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mfem/fem/fe/fe_pyramid.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.
// Finite Element classes on Pyramid shaped elements
#include "fe_pyramid.hpp"
namespace mfem
{
using namespace std;
Vector FuentesPyramid::grad_lam1(real_t x, real_t y, real_t z)
{
return Vector({CheckZ(z) ? - (1.0 - y - z) / (1.0 - z) : -0.5,
CheckZ(z) ? - (1.0 - x - z) / (1.0 - z) : -0.5,
CheckZ(z) ? x * y / ((1.0 - z) * (1.0 - z)) - 1.0 : -0.75});
}
Vector FuentesPyramid::grad_lam2(real_t x, real_t y, real_t z)
{
return Vector({CheckZ(z) ? (1.0 - y - z) / (1.0 - z) : 0.5,
CheckZ(z) ? - x / (1.0 - z) : -0.5,
CheckZ(z) ? - x * y / ((1.0 - z) * (1.0 - z)) : -0.25});
}
Vector FuentesPyramid::grad_lam3(real_t x, real_t y, real_t z)
{
return Vector({CheckZ(z) ? y / (1.0 - z) : 0.5,
CheckZ(z) ? x / (1.0 - z) : 0.5,
CheckZ(z) ? x * y / ((1.0 - z) * (1.0 - z)) : 0.25});
}
Vector FuentesPyramid::grad_lam4(real_t x, real_t y, real_t z)
{
return Vector({CheckZ(z) ? - y / (1.0 - z) : -0.5,
CheckZ(z) ? (1.0 - x - z) / (1.0 - z) : 0.5,
CheckZ(z) ? - x * y / ((1.0 - z) * (1.0 - z)) : -0.25});
}
Vector FuentesPyramid::grad_lam5(real_t x, real_t y, real_t z)
{
return Vector({0.0, 0.0, 1.0});
}
DenseMatrix FuentesPyramid::grad_lam15(real_t x, real_t y, real_t z)
{
DenseMatrix dlam(2, 3);
dlam.SetRow(0, grad_lam1(x, y, z));
dlam.SetRow(1, grad_lam5(x, y, z));
return dlam;
}
DenseMatrix FuentesPyramid::grad_lam25(real_t x, real_t y, real_t z)
{
DenseMatrix dlam(2, 3);
dlam.SetRow(0, grad_lam2(x, y, z));
dlam.SetRow(1, grad_lam5(x, y, z));
return dlam;
}
DenseMatrix FuentesPyramid::grad_lam35(real_t x, real_t y, real_t z)
{
DenseMatrix dlam(2, 3);
dlam.SetRow(0, grad_lam3(x, y, z));
dlam.SetRow(1, grad_lam5(x, y, z));
return dlam;
}
DenseMatrix FuentesPyramid::grad_lam45(real_t x, real_t y, real_t z)
{
DenseMatrix dlam(2, 3);
dlam.SetRow(0, grad_lam4(x, y, z));
dlam.SetRow(1, grad_lam5(x, y, z));
return dlam;
}
Vector FuentesPyramid::lam15_grad_lam15(real_t x, real_t y, real_t z)
{
Vector lam = lam15(x, y, z);
Vector lamdlam(3);
add(lam(0), grad_lam5(x, y, z), -lam(1), grad_lam1(x, y, z), lamdlam);
return lamdlam;
}
Vector FuentesPyramid::lam25_grad_lam25(real_t x, real_t y, real_t z)
{
Vector lam = lam25(x, y, z);
Vector lamdlam(3);
add(lam(0), grad_lam5(x, y, z), -lam(1), grad_lam2(x, y, z), lamdlam);
return lamdlam;
}
Vector FuentesPyramid::lam35_grad_lam35(real_t x, real_t y, real_t z)
{
Vector lam = lam35(x, y, z);
Vector lamdlam(3);
add(lam(0), grad_lam5(x, y, z), -lam(1), grad_lam3(x, y, z), lamdlam);
return lamdlam;
}
Vector FuentesPyramid::lam45_grad_lam45(real_t x, real_t y, real_t z)
{
Vector lam = lam45(x, y, z);
Vector lamdlam(3);
add(lam(0), grad_lam5(x, y, z), -lam(1), grad_lam4(x, y, z), lamdlam);
return lamdlam;
}
Vector FuentesPyramid::lam125_grad_lam125(real_t x, real_t y, real_t z)
{
Vector lgl({-x * z / (one - z), y - one, z});
lgl *= (one - y - z) / (one - z);
return lgl;
}
Vector FuentesPyramid::lam235_grad_lam235(real_t x, real_t y, real_t z)
{
Vector lgl({x, -y * z / (one - z), z});
lgl *= x / (one - z);
return lgl;
}
Vector FuentesPyramid::lam345_grad_lam345(real_t x, real_t y, real_t z)
{
Vector lgl({-x * z / (one - z), y, z});
lgl *= y / (one - z);
return lgl;
}
Vector FuentesPyramid::lam435_grad_lam435(real_t x, real_t y, real_t z)
{
Vector lgl({x * z / (one - z), -y, -z});
lgl *= y / (one - z);
return lgl;
}
Vector FuentesPyramid::lam415_grad_lam415(real_t x, real_t y, real_t z)
{
Vector lgl({x - one, -y * z / (one - z), z});
lgl *= (one - x - z) / (one - z);
return lgl;
}
Vector FuentesPyramid::lam145_grad_lam145(real_t x, real_t y, real_t z)
{
Vector lgl({one - x, y * z / (one - z), -z});
lgl *= (one - x - z) / (one - z);
return lgl;
}
real_t FuentesPyramid::div_lam125_grad_lam125(real_t x, real_t y, real_t z)
{ return (1.0 - z - y) / (1.0 - z); }
real_t FuentesPyramid::div_lam235_grad_lam235(real_t x, real_t y, real_t z)
{ return x / (1.0 - z); }
real_t FuentesPyramid::div_lam345_grad_lam345(real_t x, real_t y, real_t z)
{ return y / (1.0 - z); }
real_t FuentesPyramid::div_lam435_grad_lam435(real_t x, real_t y, real_t z)
{ return -y / (1.0 - z); }
real_t FuentesPyramid::div_lam415_grad_lam415(real_t x, real_t y, real_t z)
{ return (1.0 - z - x) / (1.0 - z); }
real_t FuentesPyramid::div_lam145_grad_lam145(real_t x, real_t y, real_t z)
{ return -(1.0 - z - x) / (1.0 - z); }
DenseMatrix FuentesPyramid::grad_mu01(real_t z)
{
DenseMatrix dmu(2, 3);
dmu.SetRow(0, grad_mu0(z));
dmu.SetRow(1, grad_mu1(z));
return dmu;
}
Vector FuentesPyramid::grad_mu0(real_t z, const Vector xy, unsigned int ab)
{
Vector dmu({0.0, 0.0, - xy[ab-1] / pow(1.0 - z, 2)});
dmu[ab-1] = -1.0 / (1.0 - z);
return dmu;
}
Vector FuentesPyramid::grad_mu1(real_t z, const Vector xy, unsigned int ab)
{
Vector dmu({0.0, 0.0, xy[ab-1] / pow(1.0 - z, 2)});
dmu[ab-1] = 1.0 / (1.0 - z);
