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ex42mod.c
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ex42mod.c
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/* This file contains source code from PETSc
Copyright (c) 1991-2014, UChicago Argonne, LLC and the PETSc Development Team
All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice, this
list of conditions and the following disclaimer in the documentation and/or
other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
static char help[] = "Solves a tridiagonal linear system.\n\n";
*/
static char help[] = "Solves the incompressible, variable viscosity stokes equation in 3d using Q1Q1 elements, \n\
stabilized with Bochev's polynomial projection method. Note that implementation here assumes \n\
all boundaries (except the kmax face) are free-slip, i.e. zero normal flow and zero tangential stress. \n\
Along the face kmax (zmax), we assume a free-surface boundary, i.e. zero normal and tangential stress. \n\
-mx : number elements in x-direction \n\
-my : number elements in y-direction \n\
-mz : number elements in z-direction \n\
-stokes_ksp_monitor_blocks : active monitor for each component u,v,w,p \n\
-model : defines viscosity and forcing function. Choose either: 0 (isoviscous), 1 (sinker) \n";
/* Contributed by Dave May */
#include <petscksp.h>
#include <petscdmda.h>
#if defined(EXSADDLE_WITH_PCILUPACK)
#include "pcilupack.h"
#endif
#if defined(EXSADDLE_WITH_PCILDL)
#include "pcildl.h"
#endif
#define PROFILE_TIMING
#define ASSEMBLE_LOWER_TRIANGULAR
#define NSD 3 /* number of spatial dimensions */
#define NODES_PER_EL 8 /* nodes per element */
#define U_DOFS 3 /* degrees of freedom per velocity node */
#define P_DOFS 1 /* degrees of freedom per pressure node */
#define GAUSS_POINTS 8
/* Gauss point based evaluation */
typedef struct {
PetscScalar gp_coords[NSD*GAUSS_POINTS];
PetscScalar eta[GAUSS_POINTS];
PetscScalar fx[GAUSS_POINTS];
PetscScalar fy[GAUSS_POINTS];
PetscScalar fz[GAUSS_POINTS];
PetscScalar hc[GAUSS_POINTS];
} GaussPointCoefficients;
typedef struct {
PetscScalar u_dof;
PetscScalar v_dof;
PetscScalar w_dof;
PetscScalar p_dof;
} StokesDOF;
typedef struct _p_CellProperties *CellProperties;
struct _p_CellProperties {
PetscInt ncells;
PetscInt mx,my,mz;
PetscInt sex,sey,sez;
GaussPointCoefficients *gpc;
};
static PetscErrorCode DMDAGetElementCorners(DM da,PetscInt *sx,PetscInt *sy,PetscInt *sz,PetscInt *mx,PetscInt *my,PetscInt *mz);
/* elements */
#undef __FUNCT__
#define __FUNCT__ "CellPropertiesCreate"
PetscErrorCode CellPropertiesCreate(DM da_stokes,CellProperties *C)
{
PetscErrorCode ierr;
CellProperties cells;
PetscInt mx=0,my=0,mz=0,sex=0,sey=0,sez=0;
PetscFunctionBeginUser;
ierr = PetscMalloc(sizeof(struct _p_CellProperties),&cells);CHKERRQ(ierr);
ierr = DMDAGetElementCorners(da_stokes,&sex,&sey,&sez,&mx,&my,&mz);CHKERRQ(ierr);
cells->mx = mx;
cells->my = my;
cells->mz = mz;
cells->ncells = mx * my * mz;
cells->sex = sex;
cells->sey = sey;
cells->sez = sez;
ierr = PetscMalloc1(mx*my*mz,&cells->gpc);CHKERRQ(ierr);
*C = cells;
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "CellPropertiesDestroy"
PetscErrorCode CellPropertiesDestroy(CellProperties *C)
{
PetscErrorCode ierr;
CellProperties cells;
PetscFunctionBeginUser;
if (!C) PetscFunctionReturn(0);
cells = *C;
ierr = PetscFree(cells->gpc);CHKERRQ(ierr);
ierr = PetscFree(cells);CHKERRQ(ierr);
*C = NULL;
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "CellPropertiesGetCell"
