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Pre-update commit containing much temporary code

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This commit is contained in:
Stowell, Mark L
2024-05-02 09:40:33 -07:00
parent 1d46fbba57
commit c5be56264c
22 changed files with 3056 additions and 1202 deletions
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fem/fe/fe_h1.cpp
+76 -528
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@@ -1048,44 +1048,15 @@ H1_FuentesPyramidElement::H1_FuentesPyramidElement(const int p, const int btype)
const double *cp = poly1d.ClosedPoints(p, VerifyNodal(VerifyClosed(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);
ddshape_x.SetSize(p + 1);
ddshape_y.SetSize(p + 1);
ddshape_z.SetSize(p + 1);
u.SetSize(dof);
du.SetSize(dof, dim);
ddu.SetSize(dof, (dim * (dim + 1)) / 2);
*/
shape_0.SetSize(p + 1);
shape_1.SetSize(p + 1);
shape_2.SetSize(p + 1);
dshape_0_0.SetSize(p + 1);
dshape_1_0.SetSize(p + 1);
dshape_2_0.SetSize(p + 1);
dshape_0_1.SetSize(p + 1);
dshape_1_1.SetSize(p + 1);
dshape_2_1.SetSize(p + 1);
tmp_i.SetSize(p + 1);
tmp_ij.SetSize(p + 1, p + 1);
u.SetSize(dof);
du.SetSize(dof, dim);
#else
Vector shape_x(p + 1), shape_y(p + 1), shape_z(p + 1);
/*
Vector shape_0(p + 1);
Vector shape_1(p + 1);
Vector shape_2(p + 1);
Vector dshape_0_0(p + 1);
Vector dshape_1_0(p + 1);
Vector dshape_2_0(p + 1);
Vector dshape_0_1(p + 1);
Vector dshape_1_1(p + 1);
Vector dshape_2_1(p + 1);
*/
Vector tmp_i(p + 1);
Vector u(dof);
DenseMatrix tmp_ij(p + 1, p + 1);
DenseMatrix du(dof, dim);
#endif
// vertices
@@ -1145,21 +1116,18 @@ H1_FuentesPyramidElement::H1_FuentesPyramidElement(const int p, const int btype)
{
double w = cp[i] + cp[j] + cp[p-i-j];
Nodes.IntPoint(o++).Set3(cp[i]/w, cp[0], cp[j]/w);
// mfem::out << i << " " << j << "\t" << cp[i]/w << " " << cp[0] << " " << cp[j]/w << std::endl;
}
for (int j = 1; j < p; j++)
for (int i = 1; i + j < p; i++) // (1,2,4)
{
double w = cp[i] + cp[j] + cp[p-i-j];
Nodes.IntPoint(o++).Set3(1.0 - cp[j]/w, cp[i]/w, cp[j]/w);
// mfem::out << i << " " << j << "\t" << 1.0 - cp[j]/w << " " << cp[i]/w << " " << cp[j]/w << std::endl;
}
for (int j = 1; j < p; j++)
for (int i = 1; i + j < p; i++) // (3,4,2)
{
double w = cp[i] + cp[j] + cp[p-i-j];
Nodes.IntPoint(o++).Set3(cp[j]/w, 1.0 - cp[i]/w, cp[i]/w);
// mfem::out << i << " " << j << "\t" << cp[j]/w << " " << 1.0 - cp[i]/w << " " << cp[i]/w << std::endl;
}
for (int j = 1; j < p; j++)
for (int i = 1; i + j < p; i++) // (0,4,3)
@@ -1167,63 +1135,20 @@ H1_FuentesPyramidElement::H1_FuentesPyramidElement(const int p, const int btype)
double w = cp[i] + cp[j] + cp[p-i-j];
Nodes.IntPoint(o++).Set3(cp[0], cp[j]/w, cp[i]/w);
}
/*
mfem::out << "pts342 = {";
for (int j = 0; j <= p; j++)