return dmu;
}
DenseMatrix FuentesPyramid::grad_mu01(real_t z, Vector xy, unsigned int ab)
{
DenseMatrix dmu(2, 3);
dmu.SetRow(0, grad_mu0(z, xy, ab));
dmu.SetRow(1, grad_mu1(z, xy, ab));
return dmu;
}
Vector FuentesPyramid::mu01_grad_mu01(real_t z, Vector xy, unsigned int ab)
{
Vector mu = mu01(z, xy, ab);
Vector mudmu(3);
add(mu(0), grad_mu1(z, xy, ab), -mu(1), grad_mu0(z, xy, ab), mudmu);
return mudmu;
}
Vector FuentesPyramid::grad_nu0(real_t z, const Vector xy, unsigned int ab)
{
Vector dnu({0.0, 0.0, -1.0}); dnu[ab-1] = -1.0;
return dnu;
}
Vector FuentesPyramid::grad_nu1(real_t z, const Vector xy, unsigned int ab)
{
Vector dnu({0.0, 0.0, 0.0}); dnu[ab-1] = 1.0;
return dnu;
}
Vector FuentesPyramid::grad_nu2(real_t z, const Vector xy, unsigned int ab)
{
return Vector({0.0, 0.0, 1.0});
}
DenseMatrix FuentesPyramid::grad_nu01(real_t z, Vector xy, unsigned int ab)
{
DenseMatrix dnu(2, 3);
dnu.SetRow(0, grad_nu0(z, xy, ab));
dnu.SetRow(1, grad_nu1(z, xy, ab));
return dnu;
}
DenseMatrix FuentesPyramid::grad_nu012(real_t z, Vector xy, unsigned int ab)
{
DenseMatrix dnu(3, 3);
dnu.SetRow(0, grad_nu0(z, xy, ab));
dnu.SetRow(1, grad_nu1(z, xy, ab));
dnu.SetRow(2, grad_nu2(z, xy, ab));
return dnu;
}
DenseMatrix FuentesPyramid::grad_nu120(real_t z, Vector xy, unsigned int ab)
{
DenseMatrix dnu(3, 3);
dnu.SetRow(0, grad_nu1(z, xy, ab));
dnu.SetRow(1, grad_nu2(z, xy, ab));
dnu.SetRow(2, grad_nu0(z, xy, ab));
return dnu;
}
Vector FuentesPyramid::nu01_grad_nu01(real_t z, Vector xy, unsigned int ab)
{
Vector nu = nu01(z, xy, ab);
Vector nudnu(3);
add(nu(0), grad_nu1(z, xy, ab), -nu(1), grad_nu0(z, xy, ab), nudnu);
return nudnu;
}
Vector FuentesPyramid::nu12_grad_nu12(real_t z, Vector xy, unsigned int ab)
{
Vector nu = nu12(z, xy, ab);
Vector nudnu(3);
add(nu(0), grad_nu2(z, xy, ab), -nu(1), grad_nu1(z, xy, ab), nudnu);
return nudnu;
}
Vector FuentesPyramid::nu012_grad_nu012(real_t z, Vector xy, unsigned int ab)
{
Vector nu(nu012(z, xy, ab));
Vector dnu0(grad_nu0(z, xy, ab));
Vector dnu1(grad_nu1(z, xy, ab));
Vector dnu2(grad_nu2(z, xy, ab));
Vector v01(3), v12(3), v20(3);
dnu0.cross3D(dnu1, v01);
dnu1.cross3D(dnu2, v12);
dnu2.cross3D(dnu0, v20);
Vector nudnu(3);
add(nu(0), v12, nu(1), v20, nudnu);
nudnu.Add(nu(2), v01);
return nudnu;
}
void FuentesPyramid::CalcScaledLegendre(int p, real_t x, real_t t,
real_t *u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
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 FuentesPyramid::CalcScaledLegendre(int p, real_t x, real_t t,
real_t *u,
real_t *dudx, real_t *dudt)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
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 FuentesPyramid::CalcScaledLegendre(int p, real_t x, real_t t,
Vector &u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
CalcScaledLegendre(p, x, t, u.GetData());
}
void FuentesPyramid::CalcScaledLegendre(int p, real_t x, real_t t,
Vector &u, Vector &dudx, Vector &dudt)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
MFEM_ASSERT(dudx.Size() >= p+1, "Size of dudx is too small");
MFEM_ASSERT(dudt.Size() >= p+1, "Size of dudt is too small");
CalcScaledLegendre(p, x, t, u.GetData(), dudx.GetData(), dudt.GetData());
}
void FuentesPyramid::CalcIntegratedLegendre(int p, real_t x, real_t t,
real_t *u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
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 FuentesPyramid::CalcIntegratedLegendre(int p, real_t x, real_t t,
real_t *u,
real_t *dudx, real_t *dudt)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
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;
}
}
}
void FuentesPyramid::CalcIntegratedLegendre(int p, real_t x,
real_t t, Vector &u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
CalcIntegratedLegendre(p, x, t, u.GetData());
}
void FuentesPyramid::CalcIntegratedLegendre(int p, real_t x,
real_t t, Vector &u,
Vector &dudx, Vector &dudt)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
MFEM_ASSERT(dudx.Size() >= p+1, "Size of dudx is too small");
MFEM_ASSERT(dudt.Size() >= p+1, "Size of dudt is too small");
CalcIntegratedLegendre(p, x, t, u.GetData(),
dudx.GetData(), dudt.GetData());
}
void FuentesPyramid::CalcHomogenizedScaLegendre(int p, real_t s0, real_t s1,
real_t *u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
CalcScaledLegendre(p, s1, s0 + s1, u);
}
void FuentesPyramid::CalcHomogenizedScaLegendre(int p,
real_t s0, real_t s1,
real_t *u,
real_t *duds0, real_t *duds1)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
CalcScaledLegendre(p, s1, s0+s1, u, duds1, duds0);
for (int i = 0; i <= p; i++) { duds1[i] += duds0[i]; }
}
void FuentesPyramid::CalcHomogenizedScaLegendre(int p, real_t s0, real_t s1,
Vector &u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
CalcHomogenizedScaLegendre(p, s0, s1, u.GetData());
}
void FuentesPyramid::CalcHomogenizedScaLegendre(int p,
real_t s0, real_t s1,
