2sum[2] = 0.0;
for (int o = 0, j = 0; j <= orders[1]; j++)
{
const real_t sy = shape_y(j), dsy = dshape_y(j), d2sy = d2shape_y(j);
for (int i = 0; i <= orders[0]; i++, o++)
{
const real_t sx = shape_x(i), dsx = dshape_x(i), d2sx = d2shape_x(i);
sum += ( u(o) = sx*sy*weights(o) );
dsum[0] += ( du(o,0) = dsx*sy*weights(o) );
dsum[1] += ( du(o,1) = sx*dsy*weights(o) );
d2sum[0] += ( hessian(o,0) = d2sx*sy*weights(o) );
d2sum[1] += ( hessian(o,1) = dsx*dsy*weights(o) );
d2sum[2] += ( hessian(o,2) = sx*d2sy*weights(o) );
}
}
sum = 1.0/sum;
dsum[0] *= sum;
dsum[1] *= sum;
d2sum[0] *= sum;
d2sum[1] *= sum;
d2sum[2] *= sum;
for (int o = 0; o < dof; o++)
{
hessian(o,0) = hessian(o,0)*sum
- 2*du(o,0)*sum*dsum[0]
+ u[o]*sum*(2*dsum[0]*dsum[0] - d2sum[0]);
hessian(o,1) = hessian(o,1)*sum
- du(o,0)*sum*dsum[1]
- du(o,1)*sum*dsum[0]
+ u[o]*sum*(2*dsum[0]*dsum[1] - d2sum[1]);
hessian(o,2) = hessian(o,2)*sum
- 2*du(o,1)*sum*dsum[1]
+ u[o]*sum*(2*dsum[1]*dsum[1] - d2sum[2]);
}
}
void NURBS2DFiniteElement::Project(Coefficient &coeff,
ElementTransformation &Trans,
Vector &dofs) const
{
IntegrationPoint ip;
for (int o = 0, j = 0; j <= orders[1]; j++)
{
real_t ky = kv[1]->GetBotella(ijk[1] + j);
if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
{
o += orders[0] + 1;
continue;
}
ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
for (int i = 0; i <= orders[0]; i++, o++)
{
real_t kx = kv[0]->GetBotella(ijk[0] + i);
if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
Trans.SetIntPoint(&ip);
dofs(o) = coeff.Eval(Trans, ip);
}
}
}
void NURBS2DFiniteElement::Project(VectorCoefficient &vc,
ElementTransformation &Trans,
Vector &dofs) const
{
MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
Vector x(vc.GetVDim());
IntegrationPoint ip;
for (int o = 0, j = 0; j <= orders[1]; j++)
{
real_t ky = kv[1]->GetBotella(ijk[1] + j);
if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
{
o += orders[0] + 1;
continue;
}
ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
for (int i = 0; i <= orders[0]; i++, o++)
{
real_t kx = kv[0]->GetBotella(ijk[0] + i);
if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
for (int v = 0; v < x.Size(); v++)
{
dofs(dof*v+o) = x(v);
}
}
}
}
void NURBS3DFiniteElement::SetOrder() const
{
orders[0] = kv[0]->GetOrder();
orders[1] = kv[1]->GetOrder();
orders[2] = kv[2]->GetOrder();
shape_x.SetSize(orders[0]+1);
shape_y.SetSize(orders[1]+1);
shape_z.SetSize(orders[2]+1);
dshape_x.SetSize(orders[0]+1);
dshape_y.SetSize(orders[1]+1);
dshape_z.SetSize(orders[2]+1);
d2shape_x.SetSize(orders[0]+1);
d2shape_y.SetSize(orders[1]+1);
d2shape_z.SetSize(orders[2]+1);
order = max(max(orders[0], orders[1]), orders[2]);
dof = (orders[0] + 1)*(orders[1] + 1)*(orders[2] + 1);
u.SetSize(dof);
du.SetSize(dof);
weights.SetSize(dof);
}
void NURBS3DFiniteElement::CalcShape(const IntegrationPoint &ip,
Vector &shape) const
{
kv[0]->CalcShape(shape_x, ijk[0], ip.x);
kv[1]->CalcShape(shape_y, ijk[1], ip.y);
kv[2]->CalcShape(shape_z, ijk[2], ip.z);
real_t sum = 0.0;
for (int o = 0, k = 0; k <= orders[2]; k++)
{
const real_t sz = shape_z(k);
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy_sz = shape_y(j)*sz;
for (int i = 0; i <= orders[0]; i++, o++)
{
sum += ( shape(o) = shape_x(i)*sy_sz*weights(o) );
}
}
}
shape /= sum;
}
void NURBS3DFiniteElement::CalcDShape(const IntegrationPoint &ip,
DenseMatrix &dshape) const
{
real_t sum, dsum[3];
kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
kv[2]->CalcShape ( shape_z, ijk[2], ip.z);
kv[0]->CalcDShape(dshape_x, ijk[0], ip.x);
kv[1]->CalcDShape(dshape_y, ijk[1], ip.y);
kv[2]->CalcDShape(dshape_z, ijk[2], ip.z);