PetscErrorCode CellPropertiesGetCell(CellProperties C,PetscInt II,PetscInt J,PetscInt K,GaussPointCoefficients **G)
{
PetscFunctionBeginUser;
*G = &C->gpc[(II-C->sex) + (J-C->sey)*C->mx + (K-C->sez)*C->mx*C->my];
PetscFunctionReturn(0);
}
/* FEM routines */
/*
Element: Local basis function ordering
1-----2
| |
| |
0-----3
*/
static void ShapeFunctionQ13D_Evaluate(PetscScalar _xi[],PetscScalar Ni[])
{
PetscReal xi = PetscRealPart(_xi[0]);
PetscReal eta = PetscRealPart(_xi[1]);
PetscReal zeta = PetscRealPart(_xi[2]);
Ni[0] = 0.125 * (1.0 - xi) * (1.0 - eta) * (1.0 - zeta);
Ni[1] = 0.125 * (1.0 - xi) * (1.0 + eta) * (1.0 - zeta);
Ni[2] = 0.125 * (1.0 + xi) * (1.0 + eta) * (1.0 - zeta);
Ni[3] = 0.125 * (1.0 + xi) * (1.0 - eta) * (1.0 - zeta);
Ni[4] = 0.125 * (1.0 - xi) * (1.0 - eta) * (1.0 + zeta);
Ni[5] = 0.125 * (1.0 - xi) * (1.0 + eta) * (1.0 + zeta);
Ni[6] = 0.125 * (1.0 + xi) * (1.0 + eta) * (1.0 + zeta);
Ni[7] = 0.125 * (1.0 + xi) * (1.0 - eta) * (1.0 + zeta);
}
static void ShapeFunctionQ13D_Evaluate_dxi(PetscScalar _xi[],PetscScalar GNi[][NODES_PER_EL])
{
PetscReal xi = PetscRealPart(_xi[0]);
PetscReal eta = PetscRealPart(_xi[1]);
PetscReal zeta = PetscRealPart(_xi[2]);
/* xi deriv */
GNi[0][0] = -0.125 * (1.0 - eta) * (1.0 - zeta);
GNi[0][1] = -0.125 * (1.0 + eta) * (1.0 - zeta);
GNi[0][2] = 0.125 * (1.0 + eta) * (1.0 - zeta);
GNi[0][3] = 0.125 * (1.0 - eta) * (1.0 - zeta);
GNi[0][4] = -0.125 * (1.0 - eta) * (1.0 + zeta);
GNi[0][5] = -0.125 * (1.0 + eta) * (1.0 + zeta);
GNi[0][6] = 0.125 * (1.0 + eta) * (1.0 + zeta);
GNi[0][7] = 0.125 * (1.0 - eta) * (1.0 + zeta);
/* eta deriv */
GNi[1][0] = -0.125 * (1.0 - xi) * (1.0 - zeta);
GNi[1][1] = 0.125 * (1.0 - xi) * (1.0 - zeta);
GNi[1][2] = 0.125 * (1.0 + xi) * (1.0 - zeta);
GNi[1][3] = -0.125 * (1.0 + xi) * (1.0 - zeta);
GNi[1][4] = -0.125 * (1.0 - xi) * (1.0 + zeta);
GNi[1][5] = 0.125 * (1.0 - xi) * (1.0 + zeta);
GNi[1][6] = 0.125 * (1.0 + xi) * (1.0 + zeta);
GNi[1][7] = -0.125 * (1.0 + xi) * (1.0 + zeta);
/* zeta deriv */
GNi[2][0] = -0.125 * (1.0 - xi) * (1.0 - eta);
GNi[2][1] = -0.125 * (1.0 - xi) * (1.0 + eta);
GNi[2][2] = -0.125 * (1.0 + xi) * (1.0 + eta);
GNi[2][3] = -0.125 * (1.0 + xi) * (1.0 - eta);
GNi[2][4] = 0.125 * (1.0 - xi) * (1.0 - eta);
GNi[2][5] = 0.125 * (1.0 - xi) * (1.0 + eta);
GNi[2][6] = 0.125 * (1.0 + xi) * (1.0 + eta);
GNi[2][7] = 0.125 * (1.0 + xi) * (1.0 - eta);
}
static void matrix_inverse_3x3(PetscScalar A[3][3],PetscScalar B[3][3])
{
PetscScalar t4, t6, t8, t10, t12, t14, t17;
t4 = A[2][0] * A[0][1];
t6 = A[2][0] * A[0][2];
t8 = A[1][0] * A[0][1];
t10 = A[1][0] * A[0][2];
t12 = A[0][0] * A[1][1];
t14 = A[0][0] * A[1][2];
t17 = 0.1e1 / (t4 * A[1][2] - t6 * A[1][1] - t8 * A[2][2] + t10 * A[2][1] + t12 * A[2][2] - t14 * A[2][1]);
B[0][0] = (A[1][1] * A[2][2] - A[1][2] * A[2][1]) * t17;
B[0][1] = -(A[0][1] * A[2][2] - A[0][2] * A[2][1]) * t17;
B[0][2] = (A[0][1] * A[1][2] - A[0][2] * A[1][1]) * t17;
B[1][0] = -(-A[2][0] * A[1][2] + A[1][0] * A[2][2]) * t17;
B[1][1] = (-t6 + A[0][0] * A[2][2]) * t17;
B[1][2] = -(-t10 + t14) * t17;
B[2][0] = (-A[2][0] * A[1][1] + A[1][0] * A[2][1]) * t17;
B[2][1] = -(-t4 + A[0][0] * A[2][1]) * t17;
B[2][2] = (-t8 + t12) * t17;
}
static void ShapeFunctionQ13D_Evaluate_dx(PetscScalar GNi[][NODES_PER_EL],PetscScalar GNx[][NODES_PER_EL],PetscScalar coords[],PetscScalar *det_J)
{
PetscScalar J00,J01,J02,J10,J11,J12,J20,J21,J22;
PetscInt n;
PetscScalar iJ[3][3],JJ[3][3];
J00 = J01 = J02 = 0.0;