Vector &u,
Vector &duds0, Vector &duds1)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
MFEM_ASSERT(duds0.Size() >= p+1, "Size of duds0 is too small");
MFEM_ASSERT(duds1.Size() >= p+1, "Size of duds1 is too small");
CalcHomogenizedScaLegendre(p, s0, s1, u.GetData(),
duds0.GetData(), duds1.GetData());
}
void FuentesPyramid::CalcHomogenizedIntLegendre(int p,
real_t t0, real_t t1,
real_t *u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
CalcIntegratedLegendre(p, t1, t0 + t1, u);
}
void FuentesPyramid::CalcHomogenizedIntLegendre(int p,
real_t t0, real_t t1,
real_t *u,
real_t *dudt0, real_t *dudt1)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
CalcIntegratedLegendre(p, t1, t0+t1, u, dudt1, dudt0);
for (int i = 0; i <= p; i++) { dudt1[i] += dudt0[i]; }
}
void FuentesPyramid::CalcHomogenizedIntLegendre(int p,
real_t t0, real_t t1,
Vector &u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
CalcHomogenizedIntLegendre(p, t0, t1, u.GetData());
}
void FuentesPyramid::CalcHomogenizedIntLegendre(int p,
real_t t0, real_t t1,
Vector &u,
Vector &dudt0, Vector &dudt1)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
MFEM_ASSERT(dudt0.Size() >= p+1, "Size of dudt0 is too small");
MFEM_ASSERT(dudt1.Size() >= p+1, "Size of dudt1 is too small");
CalcHomogenizedIntLegendre(p, t0, t1, u.GetData(),
dudt0.GetData(), dudt1.GetData());
}
void FuentesPyramid::CalcIntegratedJacobi(int p, real_t alpha,
real_t x, real_t t,
real_t *u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
if (t > 0.0)
{
CalcScaledJacobi(p, alpha, x, t, u);
for (int i = p; i >= 2; i--)
{
real_t d0 = 2.0 * i + alpha;
real_t d1 = d0 - 1.0;
real_t d2 = d0 - 2.0;
real_t a = (alpha + i) / (d0 * d1);
real_t b = alpha / (d0 * d2);
real_t c = (real_t)(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 FuentesPyramid::CalcIntegratedJacobi(int p, real_t alpha,
real_t x, real_t t,
real_t *u,
real_t *dudx,
real_t *dudt)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
CalcScaledJacobi(p, alpha, x, t, u, dudx, dudt);
for (int i = p; i >= 2; i--)
{
real_t d0 = 2.0 * i + alpha;
real_t d1 = d0 - 1.0;
real_t d2 = d0 - 2.0;
real_t a = (alpha + i) / (d0 * d1);
real_t b = alpha / (d0 * d2);
real_t c = (real_t)(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;
}
void FuentesPyramid::CalcScaledJacobi(int p, real_t alpha,
real_t x, real_t t,
real_t *u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
u[0] = 1.0;
if (p >= 1)
{
u[1] = (2.0 + alpha) * x - t;
}
for (int i = 2; i <= p; i++)
{
real_t a = 2.0 * i * (alpha + i) * (2.0 * i + alpha - 2.0);
real_t b = 2.0 * i + alpha - 1.0;
real_t c = (2.0 * i + alpha) * (2.0 * i + alpha - 2.0);
real_t 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 FuentesPyramid::CalcScaledJacobi(int p, real_t alpha,
real_t x, real_t t,
real_t *u, real_t *dudx, real_t *dudt)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
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++)
{
real_t a = 2.0 * i * (alpha + i) * (2.0 * i + alpha - 2.0);
real_t b = 2.0 * i + alpha - 1.0;
real_t c = (2.0 * i + alpha) * (2.0 * i + alpha - 2.0);
real_t 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;
}
}
void FuentesPyramid::CalcScaledJacobi(int p, real_t alpha,
real_t x, real_t t,
Vector &u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
CalcScaledJacobi(p, alpha, x, t, u.GetData());
}
void FuentesPyramid::CalcScaledJacobi(int p, real_t alpha,
real_t x, real_t t,
Vector &u, Vector &dudx, Vector &dudt)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
MFEM_ASSERT(dudx.Size() >= p+1, "Size of dudx is too small");
MFEM_ASSERT(dudt.Size() >= p+1, "Size of dudt is too small");
CalcScaledJacobi(p, alpha, x, t, u.GetData(),
dudx.GetData(), dudt.GetData());
}
void FuentesPyramid::CalcHomogenizedScaJacobi(int p, real_t alpha,
real_t t0, real_t t1,
real_t *u,
real_t *dudt0, real_t *dudt1)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
CalcScaledJacobi(p, alpha, t1, t0+t1, u, dudt1, dudt0);
for (int i = 0; i <= p; i++) { dudt1[i] += dudt0[i]; }
}
void FuentesPyramid::CalcHomogenizedScaJacobi(int p, real_t alpha,
real_t t0, real_t t1,
Vector &u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
CalcHomogenizedScaJacobi(p, alpha, t0, t1, u.GetData());
}
void FuentesPyramid::CalcHomogenizedScaJacobi(int p, real_t alpha,
real_t t0, real_t t1,
Vector &u,
Vector &dudt0, Vector &dudt1)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
MFEM_ASSERT(dudt0.Size() >= p+1, "Size of dudt0 is too small");
MFEM_ASSERT(dudt1.Size() >= p+1, "Size of dudt1 is too small");
CalcHomogenizedScaJacobi(p, alpha, t0, t1, u.GetData(),
dudt0.GetData(), dudt1.GetData());
}
void FuentesPyramid::CalcHomogenizedIntJacobi(int p, real_t alpha,
real_t t0, real_t t1,
real_t *u,
real_t *dudt0, real_t *dudt1)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
CalcIntegratedJacobi(p, alpha, t1, t0+t1, u, dudt1, dudt0);