sum = dsum[0] = dsum[1] = dsum[2] = 0.0;
for (int o = 0, k = 0; k <= orders[2]; k++)
{
const real_t sz = shape_z(k), dsz = dshape_z(k);
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy_sz = shape_y(j)* sz;
const real_t dsy_sz = dshape_y(j)* sz;
const real_t sy_dsz = shape_y(j)*dsz;
for (int i = 0; i <= orders[0]; i++, o++)
{
sum += ( u(o) = shape_x(i)*sy_sz*weights(o) );
dsum[0] += ( dshape(o,0) = dshape_x(i)* sy_sz *weights(o) );
dsum[1] += ( dshape(o,1) = shape_x(i)*dsy_sz *weights(o) );
dsum[2] += ( dshape(o,2) = shape_x(i)* sy_dsz*weights(o) );
}
}
}
sum = 1.0/sum;
dsum[0] *= sum*sum;
dsum[1] *= sum*sum;
dsum[2] *= sum*sum;
for (int o = 0; o < dof; o++)
{
dshape(o,0) = dshape(o,0)*sum - u(o)*dsum[0];
dshape(o,1) = dshape(o,1)*sum - u(o)*dsum[1];
dshape(o,2) = dshape(o,2)*sum - u(o)*dsum[2];
}
}
void NURBS3DFiniteElement::CalcHessian (const IntegrationPoint &ip,
DenseMatrix &hessian) const
{
real_t sum, dsum[3], d2sum[6];
kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
kv[2]->CalcShape ( shape_z, ijk[2], ip.z);
kv[0]->CalcDShape(dshape_x, ijk[0], ip.x);
kv[1]->CalcDShape(dshape_y, ijk[1], ip.y);
kv[2]->CalcDShape(dshape_z, ijk[2], ip.z);
kv[0]->CalcD2Shape(d2shape_x, ijk[0], ip.x);
kv[1]->CalcD2Shape(d2shape_y, ijk[1], ip.y);
kv[2]->CalcD2Shape(d2shape_z, ijk[2], ip.z);
sum = dsum[0] = dsum[1] = dsum[2] = 0.0;
d2sum[0] = d2sum[1] = d2sum[2] = d2sum[3] = d2sum[4] = d2sum[5] = 0.0;
for (int o = 0, k = 0; k <= orders[2]; k++)
{
const real_t sz = shape_z(k), dsz = dshape_z(k), d2sz = d2shape_z(k);
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy = shape_y(j), dsy = dshape_y(j), d2sy = d2shape_y(j);
for (int i = 0; i <= orders[0]; i++, o++)
{
const real_t sx = shape_x(i), dsx = dshape_x(i), d2sx = d2shape_x(i);
sum += ( u(o) = sx*sy*sz*weights(o) );
dsum[0] += ( du(o,0) = dsx*sy*sz*weights(o) );
dsum[1] += ( du(o,1) = sx*dsy*sz*weights(o) );
dsum[2] += ( du(o,2) = sx*sy*dsz*weights(o) );
d2sum[0] += ( hessian(o,0) = d2sx*sy*sz*weights(o) );
d2sum[1] += ( hessian(o,1) = dsx*dsy*sz*weights(o) );
d2sum[2] += ( hessian(o,2) = dsx*sy*dsz*weights(o) );
d2sum[3] += ( hessian(o,3) = sx*d2sy*sz*weights(o) );
d2sum[4] += ( hessian(o,4) = sx*dsy*dsz*weights(o) );
d2sum[5] += ( hessian(o,5) = sx*sy*d2sz*weights(o) );
}
}
}
sum = 1.0/sum;
dsum[0] *= sum;
dsum[1] *= sum;
dsum[2] *= sum;
d2sum[0] *= sum;
d2sum[1] *= sum;
d2sum[2] *= sum;
d2sum[3] *= sum;
d2sum[4] *= sum;
d2sum[5] *= sum;
for (int o = 0; o < dof; o++)
{
hessian(o,0) = hessian(o,0)*sum
- 2*du(o,0)*sum*dsum[0]
+ u[o]*sum*(2*dsum[0]*dsum[0] - d2sum[0]);
hessian(o,1) = hessian(o,1)*sum
- du(o,0)*sum*dsum[1]
- du(o,1)*sum*dsum[0]
+ u[o]*sum*(2*dsum[0]*dsum[1] - d2sum[1]);
hessian(o,2) = hessian(o,2)*sum
- du(o,0)*sum*dsum[2]
- du(o,2)*sum*dsum[0]
+ u[o]*sum*(2*dsum[0]*dsum[2] - d2sum[2]);
hessian(o,3) = hessian(o,3)*sum
- du(o,1)*sum*dsum[2]
- du(o,2)*sum*dsum[1]
+ u[o]*sum*(2*dsum[1]*dsum[2] - d2sum[3]);
hessian(o,4) = hessian(o,4)*sum
- 2*du(o,2)*sum*dsum[2]
+ u[o]*sum*(2*dsum[2]*dsum[2] - d2sum[4]);
hessian(o,5) = hessian(o,5)*sum
- 2*du(o,1)*sum*dsum[1]
+ u[o]*sum*(2*dsum[1]*dsum[1] - d2sum[5]);
}
}
void NURBS3DFiniteElement::Project(Coefficient &coeff,
ElementTransformation &Trans,
Vector &dofs) const
{
IntegrationPoint ip;
for (int o = 0, k = 0; k <= orders[2]; k++)
{
real_t kz = kv[2]->GetBotella(ijk[2] + k);
if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
{
o += (orders[0] + 1)*(orders[1] + 1);
continue;
}
ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
for (int j = 0; j <= orders[1]; j++)
{
real_t ky = kv[1]->GetBotella(ijk[1] + j);
if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