J10 = J11 = J12 = 0.0;
J20 = J21 = J22 = 0.0;
for (n=0; n<NODES_PER_EL; n++) {
PetscScalar cx = coords[NSD*n + 0];
PetscScalar cy = coords[NSD*n + 1];
PetscScalar cz = coords[NSD*n + 2];
/* J_ij = d(x_j) / d(xi_i) */ /* J_ij = \sum _I GNi[j][I} * x_i */
J00 = J00 + GNi[0][n] * cx; /* J_xx */
J01 = J01 + GNi[0][n] * cy; /* J_xy = dx/deta */
J02 = J02 + GNi[0][n] * cz; /* J_xz = dx/dzeta */
J10 = J10 + GNi[1][n] * cx; /* J_yx = dy/dxi */
J11 = J11 + GNi[1][n] * cy; /* J_yy */
J12 = J12 + GNi[1][n] * cz; /* J_yz */
J20 = J20 + GNi[2][n] * cx; /* J_zx */
J21 = J21 + GNi[2][n] * cy; /* J_zy */
J22 = J22 + GNi[2][n] * cz; /* J_zz */
}
JJ[0][0] = J00; JJ[0][1] = J01; JJ[0][2] = J02;
JJ[1][0] = J10; JJ[1][1] = J11; JJ[1][2] = J12;
JJ[2][0] = J20; JJ[2][1] = J21; JJ[2][2] = J22;
matrix_inverse_3x3(JJ,iJ);
*det_J = J00*J11*J22 - J00*J12*J21 - J10*J01*J22 + J10*J02*J21 + J20*J01*J12 - J20*J02*J11;
for (n=0; n<NODES_PER_EL; n++) {
GNx[0][n] = GNi[0][n]*iJ[0][0] + GNi[1][n]*iJ[0][1] + GNi[2][n]*iJ[0][2];
GNx[1][n] = GNi[0][n]*iJ[1][0] + GNi[1][n]*iJ[1][1] + GNi[2][n]*iJ[1][2];
GNx[2][n] = GNi[0][n]*iJ[2][0] + GNi[1][n]*iJ[2][1] + GNi[2][n]*iJ[2][2];
}
}
static void ConstructGaussQuadrature3D(PetscInt *ngp,PetscScalar gp_xi[][NSD],PetscScalar gp_weight[])
{
*ngp = 8;
gp_xi[0][0] = -0.57735026919; gp_xi[0][1] = -0.57735026919; gp_xi[0][2] = -0.57735026919;
gp_xi[1][0] = -0.57735026919; gp_xi[1][1] = 0.57735026919; gp_xi[1][2] = -0.57735026919;
gp_xi[2][0] = 0.57735026919; gp_xi[2][1] = 0.57735026919; gp_xi[2][2] = -0.57735026919;
gp_xi[3][0] = 0.57735026919; gp_xi[3][1] = -0.57735026919; gp_xi[3][2] = -0.57735026919;
gp_xi[4][0] = -0.57735026919; gp_xi[4][1] = -0.57735026919; gp_xi[4][2] = 0.57735026919;
gp_xi[5][0] = -0.57735026919; gp_xi[5][1] = 0.57735026919; gp_xi[5][2] = 0.57735026919;
gp_xi[6][0] = 0.57735026919; gp_xi[6][1] = 0.57735026919; gp_xi[6][2] = 0.57735026919;
gp_xi[7][0] = 0.57735026919; gp_xi[7][1] = -0.57735026919; gp_xi[7][2] = 0.57735026919;
gp_weight[0] = 1.0;
gp_weight[1] = 1.0;
gp_weight[2] = 1.0;
gp_weight[3] = 1.0;
gp_weight[4] = 1.0;
gp_weight[5] = 1.0;
gp_weight[6] = 1.0;
gp_weight[7] = 1.0;
}
/* procs to the left claim the ghost node as their element */
#undef __FUNCT__
#define __FUNCT__ "DMDAGetLocalElementSize"
static PetscErrorCode DMDAGetLocalElementSize(DM da,PetscInt *mxl,PetscInt *myl,PetscInt *mzl)
{
PetscInt m,n,p,M,N,P;
PetscInt sx,sy,sz;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = DMDAGetInfo(da,0,&M,&N,&P,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&sx,&sy,&sz,&m,&n,&p);CHKERRQ(ierr);
if (mxl) {
*mxl = m;
if ((sx+m) == M) *mxl = m-1; /* last proc */
}
if (myl) {
*myl = n;
if ((sy+n) == N) *myl = n-1; /* last proc */
}
if (mzl) {
*mzl = p;
if ((sz+p) == P) *mzl = p-1; /* last proc */
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "DMDAGetElementCorners"
static PetscErrorCode DMDAGetElementCorners(DM da,PetscInt *sx,PetscInt *sy,PetscInt *sz,PetscInt *mx,PetscInt *my,PetscInt *mz)
{
PetscInt si,sj,sk;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = DMDAGetGhostCorners(da,&si,&sj,&sk,0,0,0);CHKERRQ(ierr);
if (sx) {
*sx = si;
if (si != 0) *sx = si+1;
}
if (sy) {
*sy = sj;
if (sj != 0) *sy = sj+1;
}
if (sz) {
*sz = sk;
if (sk != 0) *sz = sk+1;
}
ierr = DMDAGetLocalElementSize(da,mx,my,mz);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
i,j are the element indices
The unknown is a vector quantity.
The s[].c is used to indicate the degree of freedom.