for (int i = 0; i <= p; i++) { dudt1[i] += dudt0[i]; }
}
void FuentesPyramid::CalcHomogenizedIntJacobi(int p, real_t alpha,
real_t t0, real_t t1,
Vector &u)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
CalcHomogenizedIntJacobi(p, alpha, t0, t1, u.GetData());
}
void FuentesPyramid::CalcHomogenizedIntJacobi(int p, real_t alpha,
real_t t0, real_t t1,
Vector &u,
Vector &dudt0, Vector &dudt1)
{
MFEM_ASSERT(p >= 0, "Polynomial order must be zero or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
MFEM_ASSERT(dudt0.Size() >= p+1, "Size of dudt0 is too small");
MFEM_ASSERT(dudt1.Size() >= p+1, "Size of dudt1 is too small");
CalcHomogenizedIntJacobi(p, alpha, t0, t1, u.GetData(),
dudt0.GetData(), dudt1.GetData());
}
void FuentesPyramid::phi_E(int p, real_t s0, real_t s1,
real_t *u)
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
CalcHomogenizedIntLegendre(p, s0, s1, u);
}
void FuentesPyramid::phi_E(int p, real_t s0, real_t s1,
real_t *u, real_t *duds0, real_t *duds1)
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
CalcHomogenizedIntLegendre(p, s0, s1, u, duds0, duds1);
}
void FuentesPyramid::phi_E(int p, Vector s, Vector &u)
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
phi_E(p, s[0], s[1], u.GetData());
}
void FuentesPyramid::phi_E(int p, Vector s, Vector &u, DenseMatrix &duds)
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
MFEM_ASSERT(duds.Height() >= p+1, "First dimension of duds is too small");
MFEM_ASSERT(duds.Width() >= 2,
"Second dimension of duds must be 2 or larger");
phi_E(p, s[0], s[1], u.GetData(), duds.GetColumn(0), duds.GetColumn(1));
}
void FuentesPyramid::phi_E(int p, Vector s, const DenseMatrix &grad_s,
Vector &u, DenseMatrix &grad_u) const
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(grad_s.Height() >= 2,
"First dimension of grad_s must be 2");
MFEM_ASSERT(grad_s.Width() >= 3,
"Second dimension of grad_s must be 3");
MFEM_ASSERT(u.Size() >= p+1, "Size of u is too small");
MFEM_ASSERT(grad_u.Height() >= p+1,
"First dimension of grad_u is too small");
MFEM_ASSERT(grad_u.Width() == grad_s.Width(),
"Second dimension of grad_u must match that of grad_s");
#ifdef MFEM_THREAD_SAFE
DenseMatrix phi_E_mtmp;
#endif
DenseMatrix &duds = phi_E_mtmp;
duds.SetSize(p + 1, grad_s.Height());
phi_E(p, s[0], s[1], u.GetData(), duds.GetColumn(0), duds.GetColumn(1));
Mult(duds, grad_s, grad_u);
}
void FuentesPyramid::phi_Q(int p, Vector s, Vector t, DenseMatrix &u) const
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(t.Size() >= 2, "Size of t must be 2 or larger");
MFEM_ASSERT(u.Height() >= p+1, "First dimension of u is too small");
MFEM_ASSERT(u.Width() >= p+1, "Second dimension of u is too small");
#ifdef MFEM_THREAD_SAFE
Vector phi_Q_vtmp1;
Vector phi_Q_vtmp2;
#endif
Vector &phi_E_i = phi_Q_vtmp1;
Vector &phi_E_j = phi_Q_vtmp2;
phi_E_i.SetSize(p+1);
phi_E(p, s, phi_E_i);
phi_E_j.SetSize(p+1);
phi_E(p, t, phi_E_j);
for (int j=0; j<=p; j++)
for (int i=0; i<=p; i++)
{
u(i,j) = phi_E_i[i] * phi_E_j[j];
}
}
void FuentesPyramid::phi_Q(int p, Vector s, const DenseMatrix &grad_s,
Vector t, const DenseMatrix &grad_t,
DenseMatrix &u, DenseTensor &grad_u) const
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(grad_s.Height() >= 2,
"First dimension of grad_s must be 2 or larger");
MFEM_ASSERT(grad_s.Width() >= 3,
"Second dimension of grad_s must be 3 or larger");
MFEM_ASSERT(t.Size() >= 2, "Size of t must be 2 or larger");
MFEM_ASSERT(grad_t.Height() >= 2,
"First dimension of grad_t must be 2 or larger");
MFEM_ASSERT(grad_t.Width() >= 3,
"Second dimension of grad_t must be 3 or larger");
MFEM_ASSERT(u.Height() >= p+1, "First dimension of u is too small");
MFEM_ASSERT(u.Width() >= p+1, "First dimension of u is too small");
MFEM_ASSERT(grad_u.SizeI() >= p+1,
"First dimension of grad_u is too small");
MFEM_ASSERT(grad_u.SizeJ() >= p+1,
"Second dimension of grad_u is too small");
MFEM_ASSERT(grad_u.SizeK() >= 3,
"Third dimension of grad_u must be 3 or larger");
#ifdef MFEM_THREAD_SAFE
Vector phi_Q_vtmp1;
Vector phi_Q_vtmp2;
DenseMatrix phi_Q_mtmp1;
DenseMatrix phi_Q_mtmp2;
#endif
Vector &phi_E_i = phi_Q_vtmp1;
Vector &phi_E_j = phi_Q_vtmp2;
DenseMatrix &dphi_E_i = phi_Q_mtmp1;
DenseMatrix &dphi_E_j = phi_Q_mtmp2;
phi_E_i.SetSize(p+1);
dphi_E_i.SetSize(p+1, grad_s.Width());
phi_E(p, s, grad_s, phi_E_i, dphi_E_i);
phi_E_j.SetSize(p+1);
dphi_E_j.SetSize(p+1, grad_t.Width());
phi_E(p, t, grad_t, phi_E_j, dphi_E_j);
for (int j=0; j<=p; j++)
for (int i=0; i<=p; i++)
{
u(i,j) = phi_E_i[i] * phi_E_j[j];
for (int k=0; k<3; k++)
grad_u(i,j,k) =
phi_E_i(i) * dphi_E_j(j,k) + dphi_E_i(i,k) * phi_E_j(j);
}
}
void FuentesPyramid::phi_T(int p, Vector s, DenseMatrix &u) const
{
MFEM_ASSERT(p >= 3, "Polynomial order must be three or larger");
MFEM_ASSERT(s.Size() >= 3, "Size of s must be 3 or larger");
MFEM_ASSERT(u.Height() >= p, "First dimension of u is too small");
