jwpeterson

# Quadratic shape functions, as defined in R. Graglia, "Higher order
# bases on pyramidal elements", IEEE Trans Antennas and Propagation,
# vol 47, no 5, May 1999.
pyramid14 := proc()

uses LinearAlgebra;

local p, phi, x, phi_val, i, j, k, phi_sum, n, xi_vec, true_phi_sums, phi_sums,
      phi_restrict, eqns, phi_xi, phi_eta, phi_zeta, phi_xixi,
      phi_etaeta, phi_zetazeta, phi_xieta, phi_xizeta, phi_etazeta,

jwpeterson

# Shape functions, first, and second derivatives of PYRAMID5 basis functions using Maple

pyramid5 := proc()

uses LinearAlgebra;

local
 phi, i, t, phi_xi, phi_eta, phi_zeta, phi_xixi, phi_etaeta, phi_zetazeta,
 phi_xieta, phi_xizeta, phi_etazeta, x, n, xi_vec, planes, phi_sum, 
 phi_xi_sum, phi_eta_sum, phi_zeta_sum;

jwpeterson

# Shape functions, first, and second derivatives of PRISM15 basis functions using Maple

prism15 := proc()

uses LinearAlgebra;

local
 x, phi, i, j, nodal_val, xi_degree, eta_degree, zeta_degree, phi_xi,
 phi_eta, phi_zeta, indexes, phi_xixi, phi_etaeta, phi_zetazeta,
 phi_xieta, phi_xizeta, phi_etazeta, phi_sum, sum_phi_xi, sum_phi_eta,

jwpeterson

# Compute second derivatives of Hex20 basis functions using Maple

hex20 := proc()

uses LinearAlgebra;

local N, i, phi, phi_x, phi_xx, phi_y, phi_yy, phi_z, phi_zz, phi_xy, phi_xz, phi_yz, indexes;

N:=20;

jwpeterson

/* The libMesh Finite Element Library. */
/* Copyright (C) 2003  Benjamin S. Kirk */

/* This library is free software; you can redistribute it and/or */
/* modify it under the terms of the GNU Lesser General Public */
/* License as published by the Free Software Foundation; either */
/* version 2.1 of the License, or (at your option) any later version. */

/* This library is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */

jwpeterson

// This utility lists all nodes on a given boundary ID.
#include "libmesh/libmesh.h"
#include "libmesh/serial_mesh.h"
#include "libmesh/parallel_mesh.h"
#include "libmesh/mesh_generation.h"
#include "libmesh/equation_systems.h"
#include "libmesh/explicit_system.h"
#include "libmesh/dof_map.h"
#include "libmesh/numeric_vector.h"
#include "libmesh/exodusII_io.h"