*/
#undef __FUNCT__
#define __FUNCT__ "DMDAGetElementEqnums3D_up"
static PetscErrorCode DMDAGetElementEqnums3D_up(MatStencil s_u[],MatStencil s_p[],PetscInt i,PetscInt j,PetscInt k)
{
PetscInt n;
PetscFunctionBeginUser;
/* velocity */
n = 0;
/* node 0 */
s_u[n].i = i; s_u[n].j = j; s_u[n].k = k; s_u[n].c = 0; n++; /* Vx0 */
s_u[n].i = i; s_u[n].j = j; s_u[n].k = k; s_u[n].c = 1; n++; /* Vy0 */
s_u[n].i = i; s_u[n].j = j; s_u[n].k = k; s_u[n].c = 2; n++; /* Vz0 */
s_u[n].i = i; s_u[n].j = j+1; s_u[n].k = k; s_u[n].c = 0; n++;
s_u[n].i = i; s_u[n].j = j+1; s_u[n].k = k; s_u[n].c = 1; n++;
s_u[n].i = i; s_u[n].j = j+1; s_u[n].k = k; s_u[n].c = 2; n++;
s_u[n].i = i+1; s_u[n].j = j+1; s_u[n].k = k; s_u[n].c = 0; n++;
s_u[n].i = i+1; s_u[n].j = j+1; s_u[n].k = k; s_u[n].c = 1; n++;
s_u[n].i = i+1; s_u[n].j = j+1; s_u[n].k = k; s_u[n].c = 2; n++;
s_u[n].i = i+1; s_u[n].j = j; s_u[n].k = k; s_u[n].c = 0; n++;
s_u[n].i = i+1; s_u[n].j = j; s_u[n].k = k; s_u[n].c = 1; n++;
s_u[n].i = i+1; s_u[n].j = j; s_u[n].k = k; s_u[n].c = 2; n++;
/* */
s_u[n].i = i; s_u[n].j = j; s_u[n].k = k+1; s_u[n].c = 0; n++; /* Vx4 */
s_u[n].i = i; s_u[n].j = j; s_u[n].k = k+1; s_u[n].c = 1; n++; /* Vy4 */
s_u[n].i = i; s_u[n].j = j; s_u[n].k = k+1; s_u[n].c = 2; n++; /* Vz4 */
s_u[n].i = i; s_u[n].j = j+1; s_u[n].k = k+1; s_u[n].c = 0; n++;
s_u[n].i = i; s_u[n].j = j+1; s_u[n].k = k+1; s_u[n].c = 1; n++;
s_u[n].i = i; s_u[n].j = j+1; s_u[n].k = k+1; s_u[n].c = 2; n++;
s_u[n].i = i+1; s_u[n].j = j+1; s_u[n].k = k+1; s_u[n].c = 0; n++;
s_u[n].i = i+1; s_u[n].j = j+1; s_u[n].k = k+1; s_u[n].c = 1; n++;
s_u[n].i = i+1; s_u[n].j = j+1; s_u[n].k = k+1; s_u[n].c = 2; n++;
s_u[n].i = i+1; s_u[n].j = j; s_u[n].k = k+1; s_u[n].c = 0; n++;
s_u[n].i = i+1; s_u[n].j = j; s_u[n].k = k+1; s_u[n].c = 1; n++;
s_u[n].i = i+1; s_u[n].j = j; s_u[n].k = k+1; s_u[n].c = 2; n++;
/* pressure */
n = 0;
s_p[n].i = i; s_p[n].j = j; s_p[n].k = k; s_p[n].c = 3; n++; /* P0 */
s_p[n].i = i; s_p[n].j = j+1; s_p[n].k = k; s_p[n].c = 3; n++;
s_p[n].i = i+1; s_p[n].j = j+1; s_p[n].k = k; s_p[n].c = 3; n++;
s_p[n].i = i+1; s_p[n].j = j; s_p[n].k = k; s_p[n].c = 3; n++;
s_p[n].i = i; s_p[n].j = j; s_p[n].k = k+1; s_p[n].c = 3; n++; /* P0 */
s_p[n].i = i; s_p[n].j = j+1; s_p[n].k = k+1; s_p[n].c = 3; n++;
s_p[n].i = i+1; s_p[n].j = j+1; s_p[n].k = k+1; s_p[n].c = 3; n++;
s_p[n].i = i+1; s_p[n].j = j; s_p[n].k = k+1; s_p[n].c = 3; n++;
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "GetElementCoords3D"
static PetscErrorCode GetElementCoords3D(DMDACoor3d ***coords,PetscInt i,PetscInt j,PetscInt k,PetscScalar el_coord[])
{
PetscFunctionBeginUser;
/* get coords for the element */
el_coord[0] = coords[k][j][i].x;
el_coord[1] = coords[k][j][i].y;
el_coord[2] = coords[k][j][i].z;
el_coord[3] = coords[k][j+1][i].x;
el_coord[4] = coords[k][j+1][i].y;
el_coord[5] = coords[k][j+1][i].z;
el_coord[6] = coords[k][j+1][i+1].x;
el_coord[7] = coords[k][j+1][i+1].y;
el_coord[8] = coords[k][j+1][i+1].z;
el_coord[9] = coords[k][j][i+1].x;
el_coord[10] = coords[k][j][i+1].y;
el_coord[11] = coords[k][j][i+1].z;
el_coord[12] = coords[k+1][j][i].x;
el_coord[13] = coords[k+1][j][i].y;
el_coord[14] = coords[k+1][j][i].z;
el_coord[15] = coords[k+1][j+1][i].x;
el_coord[16] = coords[k+1][j+1][i].y;
el_coord[17] = coords[k+1][j+1][i].z;
el_coord[18] = coords[k+1][j+1][i+1].x;
el_coord[19] = coords[k+1][j+1][i+1].y;
el_coord[20] = coords[k+1][j+1][i+1].z;
el_coord[21] = coords[k+1][j][i+1].x;
el_coord[22] = coords[k+1][j][i+1].y;
el_coord[23] = coords[k+1][j][i+1].z;
PetscFunctionReturn(0);
}
#if 0
#undef __FUNCT__
#define __FUNCT__ "StokesDAGetNodalFields3D"
static PetscErrorCode StokesDAGetNodalFields3D(StokesDOF ***field,PetscInt i,PetscInt j,PetscInt k,StokesDOF nodal_fields[])
{
PetscFunctionBeginUser;
/* get the nodal fields for u */
nodal_fields[0].u_dof = field[k][j][i].u_dof;