MFEM_ASSERT(u.Width() >= p-1, "Second dimension of u is too small");
#ifdef MFEM_THREAD_SAFE
Vector phi_T_vtmp1;
Vector phi_T_vtmp2;
#endif
Vector &phi_E_i = phi_T_vtmp1;
Vector &L_j = phi_T_vtmp2;
phi_E_i.SetSize(p);
phi_E(p-1, s, phi_E_i);
L_j.SetSize(p-1);
u = 0.0;
for (int i = 2; i < p; i++)
{
const real_t alpha = 2.0 * i;
CalcHomogenizedIntJacobi(p-2, alpha, s[0] + s[1], s[2], L_j);
for (int j = 1; i + j <= p; j++)
{
u(i,j) = phi_E_i[i] * L_j[j];
}
}
}
void FuentesPyramid::phi_T(int p, Vector s, const DenseMatrix &grad_s,
DenseMatrix &u, DenseTensor &grad_u) const
{
MFEM_ASSERT(p >= 3, "Polynomial order must be three or larger");
MFEM_ASSERT(s.Size() >= 3, "Size of s must be 3 or larger");
MFEM_ASSERT(grad_s.Height() >= 3,
"First dimension of grad_s must be 2 or larger");
MFEM_ASSERT(grad_s.Width() >= 3,
"Second dimension of grad_s must be 3 or larger");
MFEM_ASSERT(u.Height() >= p, "First dimension of u is too small");
MFEM_ASSERT(u.Width() >= p-1, "Second dimension of u is too small");
MFEM_ASSERT(grad_u.SizeI() >= p,
"First dimension of grad_u is too small");
MFEM_ASSERT(grad_u.SizeJ() >= p-1,
"Second dimension of grad_u is too small");
MFEM_ASSERT(grad_u.SizeK() >= 3,
"Third dimension of grad_u must be 3 or larger");
#ifdef MFEM_THREAD_SAFE
Vector phi_T_vtmp1;
Vector phi_T_vtmp2;
Vector phi_T_vtmp3;
Vector phi_T_vtmp4;
DenseMatrix phi_T_mtmp1;
#endif
Vector &phi_E_i = phi_T_vtmp1;
DenseMatrix &dphi_E_i = phi_T_mtmp1;
Vector &L_j = phi_T_vtmp2;
Vector &dL_j_dx = phi_T_vtmp3;
Vector &dL_j_dt = phi_T_vtmp4;
phi_E_i.SetSize(p);
dphi_E_i.SetSize(p, 3);
phi_E(p-1, s, grad_s, phi_E_i, dphi_E_i);
L_j.SetSize(p-1);
dL_j_dx.SetSize(p-1);
dL_j_dt.SetSize(p-1);
u = 0.0;
grad_u = 0.0;
for (int i = 2; i < p; i++)
{
const real_t alpha = 2.0 * i;
CalcHomogenizedIntJacobi(p-2, alpha, s[0] + s[1], s[2], L_j,
dL_j_dx, dL_j_dt);
for (int j = 1; i + j <= p; j++)
{
u(i,j) = phi_E_i[i] * L_j[j];
for (int d=0; d<3; d++)
grad_u(i, j, d) = dphi_E_i(i, d) * L_j[j] +
phi_E_i[i] * (dL_j_dx[j] * (grad_s(0, d) +
grad_s(1, d)) +
dL_j_dt[j] * grad_s(2, d));
}
}
}
void FuentesPyramid::E_E(int p, Vector s, Vector sds, DenseMatrix &u) const
{
MFEM_ASSERT(p >= 1, "Polynomial order must be one or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(sds.Size() >= 3, "Size of sds must be 3 or larger");
MFEM_ASSERT(u.Height() >= p, "First dimension of u is too small");
MFEM_ASSERT(u.Width() >= 3, "Second dimension of u must be 3 or larger");
#ifdef MFEM_THREAD_SAFE
Vector E_E_vtmp;
#endif
Vector &P_i = E_E_vtmp;
P_i.SetSize(p);
CalcHomogenizedScaLegendre(p - 1, s[0], s[1], P_i);
for (int i=0; i<p; i++)
{
u(i,0) = P_i(i) * sds(0);
u(i,1) = P_i(i) * sds(1);
u(i,2) = P_i(i) * sds(2);
}
}
void FuentesPyramid::E_E(int p, Vector s, const DenseMatrix &grad_s,
DenseMatrix &u, DenseMatrix &curl_u) const
{
MFEM_ASSERT(p >= 1, "Polynomial order must be one or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(grad_s.Height() >= 2,
"First dimension of grad_s must be 2 or larger");
MFEM_ASSERT(grad_s.Width() >= 3,
"Second dimension of grad_s must be 3 or larger");
MFEM_ASSERT(u.Height() >= p, "First dimension of u is too small");
MFEM_ASSERT(u.Width() >= 3, "Second dimension of u must be 3 or larger");
MFEM_ASSERT(curl_u.Height() >= p,
"First dimension of curl_u is too small");
MFEM_ASSERT(curl_u.Width() >= 3,
"Second dimension of curl_u must be 3 or larger");
#ifdef MFEM_THREAD_SAFE
Vector E_E_vtmp;
#endif
Vector &P_i = E_E_vtmp;
P_i.SetSize(p);
CalcHomogenizedScaLegendre(p - 1, s[0], s[1], P_i);
Vector grad_s0({grad_s(0,0), grad_s(0,1), grad_s(0,2)});
Vector grad_s1({grad_s(1,0), grad_s(1,1), grad_s(1,2)});
Vector sds(3);
add(s(0), grad_s1, -s(1), grad_s0, sds);
Vector dsxds(3);
grad_s0.cross3D(grad_s1, dsxds);
for (int i=0; i<p; i++)
{
u(i,0) = P_i(i) * sds(0);
u(i,1) = P_i(i) * sds(1);
u(i,2) = P_i(i) * sds(2);
curl_u(i, 0) = (i + 2) * P_i(i) * dsxds(0);
curl_u(i, 1) = (i + 2) * P_i(i) * dsxds(1);
curl_u(i, 2) = (i + 2) * P_i(i) * dsxds(2);
}
}
void FuentesPyramid::E_Q(int p, Vector s, Vector sds, Vector t,
DenseTensor &u) const
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(sds.Size() >= 3, "Size of sds must be 3 or larger");
MFEM_ASSERT(t.Size() >= 2, "Size of t must be 2 or larger");
MFEM_ASSERT(u.SizeI() >= p, "First dimension of u is too small");
MFEM_ASSERT(u.SizeJ() >= p+1, "Second dimension of u is too small");
MFEM_ASSERT(u.SizeK() >= 3, "Third dimension of u must be 3 or larger");
#ifdef MFEM_THREAD_SAFE
Vector E_Q_vtmp;
DenseMatrix E_Q_mtmp1;
#endif
DenseMatrix &E_E_i = E_Q_mtmp1;
Vector &phi_E_j = E_Q_vtmp;
E_E_i.SetSize(p, 3);
E_E(p, s, sds, E_E_i);
phi_E_j.SetSize(p + 1);
phi_E(p, t, phi_E_j);
for (int k=0; k<3; k++)
{
u(k).SetCol(0, 0.0);
u(k).SetCol(1, 0.0);
}
for (int j=2; j<=p; j++)
for (int i=0; i<p; i++)
for (int k=0; k<3; k++)
{
u(i, j, k) = phi_E_j(j) * E_E_i(i, k);