{
for (int i = 0; i + j <= p; i++) // (3,4,2)
{
double w = cp[i] + cp[j] + cp[p-i-j];
mfem::out << "{" << cp[j] / w
<< "," << 1.0 - cp[i] / w
<< "," << cp[i] / w << "}";
if (i + j != p) mfem::out << ",";
}
if (j != p) mfem::out << ",";
mfem::out << std::endl;
}
mfem::out << "};\npts043 = {";
for (int j = 0; j <= p; j++)
{
for (int i = 0; i + j <= p; i++) // (0,4,3)
{
double w = cp[i] + cp[j] + cp[p-i-j];
mfem::out << "{" << cp[0]
<< "," << cp[j] / w
<< "," << cp[i] / w << "}";
if (i + j != p) mfem::out << ",";
}
if (j != p) mfem::out << ",";
mfem::out << std::endl;
}
mfem::out << "};\n";
*/
// Points based on Fuentes' interior bubbles
// mfem::out << "pts = {";
for (int k = 1; k < p; k++)
{
for (int j = 1; j < p; j++)
{
// double wjk = cp[j] + cp[k] + cp[p-j-k];
for (int i = 1; i < p; i++)
{
// double wik = cp[i] + cp[k] + cp[p-i-k];
// double w = wik * wjk;
// mfem::out << "{" << cp[i] * (1.0 - cp[k])
// << "," << cp[j] * (1.0 - cp[k])
// << "," << cp[k] << "}";
// if (i != p - 1) mfem::out << ",";
Nodes.IntPoint(o++).Set3(cp[i] * (1.0 - cp[k]),
cp[j] * (1.0 - cp[k]),
cp[k]);
}
// if (j != p - 1) mfem::out << ",";
// mfem::out << std::endl;
}
// if (k != p - 1) mfem::out << ",";
}
// mfem::out << "};\n";
MFEM_ASSERT(o == dof,
"Number of nodes does not match the "
@@ -1233,46 +1158,11 @@ H1_FuentesPyramidElement::H1_FuentesPyramidElement(const int p, const int btype)
for (int m = 0; m < dof; m++)
{
const IntegrationPoint &ip = Nodes.IntPoint(m);
calcBasis(order, ip,
shape_0.GetData(), shape_1.GetData(), shape_2.GetData(),
T.GetColumn(m));
Vector col(T.GetColumn(m), dof);
calcBasis(order, ip, tmp_i, tmp_ij, col);
}
Ti.Factor(T);
if (false)
{
CalcScaledLegendre(6, 0.3, 0.7, shape_0, dshape_0_0, dshape_0_1);
mfem::out << "Scaled Legendre: ";
for (int i=0; i<6; i++) { mfem::out << '\t' << shape_0[i]; }
mfem::out << '\n';
mfem::out << "Scaled Legendre du/dx:\n";
for (int i=0; i<6; i++) { mfem::out << '\t' << dshape_0_0[i]; }
mfem::out << '\n';
double dx = 1e-8;
CalcScaledLegendre(6, 0.3+dx, 0.7, shape_2);
mfem::out << "Scaled Legendre (x+dx): ";
for (int i=0; i<6; i++) { mfem::out << '\t' << shape_2[i]; }
mfem::out << '\n';
mfem::out << "Scaled Legendre (u(x+dx) - u(x)) / dx:\n";
for (int i=0; i<6; i++) { mfem::out << '\t' << (shape_2[i] - shape_0[i]) / dx; }
mfem::out << '\n';
mfem::out << "Scaled Legendre du/dt:\n";
for (int i=0; i<6; i++) { mfem::out << '\t' << dshape_0_1[i]; }
mfem::out << '\n';
double dt = 1e-8;
CalcScaledLegendre(6, 0.3, 0.7+dt, shape_2);
mfem::out << "Scaled Legendre (t+dt): ";
for (int i=0; i<6; i++) { mfem::out << '\t' << shape_2[i]; }
mfem::out << '\n';
mfem::out << "Scaled Legendre (u(t+dt) - u(t)) / dt:\n";