nodal_fields[0].v_dof = field[k][j][i].v_dof;
nodal_fields[0].w_dof = field[k][j][i].w_dof;
nodal_fields[1].u_dof = field[k][j+1][i].u_dof;
nodal_fields[1].v_dof = field[k][j+1][i].v_dof;
nodal_fields[1].w_dof = field[k][j+1][i].w_dof;
nodal_fields[2].u_dof = field[k][j+1][i+1].u_dof;
nodal_fields[2].v_dof = field[k][j+1][i+1].v_dof;
nodal_fields[2].w_dof = field[k][j+1][i+1].w_dof;
nodal_fields[3].u_dof = field[k][j][i+1].u_dof;
nodal_fields[3].v_dof = field[k][j][i+1].v_dof;
nodal_fields[3].w_dof = field[k][j][i+1].w_dof;
nodal_fields[4].u_dof = field[k+1][j][i].u_dof;
nodal_fields[4].v_dof = field[k+1][j][i].v_dof;
nodal_fields[4].w_dof = field[k+1][j][i].w_dof;
nodal_fields[5].u_dof = field[k+1][j+1][i].u_dof;
nodal_fields[5].v_dof = field[k+1][j+1][i].v_dof;
nodal_fields[5].w_dof = field[k+1][j+1][i].w_dof;
nodal_fields[6].u_dof = field[k+1][j+1][i+1].u_dof;
nodal_fields[6].v_dof = field[k+1][j+1][i+1].v_dof;
nodal_fields[6].w_dof = field[k+1][j+1][i+1].w_dof;
nodal_fields[7].u_dof = field[k+1][j][i+1].u_dof;
nodal_fields[7].v_dof = field[k+1][j][i+1].v_dof;
nodal_fields[7].w_dof = field[k+1][j][i+1].w_dof;
/* get the nodal fields for p */
nodal_fields[0].p_dof = field[k][j][i].p_dof;
nodal_fields[1].p_dof = field[k][j+1][i].p_dof;
nodal_fields[2].p_dof = field[k][j+1][i+1].p_dof;
nodal_fields[3].p_dof = field[k][j][i+1].p_dof;
nodal_fields[4].p_dof = field[k+1][j][i].p_dof;
nodal_fields[5].p_dof = field[k+1][j+1][i].p_dof;
nodal_fields[6].p_dof = field[k+1][j+1][i+1].p_dof;
nodal_fields[7].p_dof = field[k+1][j][i+1].p_dof;
PetscFunctionReturn(0);
}
#endif
static PetscInt ASS_MAP_wIwDI_uJuDJ(PetscInt wi,PetscInt wd,PetscInt w_NPE,PetscInt w_dof,PetscInt ui,PetscInt ud,PetscInt u_NPE,PetscInt u_dof)
{
PetscInt ij;
PETSC_UNUSED PetscInt r,c,nr,nc;
nr = w_NPE*w_dof;
nc = u_NPE*u_dof;
r = w_dof*wi+wd;
c = u_dof*ui+ud;
ij = r*nc+c;
return ij;
}
#undef __FUNCT__
#define __FUNCT__ "DMDASetValuesLocalStencil3D_ADD_VALUES"
static PetscErrorCode DMDASetValuesLocalStencil3D_ADD_VALUES(StokesDOF ***fields_F,MatStencil u_eqn[],MatStencil p_eqn[],PetscScalar Fe_u[],PetscScalar Fe_p[])
{
PetscInt n,II,J,K;
PetscFunctionBeginUser;
for (n = 0; n<NODES_PER_EL; n++) {
II = u_eqn[NSD*n].i;
J = u_eqn[NSD*n].j;
K = u_eqn[NSD*n].k;
fields_F[K][J][II].u_dof = fields_F[K][J][II].u_dof+Fe_u[NSD*n];
II = u_eqn[NSD*n+1].i;
J = u_eqn[NSD*n+1].j;
K = u_eqn[NSD*n+1].k;
fields_F[K][J][II].v_dof = fields_F[K][J][II].v_dof+Fe_u[NSD*n+1];
II = u_eqn[NSD*n+2].i;
J = u_eqn[NSD*n+2].j;
K = u_eqn[NSD*n+2].k;
fields_F[K][J][II].w_dof = fields_F[K][J][II].w_dof+Fe_u[NSD*n+2];
II = p_eqn[n].i;
J = p_eqn[n].j;
K = p_eqn[n].k;
fields_F[K][J][II].p_dof = fields_F[K][J][II].p_dof+Fe_p[n];
}
PetscFunctionReturn(0);
}
static void FormStressOperatorQ13D(PetscScalar Ke[],PetscScalar coords[],PetscScalar eta[])
{
PetscInt ngp;
PetscScalar gp_xi[GAUSS_POINTS][NSD];
PetscScalar gp_weight[GAUSS_POINTS];
PetscInt p,i,j,k;
PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
PetscScalar J_p,tildeD[6];
PetscScalar B[6][U_DOFS*NODES_PER_EL];
const PetscInt nvdof = U_DOFS*NODES_PER_EL;
/* define quadrature rule */
ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
/* evaluate integral */
for (p = 0; p < ngp; p++) {
ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,coords,&J_p);
for (i = 0; i < NODES_PER_EL; i++) {
PetscScalar d_dx_i = GNx_p[0][i];
PetscScalar d_dy_i = GNx_p[1][i];
PetscScalar d_dz_i = GNx_p[2][i];
B[0][3*i] = d_dx_i; B[0][3*i+1] = 0.0; B[0][3*i+2] = 0.0;
B[1][3*i] = 0.0; B[1][3*i+1] = d_dy_i; B[1][3*i+2] = 0.0;
B[2][3*i] = 0.0; B[2][3*i+1] = 0.0; B[2][3*i+2] = d_dz_i;
B[3][3*i] = d_dy_i; B[3][3*i+1] = d_dx_i; B[3][3*i+2] = 0.0; /* e_xy */
B[4][3*i] = d_dz_i; B[4][3*i+1] = 0.0; B[4][3*i+2] = d_dx_i; /* e_xz */
B[5][3*i] = 0.0; B[5][3*i+1] = d_dz_i; B[5][3*i+2] = d_dy_i; /* e_yz */
}
tildeD[0] = 2.0*gp_weight[p]*J_p*eta[p];