{
o += orders[0] + 1;
continue;
}
ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
for (int i = 0; i <= orders[0]; i++, o++)
{
real_t kx = kv[0]->GetBotella(ijk[0] + i);
if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
Trans.SetIntPoint(&ip);
dofs(o) = coeff.Eval(Trans, ip);
}
}
}
}
void NURBS3DFiniteElement::Project(VectorCoefficient &vc,
ElementTransformation &Trans,
Vector &dofs) const
{
MFEM_ASSERT(dofs.Size() == vc.GetVDim()*dof, "");
Vector x(vc.GetVDim());
IntegrationPoint ip;
for (int o = 0, k = 0; k <= orders[2]; k++)
{
real_t kz = kv[2]->GetBotella(ijk[2] + k);
if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
{
o += (orders[0] + 1)*(orders[1] + 1);
continue;
}
ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
for (int j = 0; j <= orders[1]; j++)
{
real_t ky = kv[1]->GetBotella(ijk[1] + j);
if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
{
o += orders[0] + 1;
continue;
}
ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
for (int i = 0; i <= orders[0]; i++, o++)
{
real_t kx = kv[0]->GetBotella(ijk[0] + i);
if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
for (int v = 0; v < x.Size(); v++)
{
dofs(dof*v+o) = x(v);
}
}
}
}
}
void NURBS_HDiv2DFiniteElement::SetOrder() const
{
orders[0] = kv[0]->GetOrder();
orders[1] = kv[1]->GetOrder();
if (kv1[0]) { delete kv1[0]; }
if (kv1[1]) { delete kv1[1]; }
kv1[0] = kv[0]->DegreeElevate(1);
kv1[1] = kv[1]->DegreeElevate(1);
shape_x.SetSize(orders[0]+1);
shape_y.SetSize(orders[1]+1);
dshape_x.SetSize(orders[0]+1);
dshape_y.SetSize(orders[1]+1);
d2shape_x.SetSize(orders[0]+1);
d2shape_y.SetSize(orders[1]+1);
shape1_x.SetSize(orders[0]+2);
shape1_y.SetSize(orders[1]+2);
dshape1_x.SetSize(orders[0]+2);
dshape1_y.SetSize(orders[1]+2);
d2shape1_x.SetSize(orders[0]+2);
d2shape1_y.SetSize(orders[1]+2);
order = max(orders[0]+1, orders[1]+1);
dof = (orders[0] + 2)*(orders[1] + 1)
+ (orders[1] + 1)*(orders[1] + 2);
u.SetSize(dof);
du.SetSize(dof);
weights.SetSize(dof);
}
void NURBS_HDiv2DFiniteElement::CalcVShape(const IntegrationPoint &ip,
DenseMatrix &shape) const
{
kv[0]->CalcShape(shape_x, ijk[0], ip.x);
kv[1]->CalcShape(shape_y, ijk[1], ip.y);
kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
int o = 0;
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy = shape_y(j);
for (int i = 0; i <= orders[0]+1; i++, o++)
{
shape(o,0) = shape1_x(i)*sy;
shape(o,1) = 0.0;
}
}
for (int j = 0; j <= orders[1]+1; j++)
{
const real_t sy1 = shape1_y(j);
for (int i = 0; i <= orders[0]; i++, o++)
{
shape(o,0) = 0.0;
shape(o,1) = shape_x(i)*sy1;
}
}
}
void NURBS_HDiv2DFiniteElement::CalcVShape(ElementTransformation &Trans,
DenseMatrix &shape) const
{
CalcVShape(Trans.GetIntPoint(), shape);
const DenseMatrix & J = Trans.Jacobian();
MFEM_ASSERT(J.Width() == 2 && J.Height() == 2,
"NURBS_HDiv2DFiniteElement cannot be embedded in "
"3 dimensional spaces");
for (int i=0; i<dof; i++)
{
real_t sx = shape(i, 0);
real_t sy = shape(i, 1);
shape(i, 0) = sx * J(0, 0) + sy * J(0, 1);
shape(i, 1) = sx * J(1, 0) + sy * J(1, 1);
}
shape *= (1.0 / Trans.Weight());
}
void NURBS_HDiv2DFiniteElement::CalcDivShape(const IntegrationPoint &ip,
Vector &divshape) const
{
kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
kv1[0]->CalcDShape(dshape1_x, ijk[0], ip.x);
kv1[1]->CalcDShape(dshape1_y, ijk[1], ip.y);
int o = 0;
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy = shape_y(j);
for (int i = 0; i <= orders[0]+1; i++, o++)
{
divshape(o) = dshape1_x(i)*sy;
}
}
for (int j = 0; j <= orders[1]+1; j++)
{
const real_t dsy1 = dshape1_y(j);
for (int i = 0; i <= orders[0]; i++, o++)
{
divshape(o) = shape_x(i)*dsy1;