for (int i=0; i<6; i++) { mfem::out << '\t' << (shape_2[i] - shape_0[i]) / dt; }
mfem::out << '\n';
}
}
void H1_FuentesPyramidElement::CalcShape(const IntegrationPoint &ip,
@@ -1281,18 +1171,12 @@ void H1_FuentesPyramidElement::CalcShape(const IntegrationPoint &ip,
const int p = order;
#ifdef MFEM_THREAD_SAFE
Vector shape_0(order+1);
Vector shape_1(order+1);
Vector shape_2(order+1);
/*
Vector shape_x(order+1);
Vector shape_y(order+1);
Vector shape_z(order+1);
*/
Vector tmp_i(p + 1);
Vector u(dof);
DenseMatrix tmp_ij(p + 1, p + 1);
#endif
calcBasis(p, ip, shape_0, shape_1, shape_2, u);
calcBasis(p, ip, tmp_i, tmp_ij, u);
Ti.Mult(u, shape);
}
@@ -1323,19 +1207,15 @@ void H1_FuentesPyramidElement::CalcDShape(const IntegrationPoint &ip,
int o = 0;
// Vertices
grad_lam1(x, y, z, dlam);
for (int i = 0; i < 3; i++) { du(0, i) = dlam[i]; }
grad_lam2(x, y, z, dlam);
for (int i = 0; i < 3; i++) { du(1, i) = dlam[i]; }
grad_lam3(x, y, z, dlam);
for (int i = 0; i < 3; i++) { du(2, i) = dlam[i]; }
grad_lam4(x, y, z, dlam);
for (int i = 0; i < 3; i++) { du(3, i) = dlam[i]; }
grad_lam5(x, y, z, dlam);
for (int i = 0; i < 3; i++) { du(4, i) = dlam[i]; }
du.SetRow(0, grad_lam1(x,y,z));
du.SetRow(1, grad_lam2(x,y,z));
du.SetRow(2, grad_lam3(x,y,z));
du.SetRow(3, grad_lam4(x,y,z));
du.SetRow(4, grad_lam5(x,y,z));
o += 5;
// Mixed edges (base edges)
/*
phi_E(p, nu0(x, z), nu1(x, z), shape_0, dshape_0_0, dshape_0_1);
grad_nu0(x, z, dnu0);
grad_nu1(x, z, dnu1);
@@ -1576,6 +1456,7 @@ void H1_FuentesPyramidElement::CalcDShape(const IntegrationPoint &ip,
}
}
}
*/
/*
double x = ip.x;
double y = ip.y;
@@ -1640,12 +1521,15 @@ void H1_FuentesPyramidElement::CalcDShape(const IntegrationPoint &ip,
void H1_FuentesPyramidElement::calcBasis(const int p,
const IntegrationPoint &ip,
double * tmp_x, double * tmp_y,
double * tmp_z, double *u)
Vector &phi_i, DenseMatrix &phi_ij,
Vector &u) const
{
double x = ip.x;
double y = ip.y;
double z = ip.z;
real_t x = ip.x;
real_t y = ip.y;
real_t z = ip.z;
Vector xy({x,y});
real_t mu;
int o = 0;
@@ -1660,25 +1544,31 @@ void H1_FuentesPyramidElement::calcBasis(const int p,
// Mixed edges (base edges)
if (z < 1.0)
{
phi_E(p, nu0(x, z), nu1(x, z), tmp_x);
// (a,b) = (1,2), c = 0
phi_E(p, nu01(z, xy, 1), phi_i);
mu = mu0(z, xy, 2);
for (int i = 2; i <= p; i++, o++)
{
u[o] = mu0(y / (1.0 - z)) * tmp_x[i];
u[o] = mu * phi_i[i];
}
phi_E(p, nu0(y, z), nu1(y, z), tmp_x);
// (a,b) = (1,2), c = 1
mu = mu1(z, xy, 2);
for (int i = 2; i <= p; i++, o++)
{
u[o] = mu1(x / (1.0 - z)) * tmp_x[i];
u[o] = mu * phi_i[i];
}
phi_E(p, nu0(x, z), nu1(x, z), tmp_x);
// (a,b) = (2,1), c = 0
phi_E(p, nu01(z, xy, 2), phi_i);
mu = mu0(z, xy, 1);
for (int i = 2; i <= p; i++, o++)
{
u[o] = mu1(y / (1.0 - z)) * tmp_x[i];
u[o] = mu * phi_i[i];
}
