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Adding scalar basis on pyramids from Bergot paper with fewer interior DoFs

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This commit is contained in:
Stowell, Mark L
2024-01-24 18:38:51 -08:00
parent a5cd125342
commit 19df0ed57d
4 changed files with 986 additions and 112 deletions
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fem/fe/fe_l2.cpp
+145 -5
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@@ -923,7 +923,7 @@ void L2_WedgeElement::CalcDShape(const IntegrationPoint &ip,
}
}
L2_PyramidElement::L2_PyramidElement(const int p, const int btype)
L2_FuentesPyramidElement::L2_FuentesPyramidElement(const int p, const int btype)
: NodalFiniteElement(3, Geometry::PYRAMID, ((p + 1)*(p + 1)*(p + 1)),
p, FunctionSpace::Pk)
{
@@ -982,8 +982,8 @@ L2_PyramidElement::L2_PyramidElement(const int p, const int btype)
Ti.Factor(T);
}
void L2_PyramidElement::CalcShape(const IntegrationPoint &ip,
Vector &shape) const
void L2_FuentesPyramidElement::CalcShape(const IntegrationPoint &ip,
Vector &shape) const
{
const int p = order;
@@ -1008,8 +1008,148 @@ void L2_PyramidElement::CalcShape(const IntegrationPoint &ip,
Ti.Mult(u, shape);
}
void L2_PyramidElement::CalcDShape(const IntegrationPoint &ip,
DenseMatrix &dshape) const
void L2_FuentesPyramidElement::CalcDShape(const IntegrationPoint &ip,
DenseMatrix &dshape) const
{
const int p = order;
#ifdef MFEM_THREAD_SAFE
Vector shape_x(p + 1);
Vector shape_y(p + 1);
Vector shape_z(p + 1);
Vector dshape_x(p + 1);
Vector dshape_y(p + 1);
Vector dshape_z(p + 1);
DenseMatrix du(dof, dim);
#endif
Poly_1D::CalcLegendre(p, ip.x / (1.0 - ip.z), shape_x, dshape_x);
Poly_1D::CalcLegendre(p, ip.y / (1.0 - ip.z), shape_y, dshape_y);
Poly_1D::CalcLegendre(p, ip.z, shape_z, dshape_z);
int o = 0;
for (int k = 0; k <= p; k++)
for (int j = 0; j <= p; j++)
for (int i = 0; i <= p; i++, o++)
{
du(o, 0) = dshape_x[i] * shape_y[j] * shape_z[k] / (1.0 - ip.z);
du(o, 1) = shape_x[i] * dshape_y[j] * shape_z[k] / (1.0 - ip.z);
du(o, 2) = shape_x[i] * shape_y[j] * dshape_z[k] +
(ip.x * dshape_x[i] * shape_y[j] +
ip.y * shape_x[i] * dshape_y[j]) *
shape_z[k] / pow(1.0 - ip.z, 2);
}
Ti.Mult(du, dshape);
}
L2_BergotPyramidElement::L2_BergotPyramidElement(const int p, const int btype)
: NodalFiniteElement(3, Geometry::PYRAMID, (p + 1)*(p + 2)*(2*p + 3)/6,
p, FunctionSpace::Pk)
{
const double *op = poly1d.OpenPoints(p, VerifyNodal(VerifyOpen(btype)));
#ifndef MFEM_THREAD_SAFE
shape_x.SetSize(p + 1);
shape_y.SetSize(p + 1);
shape_z.SetSize(p + 1);
dshape_x.SetSize(p + 1);
dshape_y.SetSize(p + 1);
dshape_z.SetSize(p + 1);
u.SetSize(dof);
du.SetSize(dof, dim);
#else
Vector shape_x(p + 1);
Vector shape_y(p + 1);
Vector shape_z(p + 1);
#endif
int o = 0;
for (int k = 0; k <= p; k++)
for (int j = 0; j <= p - k; j++)
{
double wjk = op[j] + op[k] + op[p-j-k];
for (int i = 0; i <= p - k; i++)
{
double wik = op[i] + op[k] + op[p-i-k];
double w = wik * wjk * op[p-k];
Nodes.IntPoint(o++).Set3(op[i] * (op[j] + op[p-j-k]) / w,
op[j] * (op[j] + op[p-j-k]) / w,
op[k] * op[p-k] / w);
}
}
MFEM_ASSERT(o == dof,
"Number of nodes does not match the "
"number of degrees of freedom");
DenseMatrix T(dof);
for (int m = 0; m < dof; m++)
{
const IntegrationPoint &ip = Nodes.IntPoint(m);
double x = (ip.z < 1.0) ? (ip.x / (1.0 - ip.z)) : 0.0;
double y = (ip.z < 1.0) ? (ip.y / (1.0 - ip.z)) : 0.0;
double z = ip.z;
o = 0;
for (int i = 0; i <= p; i++)
{
poly1d.CalcLegendre(i, x, shape_x);
for (int j = 0; j <= p; j++)
{
poly1d.CalcLegendre(j, y, shape_y);
int maxij = std::max(i, j);
for (int k = 0; k <= p - maxij; k++)
{
poly1d.CalcJacobi(k, 2.0 * (maxij + 1.0), 0.0, z, shape_z);
T(o++, m) = shape_x(i) * shape_y(j) * shape_z(k) *
pow(1.0 - ip.z, maxij);
}
}
}
}
Ti.Factor(T);
}
void L2_BergotPyramidElement::CalcShape(const IntegrationPoint &ip,
Vector &shape) const
{
const int p = order;
#ifdef MFEM_THREAD_SAFE
Vector shape_x(p + 1);
Vector shape_y(p + 1);
Vector shape_z(p + 1);
Vector u(dof);
#endif
double x = (ip.z < 1.0) ? (ip.x / (1.0 - ip.z)) : 0.0;
double y = (ip.z < 1.0) ? (ip.y / (1.0 - ip.z)) : 0.0;
double z = ip.z;
int o = 0;
for (int i = 0; i <= p; i++)
{
poly1d.CalcLegendre(i, x, shape_x);
for (int j = 0; j <= p; j++)
{
poly1d.CalcLegendre(j, y, shape_y);
int maxij = std::max(i, j);
for (int k = 0; k <= p - maxij; k++)
{
poly1d.CalcJacobi(k, 2.0 * (maxij + 1.0), 0.0, z, shape_z);
u[o++] = shape_x(i) * shape_y(j) * shape_z(k) *
pow(1.0 - ip.z, maxij);
}
}
}
Ti.Mult(u, shape);
}
void L2_BergotPyramidElement::CalcDShape(const IntegrationPoint &ip,
DenseMatrix &dshape) const
{
const int p = order;