}
}
}
void NURBS_HDiv2DFiniteElement::Project(VectorCoefficient &vc,
ElementTransformation &Trans,
Vector &dofs) const
{
MFEM_ASSERT(dofs.Size() == dof, "");
MFEM_ASSERT(vc.GetVDim() == 2, "");
Vector x(2), mx(2);
IntegrationPoint ip;
int o = 0;
for (int j = 0; j <= orders[1]; j++)
{
real_t ky = kv[1]->GetBotella(ijk[1] + j);
if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
{
o += orders[0] + 2;
continue;
}
ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
for (int i = 0; i <= orders[0]+1; i++, o++)
{
real_t kx = kv1[0]->GetBotella(ijk[0] + i);
if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
Trans.AdjugateJacobian().Mult(x,mx);
dofs(o) = mx(0);
}
}
for (int j = 0; j <= orders[1]+1; j++)
{
real_t ky = kv1[1]->GetBotella(ijk[1] + j);
if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
{
o += orders[0] + 1;
continue;
}
ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
for (int i = 0; i <= orders[0]; i++, o++)
{
real_t kx = kv[0]->GetBotella(ijk[0] + i);
if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
Trans.AdjugateJacobian().Mult(x,mx);
dofs(o) = mx(1);
}
}
}
NURBS_HDiv2DFiniteElement::~NURBS_HDiv2DFiniteElement()
{
if (kv1[0]) { delete kv1[0]; }
if (kv1[1]) { delete kv1[1]; }
}
void NURBS_HDiv3DFiniteElement::SetOrder() const
{
orders[0] = kv[0]->GetOrder();
orders[1] = kv[1]->GetOrder();
orders[2] = kv[2]->GetOrder();
if (kv1[0]) { delete kv1[0]; }
if (kv1[1]) { delete kv1[1]; }
if (kv1[2]) { delete kv1[2]; }
kv1[0] = kv[0]->DegreeElevate(1);
kv1[1] = kv[1]->DegreeElevate(1);
kv1[2] = kv[2]->DegreeElevate(1);
shape_x.SetSize(orders[0]+1);
shape_y.SetSize(orders[1]+1);
shape_z.SetSize(orders[2]+1);
dshape_x.SetSize(orders[0]+1);
dshape_y.SetSize(orders[1]+1);
dshape_z.SetSize(orders[2]+1);
d2shape_x.SetSize(orders[0]+1);
d2shape_y.SetSize(orders[1]+1);
d2shape_z.SetSize(orders[2]+1);
shape1_x.SetSize(orders[0]+2);
shape1_y.SetSize(orders[1]+2);
shape1_z.SetSize(orders[2]+2);
dshape1_x.SetSize(orders[0]+2);
dshape1_y.SetSize(orders[1]+2);
dshape1_z.SetSize(orders[2]+2);
d2shape1_x.SetSize(orders[0]+2);
d2shape1_y.SetSize(orders[1]+2);
d2shape1_z.SetSize(orders[2]+2);
order = max(orders[0]+1, max( orders[1]+1, orders[2]+1));
dof = (orders[0] + 2)*(orders[1] + 1)*(orders[2] + 1) +
(orders[0] + 1)*(orders[1] + 2)*(orders[2] + 1) +
(orders[0] + 1)*(orders[1] + 1)*(orders[2] + 2);
u.SetSize(dof);
du.SetSize(dof);
weights.SetSize(dof);
}
void NURBS_HDiv3DFiniteElement::CalcVShape(const IntegrationPoint &ip,
DenseMatrix &shape) const
{
kv[0]->CalcShape(shape_x, ijk[0], ip.x);
kv[1]->CalcShape(shape_y, ijk[1], ip.y);
kv[2]->CalcShape(shape_z, ijk[2], ip.z);
kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
kv1[2]->CalcShape(shape1_z, ijk[2], ip.z);
shape = 0.0;
int o = 0;
for (int k = 0; k <= orders[2]; k++)
{
const real_t sz = shape_z(k);
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy_sz = shape_y(j)*sz;
for (int i = 0; i <= orders[0]+1; i++, o++)
{
shape(o,0) = shape1_x(i)*sy_sz;
}
}
}
for (int k = 0; k <= orders[2]; k++)
{
const real_t sz = shape_z(k);
for (int j = 0; j <= orders[1]+1; j++)
{
const real_t sy1_sz = shape1_y(j)*sz;
for (int i = 0; i <= orders[0]; i++, o++)
{
shape(o,1) = shape_x(i)*sy1_sz;
}
}
}
for (int k = 0; k <= orders[2]+1; k++)
{
const real_t sz1 = shape1_z(k);
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy_sz1 = shape_y(j)*sz1;
for (int i = 0; i <= orders[0]; i++, o++)
{
shape(o,2) = shape_x(i)*sy_sz1;
}
}
}
}
void NURBS_HDiv3DFiniteElement::CalcVShape(ElementTransformation &Trans,
DenseMatrix &shape) const
{
CalcVShape(Trans.GetIntPoint(), shape);
const DenseMatrix & J = Trans.Jacobian();