phi_E(p, nu0(y, z), nu1(y, z), tmp_x);
// (a,b) = (2,1), c = 1
mu = mu1(z, xy, 1);
for (int i = 2; i <= p; i++, o++)
{
u[o] = mu0(x / (1.0 - z)) * tmp_x[i];
u[o] = mu * phi_i[i];
}
}
else
@@ -1690,37 +1580,37 @@ void H1_FuentesPyramidElement::calcBasis(const int p,
}
// Triangle edges (upright edges)
phi_E(p, lam1(x, y, z), lam4(x, y, z), tmp_x);
phi_E(p, lam15(x, y, z), phi_i);
for (int i = 2; i<= p; i++, o++)
{
u[o] = tmp_x[i];
u[o] = phi_i[i];
}
phi_E(p, lam2(x, y, z), lam4(x, y, z), tmp_x);
phi_E(p, lam25(x, y, z), phi_i);
for (int i = 2; i<= p; i++, o++)
{
u[o] = tmp_x[i];
u[o] = phi_i[i];
}
phi_E(p, lam3(x, y, z), lam4(x, y, z), tmp_x);
phi_E(p, lam35(x, y, z), phi_i);
for (int i = 2; i<= p; i++, o++)
{
u[o] = tmp_x[i];
u[o] = phi_i[i];
}
phi_E(p, lam4(x, y, z), lam4(x, y, z), tmp_x);
phi_E(p, lam45(x, y, z), phi_i);
for (int i = 2; i<= p; i++, o++)
{
u[o] = tmp_x[i];
u[o] = phi_i[i];
}
// Quadrilateral face
if (z < 1.0)
{
phi_E(p, mu0(x / (1.0 - z)), mu1(x / (1.0 - z)), tmp_x);
phi_E(p, mu0(y / (1.0 - z)), mu1(y / (1.0 - z)), tmp_y);
phi_Q(p, mu01(z, xy, 1), mu01(z, xy, 2), phi_ij);
mu = mu0(z);
for (int j = 2; j <= p; j++)
{
for (int i = 2; i <= p; i++, o++)
{
u[o] = mu0(z) * tmp_x[i] * tmp_y[j];
u[o] = mu * phi_ij(i,j);
}
}
}
@@ -1738,42 +1628,36 @@ void H1_FuentesPyramidElement::calcBasis(const int p,
// Triangular faces
if (z < 1.0)
{
phi_E(p, nu0(x, z), nu1(x, z), tmp_x);
for (int i = 2; i <= p; i++)
{
CalcIntegratedJacobi(p, 2.0 * i, nu2(x, z), 1.0, tmp_y);
for (int j = 1; j <= p - i; j++, o++)
// (a,b) = (1,2), c = 0
phi_T(p, nu012(z, xy, 1), phi_ij);
mu = mu0(z, xy, 2);
for (int i = 2; i < p; i++)
for (int j = 1; i + j <= p; j++, o++)
{
u[o] = mu0(y / (1.0 - z)) * tmp_x[i] * tmp_y[j];
u[o] = mu * phi_ij(i,j);
}
}
phi_E(p, nu0(y, z), nu1(y, z), tmp_x);
for (int i = 2; i <= p; i++)
{
CalcIntegratedJacobi(p, 2.0 * i, nu2(y, z), 1.0, tmp_y);
for (int j = 1; j <= p - i; j++, o++)
// (a,b) = (1,2), c = 1
mu = mu1(z, xy, 2);
for (int i = 2; i < p; i++)
for (int j = 1; i + j <= p; j++, o++)
{
u[o] = mu1(x / (1.0 - z)) * tmp_x[i] * tmp_y[j];
u[o] = mu * phi_ij(i,j);
}
}
phi_E(p, nu0(x, z), nu1(x, z), tmp_x);
for (int i = 2; i <= p; i++)
{
CalcIntegratedJacobi(p, 2.0 * i, nu2(x, z), 1.0, tmp_y);
for (int j = 1; j <= p - i; j++, o++)
// (a,b) = (2,1), c = 0
phi_T(p, nu012(z, xy, 2), phi_ij);
mu = mu0(z, xy, 1);
for (int i = 2; i < p; i++)
for (int j = 1; i + j <= p; j++, o++)
{
u[o] = mu1(y / (1.0 - z)) * tmp_x[i] * tmp_y[j];
u[o] = mu * phi_ij(i,j);
}
}
phi_E(p, nu0(y, z), nu1(y, z), tmp_x);
for (int i = 2; i <= p; i++)
{
CalcIntegratedJacobi(p, 2.0 * i, nu2(y, z), 1.0, tmp_y);
for (int j = 1; j <= p - i; j++, o++)
// (a,b) = (2,1), c = 1
mu = mu1(z, xy, 1);
for (int i = 2; i < p; i++)