tildeD[1] = 2.0*gp_weight[p]*J_p*eta[p];
tildeD[2] = 2.0*gp_weight[p]*J_p*eta[p];
tildeD[3] = gp_weight[p]*J_p*eta[p];
tildeD[4] = gp_weight[p]*J_p*eta[p];
tildeD[5] = gp_weight[p]*J_p*eta[p];
/* form Bt tildeD B */
/*
Ke_ij = Bt_ik . D_kl . B_lj
= B_ki . D_kl . B_lj
= B_ki . D_kk . B_kj
*/
for (i = 0; i < nvdof; i++) {
for (j = i; j < nvdof; j++) {
for (k = 0; k < 6; k++) {
Ke[i*nvdof+j] += B[k][i]*tildeD[k]*B[k][j];
}
}
}
}
/* fill lower triangular part */
#if defined(ASSEMBLE_LOWER_TRIANGULAR)
for (i = 0; i < nvdof; i++) {
for (j = i; j < nvdof; j++) {
Ke[j*nvdof+i] = Ke[i*nvdof+j];
}
}
#endif
}
static void FormGradientOperatorQ13D(PetscScalar Ke[],PetscScalar coords[])
{
PetscInt ngp;
PetscScalar gp_xi[GAUSS_POINTS][NSD];
PetscScalar gp_weight[GAUSS_POINTS];
PetscInt p,i,j,di;
PetscScalar Ni_p[NODES_PER_EL];
PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
PetscScalar J_p,fac;
/* define quadrature rule */
ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
/* evaluate integral */
for (p = 0; p < ngp; p++) {
ShapeFunctionQ13D_Evaluate(gp_xi[p],Ni_p);
ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,coords,&J_p);
fac = gp_weight[p]*J_p;
for (i = 0; i < NODES_PER_EL; i++) { /* u nodes */
for (di = 0; di < NSD; di++) { /* u dofs */
for (j = 0; j < NODES_PER_EL; j++) { /* p nodes, p dofs = 1 (ie no loop) */
PetscInt IJ;
IJ = ASS_MAP_wIwDI_uJuDJ(i,di,NODES_PER_EL,3,j,0,NODES_PER_EL,1);
Ke[IJ] = Ke[IJ]-GNx_p[di][i]*Ni_p[j]*fac;
}
}
}
}
}
static void FormDivergenceOperatorQ13D(PetscScalar De[],PetscScalar coords[])
{
PetscScalar Ge[U_DOFS*NODES_PER_EL*P_DOFS*NODES_PER_EL];
PetscInt i,j;
PetscInt nr_g,nc_g;
PetscMemzero(Ge,sizeof(PetscScalar)*U_DOFS*NODES_PER_EL*P_DOFS*NODES_PER_EL);
FormGradientOperatorQ13D(Ge,coords);
nr_g = U_DOFS*NODES_PER_EL;
nc_g = P_DOFS*NODES_PER_EL;
for (i = 0; i < nr_g; i++) {
for (j = 0; j < nc_g; j++) {
De[nr_g*j+i] = Ge[nc_g*i+j];
}
}
}
static void FormStabilisationOperatorQ13D(PetscScalar Ke[],PetscScalar coords[],PetscScalar eta[])
{
PetscInt ngp;
PetscScalar gp_xi[GAUSS_POINTS][NSD];
PetscScalar gp_weight[GAUSS_POINTS];
PetscInt p,i,j;
PetscScalar Ni_p[NODES_PER_EL];
PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
PetscScalar J_p,fac,eta_avg;
/* define quadrature rule */
ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
/* evaluate integral */
for (p = 0; p < ngp; p++) {
ShapeFunctionQ13D_Evaluate(gp_xi[p],Ni_p);
ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,coords,&J_p);
fac = gp_weight[p]*J_p;
/*
for (i = 0; i < NODES_PER_EL; i++) {
for (j = i; j < NODES_PER_EL; j++) {
Ke[NODES_PER_EL*i+j] -= fac*(Ni_p[i]*Ni_p[j]-0.015625);
}
}
*/
for (i = 0; i < NODES_PER_EL; i++) {
for (j = 0; j < NODES_PER_EL; j++) {
Ke[NODES_PER_EL*i+j] -= fac*(Ni_p[i]*Ni_p[j]-0.015625);
}
}
}
/* scale */
eta_avg = 0.0;
for (p = 0; p < ngp; p++) eta_avg += eta[p];
eta_avg = (1.0/((PetscScalar)ngp))*eta_avg;
fac = 1.0/eta_avg;
/*
for (i = 0; i < NODES_PER_EL; i++) {
for (j = i; j < NODES_PER_EL; j++) {
Ke[NODES_PER_EL*i+j] = fac*Ke[NODES_PER_EL*i+j];
#if defined(ASSEMBLE_LOWER_TRIANGULAR)
Ke[NODES_PER_EL*j+i] = Ke[NODES_PER_EL*i+j];
#endif
}
}
*/
for (i = 0; i < NODES_PER_EL; i++) {
for (j = 0; j < NODES_PER_EL; j++) {
Ke[NODES_PER_EL*i+j] = fac*Ke[NODES_PER_EL*i+j];
}
}
}
#if 0
static void FormScaledMassMatrixOperatorQ13D(PetscScalar Ke[],PetscScalar coords[],PetscScalar eta[])
{
PetscInt ngp;
PetscScalar gp_xi[GAUSS_POINTS][NSD];
PetscScalar gp_weight[GAUSS_POINTS];
PetscInt p,i,j;
PetscScalar Ni_p[NODES_PER_EL];
PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
PetscScalar J_p,fac,eta_avg;
/* define quadrature rule */
ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
/* evaluate integral */
for (p = 0; p < ngp; p++) {
ShapeFunctionQ13D_Evaluate(gp_xi[p],Ni_p);
ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,coords,&J_p);
fac = gp_weight[p]*J_p;
/*
for (i = 0; i < NODES_PER_EL; i++) {