}
}
void FuentesPyramid::E_Q(int p, Vector s, const DenseMatrix &grad_s,
Vector t, const DenseMatrix &grad_t,
DenseTensor &u, DenseTensor &curl_u) const
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(grad_s.Height() >= 2,
"First dimension of grad_s must be 2");
MFEM_ASSERT(grad_s.Width() >= 3,
"Second dimension of grad_s must be 3");
MFEM_ASSERT(t.Size() >= 2, "Size of t must be 2 or larger");
MFEM_ASSERT(grad_t.Height() >= 2,
"First dimension of grad_t must be 2");
MFEM_ASSERT(grad_t.Width() >= 3,
"Second dimension of grad_t must be 3");
MFEM_ASSERT(u.SizeI() >= p, "First dimension of u is too small");
MFEM_ASSERT(u.SizeJ() >= p+1, "Second dimension of u is too small");
MFEM_ASSERT(u.SizeK() >= 3, "Third dimension of u must be 3 or larger");
MFEM_ASSERT(curl_u.SizeI() >= p, "First dimension of curl_u is too small");
MFEM_ASSERT(curl_u.SizeJ() >= p+1,
"Second dimension of curl_u is too small");
MFEM_ASSERT(curl_u.SizeK() >= 3,
"Third dimension of curl_u must be 3 or larger");
#ifdef MFEM_THREAD_SAFE
Vector E_Q_vtmp;
DenseMatrix E_Q_mtmp1;
DenseMatrix E_Q_mtmp2;
DenseMatrix E_Q_mtmp3;
#endif
Vector &phi_E_j = E_Q_vtmp;
DenseMatrix &dphi_E_j = E_Q_mtmp1;
DenseMatrix &E_E_i = E_Q_mtmp2;
DenseMatrix &dE_E_i = E_Q_mtmp3;
phi_E_j.SetSize(p + 1);
dphi_E_j.SetSize(p + 1, grad_t.Width());
phi_E(p, t, grad_t, phi_E_j, dphi_E_j);
E_E_i.SetSize(p, 3);
dE_E_i.SetSize(p, 3);
E_E(p, s, grad_s, E_E_i, dE_E_i);
for (int k=0; k<3; k++)
{
u(k).SetCol(0, 0.0);
u(k).SetCol(1, 0.0);
curl_u(k).SetCol(0, 0.0);
curl_u(k).SetCol(1, 0.0);
}
for (int j=2; j<=p; j++)
for (int i=0; i<p; i++)
{
for (int k=0; k<3; k++)
{
u(i, j, k) = phi_E_j(j) * E_E_i(i, k);
}
curl_u(i, j, 0) = phi_E_j(j) * dE_E_i(i, 0)
+ dphi_E_j(j, 1) * E_E_i(i, 2)
- dphi_E_j(j, 2) * E_E_i(i, 1);
curl_u(i, j, 1) = phi_E_j(j) * dE_E_i(i, 1)
+ dphi_E_j(j, 2) * E_E_i(i, 0)
- dphi_E_j(j, 0) * E_E_i(i, 2);
curl_u(i, j, 2) = phi_E_j(j) * dE_E_i(i, 2)
+ dphi_E_j(j, 0) * E_E_i(i, 1)
- dphi_E_j(j, 1) * E_E_i(i, 0);
}
}
void FuentesPyramid::E_T(int p, Vector s, Vector sds, DenseTensor &u) const
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
MFEM_ASSERT(s.Size() >= 3, "Size of s must be 3 or larger");
MFEM_ASSERT(sds.Size() >= 3, "Size of sds must be 3 or larger");
MFEM_ASSERT(u.SizeI() >= p - 1, "First dimension of u is too small");
MFEM_ASSERT(u.SizeJ() >= p, "Second dimension of u is too small");
MFEM_ASSERT(u.SizeK() >= 3, "Third dimension of u must be 3 or larger");
#ifdef MFEM_THREAD_SAFE
Vector E_T_vtmp1;
DenseMatrix E_T_mtmp1;
#endif
Vector &L_j = E_T_vtmp1;
DenseMatrix &E_E_i = E_T_mtmp1;
E_E_i.SetSize(p - 1, 3);
E_E(p - 1, s, sds, E_E_i);
L_j.SetSize(p);
for (int i=0; i<p-1; i++)
{
const real_t alpha = 2.0 * i + 1.0;
CalcHomogenizedIntJacobi(p - 1, alpha, s[0] + s[1], s[2], L_j);
u(i, 0, 0) = 0.0; u(i, 0, 1) = 0.0; u(i, 0, 2) = 0.0;
for (int j=1; i+j<p; j++)
for (int k=0; k<3; k++)
{
u(i, j, k) = L_j(j) * E_E_i(i, k);
}
}
}
void FuentesPyramid::E_T(int p, Vector s, const DenseMatrix & grad_s,
DenseTensor &u, DenseTensor &curl_u) const
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
MFEM_ASSERT(s.Size() >= 3, "Size of s must be 3 or larger");
MFEM_ASSERT(grad_s.Height() >= 3,
"First dimension of grad_s must be 3");
MFEM_ASSERT(grad_s.Width() >= 3,
"Second dimension of grad_s must be 3");
MFEM_ASSERT(u.SizeI() >= p - 1, "First dimension of u is too small");
MFEM_ASSERT(u.SizeJ() >= p, "Second dimension of u is too small");
MFEM_ASSERT(u.SizeK() >= 3, "Third dimension of u must be 3 or larger");
MFEM_ASSERT(curl_u.SizeI() >= p - 1,
"First dimension of curl_u is too small");
MFEM_ASSERT(curl_u.SizeJ() >= p,
"Second dimension of curl_u is too small");
MFEM_ASSERT(curl_u.SizeK() >= 3,
"Third dimension of curl_u must be 3 or larger");
#ifdef MFEM_THREAD_SAFE
Vector E_T_vtmp1;
Vector E_T_vtmp2;
Vector E_T_vtmp3;
DenseMatrix E_T_mtmp1;
DenseMatrix E_T_mtmp2;
#endif
Vector &L_j = E_T_vtmp1;
Vector &dL_j_dx = E_T_vtmp2;
Vector &dL_j_dt = E_T_vtmp3;
DenseMatrix & E_E_i = E_T_mtmp1;
DenseMatrix &dE_E_i = E_T_mtmp2;
Vector dL(3), grad_L(3);
E_E_i.SetSize(p - 1, 3);
dE_E_i.SetSize(p - 1, 3);
E_E(p - 1, s, grad_s, E_E_i, dE_E_i);
L_j.SetSize(p);
dL_j_dx.SetSize(p);
dL_j_dt.SetSize(p);
for (int i=0; i<p-1; i++)
{
const real_t alpha = 2.0 * i + 1.0;
CalcHomogenizedIntJacobi(p - 1, alpha, s[0] + s[1], s[2], L_j,
dL_j_dx, dL_j_dt);
u(i, 0, 0) = 0.0; u(i, 0, 1) = 0.0; u(i, 0, 2) = 0.0;
curl_u(i, 0, 0) = 0.0; curl_u(i, 0, 1) = 0.0; curl_u(i, 0, 2) = 0.0;
for (int j=1; i+j<p; j++)
{
dL(0) = dL_j_dx(j); dL(1) = dL_j_dx(j); dL(2) = dL_j_dt(j);
grad_s.MultTranspose(dL, grad_L);
for (int k=0; k<3; k++)
{
u(i, j, k) = L_j(j) * E_E_i(i, k);
curl_u(i, j, k) = L_j(j) * dE_E_i(i, k);
}
curl_u(i, j, 0) += grad_L(1) * E_E_i(i, 2) - grad_L(2) * E_E_i(i, 1);
curl_u(i, j, 1) += grad_L(2) * E_E_i(i, 0) - grad_L(0) * E_E_i(i, 2);