MFEM_ASSERT(J.Width() == 3 && J.Height() == 3,
"RT_R2D_FiniteElement cannot be embedded in "
"3 dimensional spaces");
for (int i=0; i<dof; i++)
{
real_t sx = shape(i, 0);
real_t sy = shape(i, 1);
real_t sz = shape(i, 2);
shape(i, 0) = sx * J(0, 0) + sy * J(0, 1) + sz * J(0, 2);
shape(i, 1) = sx * J(1, 0) + sy * J(1, 1) + sz * J(1, 2);
shape(i, 2) = sx * J(2, 0) + sy * J(2, 1) + sz * J(2, 2);
}
shape *= (1.0 / Trans.Weight());
}
void NURBS_HDiv3DFiniteElement::CalcDivShape(const IntegrationPoint &ip,
Vector &divshape) const
{
kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
kv[2]->CalcShape ( shape_z, ijk[2], ip.z);
kv1[0]->CalcDShape(dshape1_x, ijk[0], ip.x);
kv1[1]->CalcDShape(dshape1_y, ijk[1], ip.y);
kv1[2]->CalcDShape(dshape1_z, ijk[2], ip.z);
int o = 0;
for (int k = 0; k <= orders[2]; k++)
{
const real_t sz = shape_z(k);
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy_sz = shape_y(j)*sz;
for (int i = 0; i <= orders[0]+1; i++, o++)
{
divshape(o) = dshape1_x(i)*sy_sz;
}
}
}
for (int k = 0; k <= orders[2]; k++)
{
const real_t sz = shape_z(k);
for (int j = 0; j <= orders[1]+1; j++)
{
const real_t dy1_sz = dshape1_y(j)*sz;
for (int i = 0; i <= orders[0]; i++, o++)
{
divshape(o) = shape_x(i)*dy1_sz;
}
}
}
for (int k = 0; k <= orders[2]+1; k++)
{
const real_t dz1 = dshape1_z(k);
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy_dz1 = shape_y(j)*dz1;
for (int i = 0; i <= orders[0]; i++, o++)
{
divshape(o) = shape_x(i)*sy_dz1;
}
}
}
}
void NURBS_HDiv3DFiniteElement::Project(VectorCoefficient &vc,
ElementTransformation &Trans,
Vector &dofs) const
{
MFEM_ASSERT(dofs.Size() == dof, "");
MFEM_ASSERT(vc.GetVDim() == 3, "");
Vector x(2), mx(3);
IntegrationPoint ip;
int o = 0;
for (int k = 0; k <= orders[2]; k++)
{
real_t kz = kv[2]->GetBotella(ijk[2] + k);
if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
{
o += (orders[0] + 2)*(orders[1] + 1);
continue;
}
ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
for (int j = 0; j <= orders[1]; j++)
{
real_t ky = kv[1]->GetBotella(ijk[1] + j);
if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
{
o += orders[0] + 2;
continue;
}
ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
for (int i = 0; i <= orders[0]+1; i++, o++)
{
real_t kx = kv1[0]->GetBotella(ijk[0] + i);
if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
Trans.AdjugateJacobian().Mult(x,mx);
dofs(o) = mx(0);
}
}
}
for (int k = 0; k <= orders[2]; k++)
{
real_t kz = kv[2]->GetBotella(ijk[2] + k);
if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
{
o += (orders[0] + 1)*(orders[1] + 2);
continue;
}
ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
for (int j = 0; j <= orders[1]+1; j++)
{
real_t ky = kv1[1]->GetBotella(ijk[1] + j);
if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
{
o += orders[0] + 1;
continue;
}
ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
for (int i = 0; i <= orders[0]; i++, o++)
{
real_t kx = kv[0]->GetBotella(ijk[0] + i);
if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
Trans.AdjugateJacobian().Mult(x,mx);
dofs(o) = mx(1);
}
}
}
for (int k = 0; k <= orders[2]+1; k++)
{
real_t kz = kv1[2]->GetBotella(ijk[2] + k);
if (!kv1[2]->inSpan(kz, ijk[2]+orders[2]+1))
{
o += (orders[0] + 1)*(orders[1] + 1);
continue;
}
ip.z = kv1[2]->GetRefPoint(kz, ijk[2]+orders[2]+1);
for (int j = 0; j <= orders[1]; j++)
{
real_t ky = kv[1]->GetBotella(ijk[1] + j);
if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
{
o += orders[0] + 1;
continue;
}
ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
for (int i = 0; i <= orders[0]; i++, o++)
{
real_t kx = kv[0]->GetBotella(ijk[0] + i);