for (j = i; j < NODES_PER_EL; j++) {
Ke[NODES_PER_EL*i+j] = Ke[NODES_PER_EL*i+j]-fac*Ni_p[i]*Ni_p[j];
}
}
*/
for (i = 0; i < NODES_PER_EL; i++) {
for (j = 0; j < NODES_PER_EL; j++) {
Ke[NODES_PER_EL*i+j] = Ke[NODES_PER_EL*i+j]-fac*Ni_p[i]*Ni_p[j];
}
}
}
/* scale */
eta_avg = 0.0;
for (p = 0; p < ngp; p++) eta_avg += eta[p];
eta_avg = (1.0/((PetscScalar)ngp))*eta_avg;
fac = 1.0/eta_avg;
/*
for (i = 0; i < NODES_PER_EL; i++) {
for (j = i; j < NODES_PER_EL; j++) {
Ke[NODES_PER_EL*i+j] = fac*Ke[NODES_PER_EL*i+j];
#if defined(ASSEMBLE_LOWER_TRIANGULAR)
Ke[NODES_PER_EL*j+i] = Ke[NODES_PER_EL*i+j];
#endif
}
}
*/
for (i = 0; i < NODES_PER_EL; i++) {
for (j = 0; j < NODES_PER_EL; j++) {
Ke[NODES_PER_EL*i+j] = fac*Ke[NODES_PER_EL*i+j];
}
}
}
#endif
static void FormMomentumRhsQ13D(PetscScalar Fe[],PetscScalar coords[],PetscScalar fx[],PetscScalar fy[],PetscScalar fz[])
{
PetscInt ngp;
PetscScalar gp_xi[GAUSS_POINTS][NSD];
PetscScalar gp_weight[GAUSS_POINTS];
PetscInt p,i;
PetscScalar Ni_p[NODES_PER_EL];
PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
PetscScalar J_p,fac;
/* define quadrature rule */
ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
/* evaluate integral */
for (p = 0; p < ngp; p++) {
ShapeFunctionQ13D_Evaluate(gp_xi[p],Ni_p);
ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,coords,&J_p);
fac = gp_weight[p]*J_p;
for (i = 0; i < NODES_PER_EL; i++) {
Fe[NSD*i] -= fac*Ni_p[i]*fx[p];
Fe[NSD*i+1] -= fac*Ni_p[i]*fy[p];
Fe[NSD*i+2] -= fac*Ni_p[i]*fz[p];
}
}
}
static void FormContinuityRhsQ13D(PetscScalar Fe[],PetscScalar coords[],PetscScalar hc[])
{
PetscInt ngp;
PetscScalar gp_xi[GAUSS_POINTS][NSD];
PetscScalar gp_weight[GAUSS_POINTS];
PetscInt p,i;
PetscScalar Ni_p[NODES_PER_EL];
PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
PetscScalar J_p,fac;
/* define quadrature rule */
ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
/* evaluate integral */
for (p = 0; p < ngp; p++) {
ShapeFunctionQ13D_Evaluate(gp_xi[p],Ni_p);
ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,coords,&J_p);
fac = gp_weight[p]*J_p;
for (i = 0; i < NODES_PER_EL; i++) Fe[i] -= fac*Ni_p[i]*hc[p];
}
}
#define _ZERO_ROWCOL_i(A,i) { \
PetscInt KK; \
PetscScalar tmp = A[24*(i)+(i)]; \
for (KK=0;KK<24;KK++) A[24*(i)+KK]=0.0; \
for (KK=0;KK<24;KK++) A[24*KK+(i)]=0.0; \
A[24*(i)+(i)] = tmp;} \
#define _ZERO_ROW_i(A,i) { \
PetscInt KK; \
for (KK=0;KK<8;KK++) A[8*(i)+KK]=0.0;}
#define _ZERO_COL_i(A,i) { \
PetscInt KK; \
for (KK=0;KK<8;KK++) A[24*KK+(i)]=0.0;}
#undef __FUNCT__
#define __FUNCT__ "AssembleA_Stokes"
static PetscErrorCode AssembleA_Stokes(Mat A,DM stokes_da,CellProperties cell_properties)
{
DM cda;
Vec coords;
DMDACoor3d ***_coords;
MatStencil u_eqn[NODES_PER_EL*U_DOFS];
MatStencil p_eqn[NODES_PER_EL*P_DOFS];
PetscInt sex,sey,sez,mx,my,mz;
PetscInt ei,ej,ek;
PetscScalar Ae[NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS];
PetscScalar Ge[NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS];
PetscScalar De[NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS];
PetscScalar Ce[NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS];
PetscScalar el_coords[NODES_PER_EL*NSD];
GaussPointCoefficients *props;
PetscScalar *prop_eta;
PetscInt n,M,N,P;
PetscBool no_stabilization = PETSC_FALSE;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = PetscOptionsGetBool(NULL,NULL,"-no_stab",&no_stabilization,NULL);CHKERRQ(ierr);
if (no_stabilization) PetscPrintf(PETSC_COMM_WORLD,"** WARNING ** You are assembling a Q1Q1 saddle point system without the stabilization term\n");
ierr = DMDAGetInfo(stokes_da,0,&M,&N,&P,0,0,0, 0,0,0,0,0,0);CHKERRQ(ierr);
/* setup for coords */
ierr = DMGetCoordinateDM(stokes_da,&cda);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(stokes_da,&coords);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cda,coords,&_coords);CHKERRQ(ierr);