for (int j = 1; i + j <= p; j++, o++)
{
u[o] = mu0(x / (1.0 - z)) * tmp_x[i] * tmp_y[j];
u[o] = mu * phi_ij(i,j);
}
}
}
else
{
@@ -1786,16 +1670,15 @@ void H1_FuentesPyramidElement::calcBasis(const int p,
// Interior
if (z < 1.0)
{
phi_E(p, mu0(x / (1.0 - z)), mu1(x / (1.0 - z)), tmp_x);
phi_E(p, mu0(y / (1.0 - z)), mu1(y / (1.0 - z)), tmp_y);
phi_E(p, mu0(z), mu1(z), tmp_z);
phi_Q(p, mu01(z, xy, 1), mu01(z, xy, 2), phi_ij);
phi_E(p, mu01(z), phi_i);
for (int k = 2; k <= p; k++)
{
for (int j = 2; j <= p; j++)
{
for (int i = 2; i <= p; i++, o++)
{
u[o] = tmp_x[i] * tmp_y[j] * tmp_z[k];
u[o] = phi_ij(i,j) * phi_i(k);
}
}
}
@@ -1807,34 +1690,6 @@ void H1_FuentesPyramidElement::calcBasis(const int p,
u[o]= 0.0;
}
}
/*
if (p == 3)
{
if (z < 1.0)
{
phi_E(p-1, mu0(x / (1.0 - z)), mu1(x / (1.0 - z)), tmp_x);
phi_E(p-1, mu0(y / (1.0 - z)), mu1(y / (1.0 - z)), tmp_y);
phi_E(p-1, mu0(z), mu1(z), tmp_z);
for (int k = 2; k <= p-1; k++)
{
for (int j = 2; j <= p-1; j++)
{
for (int i = 2; i <= p-1; i++, o++)
{
u[o] = tmp_x[i] * tmp_y[j] * tmp_z[k];
}
}
}
}
else
{
for (int i = 0; i < (p - 2) * (p - 2) * (p - 2); i++, o++)
{
u[o]= 0.0;
}
}
}
*/
}
/*
void H1_FuentesPyramidElement::calcDBasis(const int p, const IntegrationPoint &ip,
@@ -1843,313 +1698,6 @@ void H1_FuentesPyramidElement::calcDBasis(const int p, const IntegrationPoint &i
du = 0.0;
}
*/
/*
void H1_FuentesPyramidElement::grad_lam0(const double x, const double y,
const double z, double du[])
{
du[0] = (z < 1.0) ? - (1.0 - y - z) / (1.0 - z) : 0.0;
du[1] = (z < 1.0) ? - (1.0 - x - z) / (1.0 - z) : 0.0;
du[2] = (z < 1.0) ? x * y / ((1.0 - z) * (1.0 - z)) - 1.0 : 0.0;
}
void H1_FuentesPyramidElement::grad_lam1(const double x, const double y,
const double z, double du[])
{
du[0] = (z < 1.0) ? (1.0 - y - z) / (1.0 - z) : 0.0;
du[1] = (z < 1.0) ? - x / (1.0 - z) : 0.0;
du[2] = (z < 1.0) ? - x * y / ((1.0 - z) * (1.0 - z)) : 0.0;
}
void H1_FuentesPyramidElement::grad_lam2(const double x, const double y,
const double z, double du[])
{
du[0] = (z < 1.0) ? y / (1.0 - z) : 0.0;
du[1] = (z < 1.0) ? x / (1.0 - z) : 0.0;
du[2] = (z < 1.0) ? x * y / ((1.0 - z) * (1.0 - z)) : 0.0;
}
void H1_FuentesPyramidElement::grad_lam3(const double x, const double y,
const double z, double du[])
{
du[0] = (z < 1.0) ? - y / (1.0 - z) : 0.0;
du[1] = (z < 1.0) ? (1.0 - x - z) / (1.0 - z) : 0.0;
du[2] = (z < 1.0) ? - x * y / ((1.0 - z) * (1.0 - z)) : 0.0;
}
void H1_FuentesPyramidElement::grad_lam4(const double x, const double y,
const double z, double du[])
{
du[0] = 0.0;
du[1] = 0.0;
du[2] = 1.0;
}
void H1_FuentesPyramidElement::phi_E(const int p, const double s0, double s1,
double *u)
{
calcIntegratedLegendre(p, s1, s0 + s1, u);
}
void H1_FuentesPyramidElement::phi_E(const int p, const double s0, double s1,