curl_u(i, j, 2) += grad_L(0) * E_E_i(i, 1) - grad_L(1) * E_E_i(i, 0);
}
}
}
void FuentesPyramid::V_Q(int p, Vector s, Vector sds,
Vector t, Vector tdt, DenseTensor &u) const
{
MFEM_ASSERT(p >= 1, "Polynomial order must be one or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(sds.Size() >= 3, "Size of sds must be 3 or larger");
MFEM_ASSERT(t.Size() >= 2, "Size of t must be 2 or larger");
MFEM_ASSERT(tdt.Size() >= 3, "Size of tdt must be 3 or larger");
MFEM_ASSERT(u.SizeI() >= p, "First dimension of u is too small");
MFEM_ASSERT(u.SizeJ() >= p, "Second dimension of u is too small");
MFEM_ASSERT(u.SizeK() >= 3, "Third dimension of u must be 3 or larger");
#ifdef MFEM_THREAD_SAFE
DenseMatrix V_Q_mtmp1;
DenseMatrix V_Q_mtmp2;
#endif
DenseMatrix &E_E_i = V_Q_mtmp1;
DenseMatrix &E_E_j = V_Q_mtmp2;
E_E_i.SetSize(p, 3);
E_E(p, s, sds, E_E_i);
E_E_j.SetSize(p, 3);
E_E(p, t, tdt, E_E_j);
for (int j=0; j<p; j++)
for (int i=0; i<p; i++)
{
u(i, j, 0) = E_E_i(i, 1) * E_E_j(j, 2) - E_E_i(i, 2) * E_E_j(j, 1);
u(i, j, 1) = E_E_i(i, 2) * E_E_j(j, 0) - E_E_i(i, 0) * E_E_j(j, 2);
u(i, j, 2) = E_E_i(i, 0) * E_E_j(j, 1) - E_E_i(i, 1) * E_E_j(j, 0);
}
}
void FuentesPyramid::V_T(int p, Vector s, Vector sdsxds, DenseTensor &u) const
{
MFEM_ASSERT(p >= 1, "Polynomial order must be one or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(sdsxds.Size() >= 3, "Size of sdsxds must be 3 or larger");
MFEM_ASSERT(u.SizeI() >= p, "First dimension of u is too small");
MFEM_ASSERT(u.SizeJ() >= p, "Second dimension of u is too small");
MFEM_ASSERT(u.SizeK() >= 3, "Third dimension of u must be 3 or larger");
#ifdef MFEM_THREAD_SAFE
Vector V_T_vtmp1;
Vector V_T_vtmp2;
#endif
Vector &P_i = V_T_vtmp1;
Vector &P_j = V_T_vtmp2;
P_i.SetSize(p);
CalcHomogenizedScaLegendre(p-1, s[0], s[1], P_i);
P_j.SetSize(p);
for (int i=0; i<p; i++)
{
const real_t alpha = 2.0 * i + 1.0;
CalcHomogenizedScaJacobi(p-1, alpha, s[0] + s[1], s[2], P_j);
for (int j=0; i + j < p; j++)
{
const real_t vij = P_i(i) * P_j(j);
u(i,j,0) = vij * sdsxds(0);
u(i,j,1) = vij * sdsxds(1);
u(i,j,2) = vij * sdsxds(2);
}
}
}
void FuentesPyramid::V_T(int p, Vector s, Vector sdsxds, real_t dsdsxds,
DenseTensor &u, DenseMatrix &du) const
{
MFEM_ASSERT(p >= 1, "Polynomial order must be one or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(sdsxds.Size() >= 3, "Size of sdsxds must be 3 or larger");
MFEM_ASSERT(u.SizeI() >= p, "First dimension of u is too small");
MFEM_ASSERT(u.SizeJ() >= p, "Second dimension of u is too small");
MFEM_ASSERT(u.SizeK() >= 3, "Third dimension of u must be 3 or larger");
MFEM_ASSERT(du.Height() >= p, "First dimension of du is too small");
MFEM_ASSERT(du.Width() >= p, "Second dimension of du is too small");
#ifdef MFEM_THREAD_SAFE
Vector V_T_vtmp1;
Vector V_T_vtmp2;
#endif
Vector &P_i = V_T_vtmp1;
Vector &P_j = V_T_vtmp2;
P_i.SetSize(p);
CalcHomogenizedScaLegendre(p-1, s[0], s[1], P_i);
P_j.SetSize(p);
for (int i=0; i<p; i++)
{
const real_t alpha = 2.0 * i + 1.0;
CalcHomogenizedScaJacobi(p-1, alpha, s[0] + s[1], s[2], P_j);
for (int j=0; i + j < p; j++)
{
const real_t vij = P_i(i) * P_j(j);
u(i,j,0) = vij * sdsxds(0);
u(i,j,1) = vij * sdsxds(1);
u(i,j,2) = vij * sdsxds(2);
du(i,j) = (i+j+3) * vij * dsdsxds;
}
}
}
void FuentesPyramid::VT_T(int p, Vector s, Vector sds, Vector sdsxds,
real_t mu, Vector grad_mu, DenseTensor &u) const
{
MFEM_ASSERT(p >= 1, "Polynomial order must be one or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(sds.Size() >= 3, "Size of sds must be 3 or larger");
MFEM_ASSERT(sdsxds.Size() >= 3, "Size of sdsxds must be 3 or larger");
MFEM_ASSERT(grad_mu.Size() >= 3, "Size of grad_mu must be 3 or larger");
MFEM_ASSERT(u.SizeI() >= p, "First dimension of u is too small");
MFEM_ASSERT(u.SizeJ() >= p, "Second dimension of u is too small");
MFEM_ASSERT(u.SizeK() >= 3, "Third dimension of u must be 3 or larger");
#ifdef MFEM_THREAD_SAFE
Vector VT_T_vtmp1;
Vector VT_T_vtmp2;
DenseMatrix VT_T_mtmp1;
DenseTensor VT_T_ttmp1;
#endif
Vector ms({mu * s(0), mu * s(1), s(2)});
Vector s2(s.GetData(), 2);
Vector &P_i = VT_T_vtmp1;
P_i.SetSize(p);
CalcHomogenizedScaLegendre(p-1, ms[0], ms[1], P_i);
DenseMatrix &EE0 = VT_T_mtmp1;
EE0.SetSize(1,3);
Vector EE(EE0.GetData(), 3);
E_E(1, s2, sds, EE0);
Vector dmuxEE(3);
grad_mu.cross3D(EE, dmuxEE);
DenseTensor &VT00 = VT_T_ttmp1;
VT00.SetSize(1,1,3);
V_T(1, s, sdsxds, VT00);
Vector &J_j = VT_T_vtmp2;
J_j.SetSize(p);
u = 0.0;
for (int i=0; i<p; i++)
{
CalcHomogenizedScaJacobi(p-i-1, 2*i+1, ms[0] + ms[1], ms[2], J_j);
for (int j=0; i+j<p; j++)
for (int k=0; k<3; k++)
u(i, j, k) = P_i(i) * J_j(j) *
(mu * VT00(0,0,k) + s(2) * dmuxEE(k));
}
}
void FuentesPyramid::VT_T(int p, Vector s, Vector sds, Vector sdsxds,
Vector grad_s2, real_t mu, Vector grad_mu,
DenseTensor &u, DenseMatrix &du) const
{
MFEM_ASSERT(p >= 1, "Polynomial order must be one or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(sds.Size() >= 3, "Size of sds must be 3 or larger");