if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
Trans.AdjugateJacobian().Mult(x,mx);
dofs(o) = mx(2);
}
}
}
}
NURBS_HDiv3DFiniteElement::~NURBS_HDiv3DFiniteElement()
{
if (kv1[0]) { delete kv1[0]; }
if (kv1[1]) { delete kv1[1]; }
if (kv1[2]) { delete kv1[2]; }
}
void NURBS_HCurl2DFiniteElement::SetOrder() const
{
orders[0] = kv[0]->GetOrder();
orders[1] = kv[1]->GetOrder();
if (kv1[0]) { delete kv1[0]; }
if (kv1[1]) { delete kv1[1]; }
kv1[0] = kv[0]->DegreeElevate(1);
kv1[1] = kv[1]->DegreeElevate(1);
shape_x.SetSize(orders[0]+1);
shape_y.SetSize(orders[1]+1);
dshape_x.SetSize(orders[0]+1);
dshape_y.SetSize(orders[1]+1);
d2shape_x.SetSize(orders[0]+1);
d2shape_y.SetSize(orders[1]+1);
shape1_x.SetSize(orders[0]+2);
shape1_y.SetSize(orders[1]+2);
dshape1_x.SetSize(orders[0]+2);
dshape1_y.SetSize(orders[1]+2);
d2shape1_x.SetSize(orders[0]+2);
d2shape1_y.SetSize(orders[1]+2);
order = max(orders[0]+1, orders[1]+1);
dof = (orders[0] + 1)*(orders[1] + 2)
+ (orders[1] + 2)*(orders[1] + 1);
u.SetSize(dof);
du.SetSize(dof);
weights.SetSize(dof);
}
void NURBS_HCurl2DFiniteElement::CalcVShape(const IntegrationPoint &ip,
DenseMatrix &shape) const
{
kv[0]->CalcShape(shape_x, ijk[0], ip.x);
kv[1]->CalcShape(shape_y, ijk[1], ip.y);
kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
int o = 0;
for (int j = 0; j <= orders[1]+1; j++)
{
const real_t sy1 = shape1_y(j);
for (int i = 0; i <= orders[0]; i++, o++)
{
shape(o,0) = shape_x(i)*sy1;
shape(o,1) = 0.0;
}
}
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy = shape_y(j);
for (int i = 0; i <= orders[0]+1; i++, o++)
{
shape(o,0) = 0.0;
shape(o,1) = shape1_x(i)*sy;
}
}
}
void NURBS_HCurl2DFiniteElement::CalcVShape(ElementTransformation &Trans,
DenseMatrix &shape) const
{
CalcVShape(Trans.GetIntPoint(), shape);
const DenseMatrix & JI = Trans.InverseJacobian();
MFEM_ASSERT(JI.Width() == 2 && JI.Height() == 2,
"NURBS_HCurl2DFiniteElement cannot be embedded in "
"3 dimensional spaces");
for (int i=0; i<dof; i++)
{
real_t sx = shape(i, 0);
real_t sy = shape(i, 1);
shape(i, 0) = sx * JI(0, 0) + sy * JI(1, 0);
shape(i, 1) = sx * JI(0, 1) + sy * JI(1, 1);
}
}
void NURBS_HCurl2DFiniteElement::CalcCurlShape(const IntegrationPoint &ip,
DenseMatrix &curl_shape) const
{
kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
kv1[0]->CalcDShape(dshape1_x, ijk[0], ip.x);
kv1[1]->CalcDShape(dshape1_y, ijk[1], ip.y);
int o = 0;
for (int j = 0; j <= orders[1]+1; j++)
{
const real_t dsy1 = dshape1_y(j);
for (int i = 0; i <= orders[0]; i++, o++)
{
curl_shape(o,0) = -shape_x(i)*dsy1;
}
}
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy = shape_y(j);
for (int i = 0; i <= orders[0]+1; i++, o++)
{
curl_shape(o,0) = dshape1_x(i)*sy;
}
}
}
void NURBS_HCurl2DFiniteElement::Project(VectorCoefficient &vc,
ElementTransformation &Trans,
Vector &dofs) const
{
MFEM_ASSERT(dofs.Size() == dof, "");
MFEM_ASSERT(vc.GetVDim() == 2, "");
Vector x(2), xm(2);
IntegrationPoint ip;
int i, j, o;
for (o = 0, j = 0; j <= orders[1]+1; j++)
{
real_t ky = kv1[1]->GetBotella(ijk[1] + j);
if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
{
o += orders[0] + 1;
continue;
}
ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
for (i = 0; i <= orders[0]; i++, o++)
{
real_t kx = kv[0]->GetBotella(ijk[0] + i);
if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
Trans.Jacobian().MultTranspose(x,xm);
dofs(o) = xm(0);
}
}
for (j = 0; j <= orders[1]; j++)
{
real_t ky = kv[1]->GetBotella(ijk[1] + j);
if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
{
o += orders[0] + 2;
continue;
}
ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