double *u, double *duds0, double *duds1)
{
calcIntegratedLegendre(p, s1, s0 + s1, u, duds1, duds0);
for (int i = 0; i <= p; i++) { duds1[i] += duds0[i]; }
}
void H1_FuentesPyramidElement::calcIntegratedLegendre(const int p, const double x,
const double t,
double *u)
{
if (t > 0.0)
{
calcScaledLegendre(p, x, t, u);
for (int i = p; i >= 2; i--)
{
u[i] = (u[i] - t * t * u[i-2]) / (4.0 * i - 2.0);
}
if (p >= 1)
{
u[1] = x;
}
u[0] = 0.0;
}
else
{
for (int i = 0; i <= p; i++)
{
u[i] = 0.0;
}
}
}
void H1_FuentesPyramidElement::calcIntegratedLegendre(const int p, const double x,
const double t,
double *u,
double *dudx, double *dudt)
{
if (t > 0.0)
{
calcScaledLegendre(p, x, t, u, dudx, dudt);
for (int i = p; i >= 2; i--)
{
u[i] = (u[i] - t * t * u[i-2]) / (4.0 * i - 2.0);
dudx[i] = (dudx[i] - t * t * dudx[i-2]) / (4.0 * i - 2.0);
dudt[i] = (dudt[i] - t * t * dudt[i-2] - 2.0 * t * u[i-2]) /
(4.0 * i - 2.0);
}
if (p >= 1)
{
u[1] = x; dudx[1] = 1.0; dudt[1] = 0.0;
}
u[0] = 0.0; dudx[0] = 0.0; dudt[0] = 0.0;
}
else
{
for (int i = 0; i <= p; i++)
{
u[i] = 0.0;
dudx[i] = 0.0;
dudt[i] = 0.0;
}
}
}
*/
/** Implements a scaled and shifted set of Legendre polynomials
P_i(x / t) * t^i
where t >= 0.0, x \in [0,t], and P_i is the shifted Legendre
polynomial defined on [0,1] rather than the usual [-1,1].
*/
/*
void H1_FuentesPyramidElement::calcScaledLegendre(const int p, const double x,
const double t,
double *u)
{
if (t > 0.0)
{
Poly_1D::CalcLegendre(p, x / t, u);
for (int i = 1; i <= p; i++)
{
u[i] *= pow(t, i);
}
}
else
{
// This assumes x = 0 as well as t = 0 since x \in [0,t]
u[0] = 1.0;
for (int i = 1; i <= p; i++) { u[i] = 0.0; }
}
}
void H1_FuentesPyramidElement::calcScaledLegendre(const int p, const double x,
const double t,
double *u,
double *dudx, double *dudt)
{
if (t > 0.0)
{
Poly_1D::CalcLegendre(p, x / t, u, dudx);
dudx[0] = 0.0;
dudt[0] = - dudx[0] * x / t;
for (int i = 1; i <= p; i++)
{
u[i] *= pow(t, i);
dudx[i] *= pow(t, i - 1);
dudt[i] = (u[i] * i - dudx[i] * x) / t;
}
}
else
{
// This assumes x = 0 as well as t = 0 since x \in [0,t]
u[0] = 1.0;
dudx[0] = 0.0;
dudt[0] = 0.0;
if (p >=1)
{
u[1] = 0.0;
dudx[1] = 2.0;
dudt[1] = -1.0;
}
for (int i = 2; i <= p; i++)
{
u[i] = 0.0;
dudx[i] = 0.0;
dudt[i] = 0.0;
}
}
}
void H1_FuentesPyramidElement::calcIntegratedJacobi(const int p,
const double alpha,
const double x,
const double t,
double *u)
{
if (t > 0.0)
{
calcScaledJacobi(p, alpha, x, t, u);
for (int i = p; i >= 2; i--)
{
double d0 = 2.0 * i + alpha;
double d1 = d0 - 1.0;
double d2 = d0 - 2.0;
double a = (alpha + i) / (d0 * d1);
double b = alpha / (d0 * d2);
double c = (double)(i - 1) / (d1 * d2);
u[i] = a * u[i] + b * t * u[i - 1] - c * t * t * u[i - 2];