MFEM_ASSERT(sdsxds.Size() >= 3, "Size of sdsxds must be 3 or larger");
MFEM_ASSERT(grad_s2.Size() >= 3, "Size of grad_s2 must be 3 or larger");
MFEM_ASSERT(grad_mu.Size() >= 3, "Size of grad_mu must be 3 or larger");
MFEM_ASSERT(u.SizeI() >= p, "First dimension of u is too small");
MFEM_ASSERT(u.SizeJ() >= p, "Second dimension of u is too small");
MFEM_ASSERT(u.SizeK() >= 3, "Third dimension of u must be 3 or larger");
MFEM_ASSERT(du.Height() >= p, "First dimension of du is too small");
MFEM_ASSERT(du.Width() >= p, "Second dimension of du is too small");
#ifdef MFEM_THREAD_SAFE
Vector VT_T_vtmp1;
Vector VT_T_vtmp2;
DenseMatrix VT_T_mtmp1;
DenseTensor VT_T_ttmp1;
#endif
Vector ms({mu * s(0), mu * s(1), s(2)});
Vector s2(s.GetData(), 2);
Vector &P_i = VT_T_vtmp1;
P_i.SetSize(p);
CalcHomogenizedScaLegendre(p-1, ms[0], ms[1], P_i);
DenseMatrix &EE0 = VT_T_mtmp1;
EE0.SetSize(1,3);
Vector EE(EE0.GetData(), 3);
E_E(1, s2, sds, EE0);
Vector dmuxEE(3);
grad_mu.cross3D(EE, dmuxEE);
Vector EExds2(3);
EE.cross3D(grad_s2, EExds2);
DenseTensor &VT00 = VT_T_ttmp1;
VT00.SetSize(1,1,3);
V_T(1, s, sdsxds, VT00);
Vector &J_j = VT_T_vtmp2;
J_j.SetSize(p);
Vector EV(3);
u = 0.0;
du = 0.0;
for (int i=0; i<p; i++)
{
CalcHomogenizedScaJacobi(p-i-1, 2*i+1, ms[0] + ms[1], ms[2], J_j);
for (int j=0; i+j<p; j++)
{
for (int k=0; k<3; k++)
{
u(i, j, k) = P_i(i) * J_j(j) *
(mu * VT00(0, 0, k) + s(2) * dmuxEE(k));
EV(k) = (i+j+3) * EExds2(k) - VT00(0, 0, k);
}
du(i, j) = P_i(i) * J_j(j) * (grad_mu * EV);
}
}
}
void FuentesPyramid::V_L(int p, Vector sx, const DenseMatrix &grad_sx,
Vector sy, const DenseMatrix &grad_sy,
real_t t, Vector grad_t,
DenseTensor &u) const
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
MFEM_ASSERT(sx.Size() >= 2, "Size of sx must be 2 or larger");
MFEM_ASSERT(grad_sx.Height() >= 2,
"First dimension of grad_sx must be 2 or larger");
MFEM_ASSERT(grad_sx.Width() >= 3,
"Second dimension of grad_sx must be 3 or larger");
MFEM_ASSERT(sy.Size() >= 2, "Size of sy must be 2 or larger");
MFEM_ASSERT(grad_sy.Height() >= 2,
"First dimension of grad_sy must be 2 or larger");
MFEM_ASSERT(grad_sy.Width() >= 3,
"Second dimension of grad_sy must be 3 or larger");
MFEM_ASSERT(grad_t.Size() >= 3, "Size of grad_t must be 3 or larger");
MFEM_ASSERT(u.SizeI() >= p+1, "First dimension of u is too small");
MFEM_ASSERT(u.SizeJ() >= p+1, "Second dimension of u is too small");
MFEM_ASSERT(u.SizeK() >= 3, "Third dimension of u must be 3 or larger");
#ifdef MFEM_THREAD_SAFE
Vector V_L_vtmp1;
Vector V_L_vtmp2;
DenseMatrix V_L_mtmp1;
DenseMatrix V_L_mtmp2;
#endif
Vector &phi_E_i = V_L_vtmp1;
Vector &phi_E_j = V_L_vtmp2;
DenseMatrix &dphi_E_i = V_L_mtmp1;
DenseMatrix &dphi_E_j = V_L_mtmp2;
Vector grad_t3(grad_t.GetData(), 3);
phi_E_i.SetSize(p+1);
dphi_E_i.SetSize(p+1, grad_sx.Width());
phi_E(p, sx, grad_sx, phi_E_i, dphi_E_i);
phi_E_j.SetSize(p+1);
dphi_E_j.SetSize(p+1, grad_sy.Width());
phi_E(p, sy, grad_sy, phi_E_j, dphi_E_j);
Vector dphii(3);
Vector dphij(3);
Vector dphidphi(3);
Vector phidphi(3);
Vector dtphidphi(3);
for (int j=2; j<=p; j++)
{
for (int l=0; l<3; l++) { dphij[l] = dphi_E_j(j, l); }
for (int i=2; i<=p; i++)
{
for (int l=0; l<3; l++) { dphii[l] = dphi_E_i(i, l); }
dphii.cross3D(dphij, dphidphi);
add(phi_E_i(i), dphij, -phi_E_j(j), dphii, phidphi);
grad_t3.cross3D(phidphi, dtphidphi);
for (int l=0; l<3; l++)
{
u(i, j, l) = t * (t * dphidphi(l) + dtphidphi(l));
}
}
}
}
void FuentesPyramid::V_R(int p, Vector s, const DenseMatrix &grad_s,
real_t mu, Vector dmu, real_t t, Vector dt,
DenseMatrix &u) const
{
MFEM_ASSERT(p >= 2, "Polynomial order must be two or larger");
MFEM_ASSERT(s.Size() >= 2, "Size of s must be 2 or larger");
MFEM_ASSERT(grad_s.Height() >= 2,
"First dimension of grad_s must be 2");
MFEM_ASSERT(grad_s.Width() >= 3,
"Second dimension of grad_s must be 3");
MFEM_ASSERT(dmu.Size() >= 3, "Size of dmu must be 3 or larger");
MFEM_ASSERT(dt.Size() >= 3, "Size of dt must be 3 or larger");
MFEM_ASSERT(u.Height() >= p+1, "First dimension of u is too small");
MFEM_ASSERT(u.Width() >= 3, "Second dimension of u is too small");
#ifdef MFEM_THREAD_SAFE
Vector V_R_vtmp;
DenseMatrix V_R_mtmp;
#endif
Vector &phi_E_i = V_R_vtmp;
DenseMatrix &dphi_E_i = V_R_mtmp;
phi_E_i.SetSize(p+1);
dphi_E_i.SetSize(p+1, grad_s.Width());
phi_E(p, s, grad_s, phi_E_i, dphi_E_i);
u.SetRow(0, 0.0);
u.SetRow(1, 0.0);
Vector dmu3(dmu.GetData(), 3);
Vector dt3(dt.GetData(), 3);
Vector dphit2(3);
Vector dphixdmu(3);
Vector dphi(3);
for (int i=2; i<=p; i++)
{
// dphi_E_i.GetRow(i, dphi);
for (int l=0; l<3; l++) { dphi[l] = dphi_E_i(i, l); }
add(t * t, dphi, 2.0 * t * phi_E_i(i), dt3, dphit2);
dphit2.cross3D(dmu3, dphixdmu);
// u.SetRow(i, dphixdmu);
for (int l=0; l<3; l++) { u(i, l) = dphixdmu(l); }
}
}
} // namespace mfem
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