for (i = 0; i <= orders[0]+1; i++, o++)
{
real_t kx = kv1[0]->GetBotella(ijk[0] + i);
if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
Trans.Jacobian().MultTranspose(x,xm);
dofs(o) = xm(1);
}
}
}
NURBS_HCurl2DFiniteElement::~NURBS_HCurl2DFiniteElement()
{
if (kv1[0]) { delete kv1[0]; }
if (kv1[1]) { delete kv1[1]; }
}
void NURBS_HCurl3DFiniteElement::SetOrder() const
{
orders[0] = kv[0]->GetOrder();
orders[1] = kv[1]->GetOrder();
orders[2] = kv[2]->GetOrder();
if (kv1[0]) { delete kv1[0]; }
if (kv1[1]) { delete kv1[1]; }
if (kv1[2]) { delete kv1[2]; }
kv1[0] = kv[0]->DegreeElevate(1);
kv1[1] = kv[1]->DegreeElevate(1);
kv1[2] = kv[2]->DegreeElevate(1);
shape_x.SetSize(orders[0]+1);
shape_y.SetSize(orders[1]+1);
shape_z.SetSize(orders[2]+1);
dshape_x.SetSize(orders[0]+1);
dshape_y.SetSize(orders[1]+1);
dshape_z.SetSize(orders[2]+1);
d2shape_x.SetSize(orders[0]+1);
d2shape_y.SetSize(orders[1]+1);
d2shape_z.SetSize(orders[2]+1);
shape1_x.SetSize(orders[0]+2);
shape1_y.SetSize(orders[1]+2);
shape1_z.SetSize(orders[2]+2);
dshape1_x.SetSize(orders[0]+2);
dshape1_y.SetSize(orders[1]+2);
dshape1_z.SetSize(orders[2]+2);
d2shape1_x.SetSize(orders[0]+2);
d2shape1_y.SetSize(orders[1]+2);
d2shape1_z.SetSize(orders[2]+2);
order = max(orders[0]+1, max( orders[1]+1, orders[2]+1));
dof = (orders[0] + 1)*(orders[1] + 2)*(orders[2] + 2) +
(orders[0] + 2)*(orders[1] + 1)*(orders[2] + 2) +
(orders[0] + 2)*(orders[1] + 2)*(orders[2] + 1);
u.SetSize(dof);
du.SetSize(dof);
weights.SetSize(dof);
}
void NURBS_HCurl3DFiniteElement::CalcVShape(const IntegrationPoint &ip,
DenseMatrix &shape) const
{
kv[0]->CalcShape(shape_x, ijk[0], ip.x);
kv[1]->CalcShape(shape_y, ijk[1], ip.y);
kv[2]->CalcShape(shape_z, ijk[2], ip.z);
kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
kv1[2]->CalcShape(shape1_z, ijk[2], ip.z);
shape = 0.0;
int o = 0;
for (int k = 0; k <= orders[2]+1; k++)
{
const real_t sz1 = shape1_z(k);
for (int j = 0; j <= orders[1]+1; j++)
{
const real_t sy1_sz1 = shape1_y(j)*sz1;
for (int i = 0; i <= orders[0]; i++, o++)
{
shape(o,0) = shape_x(i)*sy1_sz1;
}
}
}
for (int k = 0; k <= orders[2]+1; k++)
{
const real_t sz1 = shape1_z(k);
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy_sz1 = shape_y(j)*sz1;
for (int i = 0; i <= orders[0]+1; i++, o++)
{
shape(o,1) = shape1_x(i)*sy_sz1;
}
}
}
for (int k = 0; k <= orders[2]; k++)
{
const real_t sz = shape_z(k);
for (int j = 0; j <= orders[1]+1; j++)
{
const real_t sy1_sz = shape1_y(j)*sz;
for (int i = 0; i <= orders[0]+1; i++, o++)
{
shape(o,2) = shape1_x(i)*sy1_sz;
}
}
}
}
void NURBS_HCurl3DFiniteElement::CalcVShape(ElementTransformation &Trans,
DenseMatrix &shape) const
{
CalcVShape(Trans.GetIntPoint(), shape);
const DenseMatrix & JI = Trans.InverseJacobian();
MFEM_ASSERT(JI.Width() == 3 && JI.Height() == 3,
"NURBS_HCurl3DFiniteElement must be in a"
"3 dimensional spaces");
for (int i=0; i<dof; i++)
{
real_t sx = shape(i, 0);
real_t sy = shape(i, 1);
real_t sz = shape(i, 2);
shape(i, 0) = sx * JI(0, 0) + sy * JI(1, 0) + sz * JI(2, 0);
shape(i, 1) = sx * JI(0, 1) + sy * JI(1, 1) + sz * JI(2, 1);
shape(i, 2) = sx * JI(0, 2) + sy * JI(1, 2) + sz * JI(2, 2);
}
}
void NURBS_HCurl3DFiniteElement::CalcCurlShape(const IntegrationPoint &ip,
DenseMatrix &curl_shape) const
{
kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
kv[2]->CalcShape ( shape_z, ijk[2], ip.z);
kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
kv1[2]->CalcShape(shape1_z, ijk[2], ip.z);
kv1[0]->CalcDShape(dshape1_x, ijk[0], ip.x);
kv1[1]->CalcDShape(dshape1_y, ijk[1], ip.y);
kv1[2]->CalcDShape(dshape1_z, ijk[2], ip.z);
int o = 0;
for (int k = 0; k <= orders[2]+1; k++)