ierr = DMDAGetElementCorners(stokes_da,&sex,&sey,&sez,&mx,&my,&mz);CHKERRQ(ierr);
for (ek = sez; ek < sez+mz; ek++) {
for (ej = sey; ej < sey+my; ej++) {
for (ei = sex; ei < sex+mx; ei++) {
/* get coords for the element */
ierr = GetElementCoords3D(_coords,ei,ej,ek,el_coords);CHKERRQ(ierr);
/* get cell properties */
ierr = CellPropertiesGetCell(cell_properties,ei,ej,ek,&props);CHKERRQ(ierr);
/* get coefficients for the element */
prop_eta = props->eta;
/* initialise element stiffness matrix */
ierr = PetscMemzero(Ae,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS);CHKERRQ(ierr);
ierr = PetscMemzero(Ge,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS);CHKERRQ(ierr);
ierr = PetscMemzero(De,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS);CHKERRQ(ierr);
ierr = PetscMemzero(Ce,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS);CHKERRQ(ierr);
/* form element stiffness matrix */
FormStressOperatorQ13D(Ae,el_coords,prop_eta);
FormGradientOperatorQ13D(Ge,el_coords);
/*#if defined(ASSEMBLE_LOWER_TRIANGULAR)*/
FormDivergenceOperatorQ13D(De,el_coords);
/*#endif*/
FormStabilisationOperatorQ13D(Ce,el_coords,prop_eta);
/* insert element matrix into global matrix */
ierr = DMDAGetElementEqnums3D_up(u_eqn,p_eqn,ei,ej,ek);CHKERRQ(ierr);
for (n=0; n<NODES_PER_EL; n++) {
if ((u_eqn[3*n].i == 0) || (u_eqn[3*n].i == M-1)) {
_ZERO_ROWCOL_i(Ae,3*n);
_ZERO_ROW_i (Ge,3*n);
_ZERO_COL_i (De,3*n);
}
if ((u_eqn[3*n+1].j == 0) || (u_eqn[3*n+1].j == N-1)) {
_ZERO_ROWCOL_i(Ae,3*n+1);
_ZERO_ROW_i (Ge,3*n+1);
_ZERO_COL_i (De,3*n+1);
}
if (u_eqn[3*n+2].k == 0) {
_ZERO_ROWCOL_i(Ae,3*n+2);
_ZERO_ROW_i (Ge,3*n+2);
_ZERO_COL_i (De,3*n+2);
}
}
ierr = MatSetValuesStencil(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*U_DOFS,u_eqn,Ae,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ge,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*U_DOFS,u_eqn,De,ADD_VALUES);CHKERRQ(ierr);
if (!no_stabilization) {
ierr = MatSetValuesStencil(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ce,ADD_VALUES);CHKERRQ(ierr);
}
}
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(cda,coords,&_coords);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "AssembleF_Stokes"
static PetscErrorCode AssembleF_Stokes(Vec F,DM stokes_da,CellProperties cell_properties)
{
DM cda;
Vec coords;
DMDACoor3d ***_coords;
MatStencil u_eqn[NODES_PER_EL*U_DOFS];
MatStencil p_eqn[NODES_PER_EL*P_DOFS];
PetscInt sex,sey,sez,mx,my,mz;
PetscInt ei,ej,ek;
PetscScalar Fe[NODES_PER_EL*U_DOFS];
PetscScalar He[NODES_PER_EL*P_DOFS];
PetscScalar el_coords[NODES_PER_EL*NSD];
GaussPointCoefficients *props;
PetscScalar *prop_fx,*prop_fy,*prop_fz,*prop_hc;
Vec local_F;
StokesDOF ***ff;
PetscInt n,M,N,P;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = DMDAGetInfo(stokes_da,0,&M,&N,&P,0,0,0, 0,0,0,0,0,0);CHKERRQ(ierr);
/* setup for coords */
ierr = DMGetCoordinateDM(stokes_da,&cda);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(stokes_da,&coords);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cda,coords,&_coords);CHKERRQ(ierr);
/* get acces to the vector */
ierr = DMGetLocalVector(stokes_da,&local_F);CHKERRQ(ierr);
ierr = VecZeroEntries(local_F);CHKERRQ(ierr);
ierr = DMDAVecGetArray(stokes_da,local_F,&ff);CHKERRQ(ierr);
ierr = DMDAGetElementCorners(stokes_da,&sex,&sey,&sez,&mx,&my,&mz);CHKERRQ(ierr);
for (ek = sez; ek < sez+mz; ek++) {
for (ej = sey; ej < sey+my; ej++) {
for (ei = sex; ei < sex+mx; ei++) {
/* get coords for the element */
ierr = GetElementCoords3D(_coords,ei,ej,ek,el_coords);CHKERRQ(ierr);
/* get cell properties */
ierr = CellPropertiesGetCell(cell_properties,ei,ej,ek,&props);CHKERRQ(ierr);
/* get coefficients for the element */
prop_fx = props->fx;
prop_fy = props->fy;
prop_fz = props->fz;
prop_hc = props->hc;
/* initialise element stiffness matrix */
ierr = PetscMemzero(Fe,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS);CHKERRQ(ierr);