}
if (p >= 1)
{
u[1] = x;
}
u[0] = 0.0;
}
else
{
u[0] = 1.0;
for (int i = 1; i <= p; i++)
{
u[i] = 0.0;
}
}
}
void H1_FuentesPyramidElement::calcIntegratedJacobi(const int p,
const double alpha,
const double x,
const double t,
double *u,
double *dudx,
double *dudt)
{
calcScaledJacobi(p, alpha, x, t, u, dudx, dudt);
for (int i = p; i >= 2; i--)
{
double d0 = 2.0 * i + alpha;
double d1 = d0 - 1.0;
double d2 = d0 - 2.0;
double a = (alpha + i) / (d0 * d1);
double b = alpha / (d0 * d2);
double c = (double)(i - 1) / (d1 * d2);
u[i] = a * u[i] + b * t * u[i - 1] - c * t * t * u[i - 2];
dudx[i] = a * dudx[i] + b * t * dudx[i - 1] - c * t * t * dudx[i - 2];
dudt[i] = a * dudt[i] + b * t * dudt[i - 1] + b * u[i - 1]
- c * t * t * dudt[i - 2] - 2.0 * c * t * u[i - 2];
}
if (p >= 1)
{
u[1] = x;
dudx[1] = 1.0;
dudt[1] = 0.0;
}
u[0] = 0.0;
dudx[0] = 0.0;
dudt[0] = 0.0;
}
*/
/** Implements a set of scaled and shifted subset of Jacobi polynomials
P_i^{\alpha, 0}(x / t) * t^i
where t >= 0.0, x \in [0,t], and P_i^{\alpha, \beta} is the shifted Jacobi
polynomial defined on [0,1] rather than the usual [-1,1]. Note that we only
consider the special case when \beta = 0.
*/
/*
void H1_FuentesPyramidElement::calcScaledJacobi(const int p, const double alpha,
const double x,
const double t,
double *u)
{
u[0] = 1.0;
if (p >= 1)
{
u[1] = (2.0 + alpha) * x - t;
}
for (int i = 2; i <= p; i++)
{
double a = 2.0 * i * (alpha + i) * (2.0 * i + alpha - 2.0);
double b = 2.0 * i + alpha - 1.0;
double c = (2.0 * i + alpha) * (2.0 * i + alpha - 2.0);
double d = 2.0 * (alpha + i - 1.0) * (i - 1) * (2.0 * i - alpha);
u[i] = (b * (c * (2.0 * x - t) + alpha * alpha * t) * u[i - 1]
- d * t * t * u[i - 2]) / a;
}
}
void H1_FuentesPyramidElement::calcScaledJacobi(const int p, const double alpha,
const double x,
const double t,
double *u, double *dudx, double *dudt)
{
u[0] = 1.0;
dudx[0] = 0.0;
dudt[0] = 0.0;
if (p >= 1)
{
u[1] = (2.0 + alpha) * x - t;
dudx[1] = 2.0 + alpha;
dudt[1] = -1.0;
}
for (int i = 2; i <= p; i++)
{
double a = 2.0 * i * (alpha + i) * (2.0 * i + alpha - 2.0);
double b = 2.0 * i + alpha - 1.0;
double c = (2.0 * i + alpha) * (2.0 * i + alpha - 2.0);
double d = 2.0 * (alpha + i - 1.0) * (i - 1) * (2.0 * i - alpha);
u[i] = (b * (c * (2.0 * x - t) + alpha * alpha * t) * u[i - 1]
- d * t * t * u[i - 2]) / a;
dudx[i] = (b * ((c * (2.0 * x - t) + alpha * alpha * t) * dudx[i - 1] +
2.0 * c * u[i - 1])
- d * t * t * dudx[i - 2]) / a;
dudt[i] = (b * ((c * (2.0 * x - t) + alpha * alpha * t) * dudt[i - 1] +
(alpha * alpha - c) * u[i - 1])
- d * t * t * dudt[i - 2] - 2.0 * d * t * u[i - 2]) / a;
}
}
*/
H1_BergotPyramidElement::H1_BergotPyramidElement(const int p, const int btype)
: NodalFiniteElement(3, Geometry::PYRAMID,