{
const real_t sz1 = shape1_z(k), dsz1 = dshape1_z(k);
for (int j = 0; j <= orders[1]+1; j++)
{
const real_t sy1_dsz1 = shape1_y(j)*dsz1,
dsy1_sz1 = dshape1_y(j)*sz1;
for (int i = 0; i <= orders[0]; i++, o++)
{
curl_shape(o,0) = 0.0;
curl_shape(o,1) = shape_x(i)*sy1_dsz1;
curl_shape(o,2) = -shape_x(i)*dsy1_sz1;
}
}
}
for (int k = 0; k <= orders[2]+1; k++)
{
const real_t sz1 = shape1_z(k), dsz1 = dshape1_z(k);
for (int j = 0; j <= orders[1]; j++)
{
const real_t sy_dsz1 = shape_y(j)*dsz1,
sy_sz1 = shape_y(j)*sz1;
for (int i = 0; i <= orders[0]+1; i++, o++)
{
curl_shape(o,0) = -shape1_x(i)*sy_dsz1;
curl_shape(o,1) = 0.0;
curl_shape(o,2) = dshape1_x(i)*sy_sz1;
}
}
}
for (int k = 0; k <= orders[2]; k++)
{
const real_t sz = shape_z(k);
for (int j = 0; j <= orders[1]+1; j++)
{
const real_t sy1_sz = shape1_y(j)*sz,
dsy1_sz = dshape1_y(j)*sz;
for (int i = 0; i <= orders[0]+1; i++, o++)
{
curl_shape(o,0) = shape1_x(i)*dsy1_sz;
curl_shape(o,1) = -dshape1_x(i)*sy1_sz;
curl_shape(o,2) = 0.0;
}
}
}
}
void NURBS_HCurl3DFiniteElement::Project(VectorCoefficient &vc,
ElementTransformation &Trans,
Vector &dofs) const
{
MFEM_ASSERT(dofs.Size() == dof, "");
MFEM_ASSERT(vc.GetVDim() == 3, "");
Vector x(3), xm(3);
IntegrationPoint ip;
int o = 0;
for (int k = 0; k <= orders[2]+1; k++)
{
real_t kz = kv1[2]->GetBotella(ijk[2] + k);
if (!kv1[2]->inSpan(kz, ijk[2]+orders[2]+1))
{
o += (orders[0] + 1)*(orders[1] + 2);
continue;
}
ip.z = kv1[2]->GetRefPoint(kz, ijk[2]+orders[2]+1);
for (int j = 0; j <= orders[1]+1; j++)
{
real_t ky = kv1[1]->GetBotella(ijk[1] + j);
if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
{
o += orders[0] + 1;
continue;
}
ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
for (int i = 0; i <= orders[0]; i++, o++)
{
real_t kx = kv[0]->GetBotella(ijk[0] + i);
if (!kv[0]->inSpan(kx, ijk[0]+orders[0])) { continue; }
ip.x = kv[0]->GetRefPoint(kx, ijk[0]+orders[0]);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
Trans.Jacobian().MultTranspose(x,xm);
dofs(o) = xm(0);
}
}
}
for (int k = 0; k <= orders[2]+1; k++)
{
real_t kz = kv1[2]->GetBotella(ijk[2] + k);
if (!kv1[2]->inSpan(kz, ijk[2]+orders[2]+1))
{
o += (orders[0] + 2)*(orders[1] + 1);
continue;
}
ip.z = kv1[2]->GetRefPoint(kz, ijk[2]+orders[2]+1);
for (int j = 0; j <= orders[1]; j++)
{
real_t ky = kv[1]->GetBotella(ijk[1] + j);
if (!kv[1]->inSpan(ky, ijk[1]+orders[1]))
{
o += orders[0] + 2;
continue;
}
ip.y = kv[1]->GetRefPoint(ky, ijk[1]+orders[1]);
for (int i = 0; i <= orders[0]+1; i++, o++)
{
real_t kx = kv1[0]->GetBotella(ijk[0] + i);
if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
Trans.Jacobian().MultTranspose(x,xm);
dofs(o) = xm(1);
}
}
}
for (int k = 0; k <= orders[2]; k++)
{
real_t kz = kv[2]->GetBotella(ijk[2] + k);
if (!kv[2]->inSpan(kz, ijk[2]+orders[2]))
{
o += (orders[0] + 2)*(orders[1] + 2);
continue;
}
ip.z = kv[2]->GetRefPoint(kz, ijk[2]+orders[2]);
for (int j = 0; j <= orders[1]+1; j++)
{
real_t ky = kv1[1]->GetBotella(ijk[1] + j);
if (!kv1[1]->inSpan(ky, ijk[1]+orders[1]+1))
{
o += orders[0] + 2;
continue;
}
ip.y = kv1[1]->GetRefPoint(ky, ijk[1]+orders[1]+1);
for (int i = 0; i <= orders[0]+1; i++, o++)
{
real_t kx = kv1[0]->GetBotella(ijk[0] + i);
if (!kv1[0]->inSpan(kx, ijk[0]+orders[0]+1)) { continue; }
ip.x = kv1[0]->GetRefPoint(kx, ijk[0]+orders[0]+1);
Trans.SetIntPoint(&ip);
vc.Eval(x, Trans, ip);
Trans.Jacobian().MultTranspose(x,xm);
dofs(o) = xm(2);
}
}
}
}
NURBS_HCurl3DFiniteElement::~NURBS_HCurl3DFiniteElement()
{
if (kv1[0]) { delete kv1[0]; }
if (kv1[1]) { delete kv1[1]; }
if (kv1[2]) { delete kv1[2]; }
}
}
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