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PDEFilter.cc
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PDEFilter.cc
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#include <PDEFilter.h>
#include <TopOpt.h>
//#include <petsc-private/dmdaimpl.h>
#include <petsc/private/dmdaimpl.h>
/* -----------------------------------------------------------------------------
Authors: Niels Aage, Erik Andreassen, Boyan Lazarov, August 2013
Updated: June 2019, Niels Aage
Copyright (C) 2013-2019,
This PDEFilter implementation is licensed under Version 2.1 of the GNU
Lesser General Public License.
This MMA implementation 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 Module is distributed in the hope that it will be useful,implementation
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this Module; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
-------------------------------------------------------------------------- */
PDEFilt::PDEFilt(DM da_nodes, PetscScalar rmin) {
PetscPrintf(PETSC_COMM_WORLD,"Setting up PDE filter ... \n");
R = rmin / 2.0 / sqrt(3); // conversion factor for the PDEfilter
nlvls = 3; // MG levels
// number of nodal dofs
PetscInt numnodaldof = 1;
// Stencil width: each node connects to a box around it - linear elements
PetscInt stencilwidth = 1;
PetscScalar dx, dy, dz;
DMBoundaryType bx, by, bz;
DMDAStencilType stype;
{
// Extract information from the nodal mesh
PetscInt M, N, P, md, nd, pd;
DMDAGetInfo(da_nodes, NULL, &M, &N, &P, &md, &nd, &pd, NULL, NULL, &bx, &by, &bz, &stype);
// Find the element size
Vec lcoor;
DMGetCoordinatesLocal(da_nodes, &lcoor);
PetscScalar* lcoorp;
VecGetArray(lcoor, &lcoorp);
PetscInt nel, nen;
const PetscInt* necon;
DMDAGetElements_3D(da_nodes, &nel, &nen, &necon);
// Use the first element to compute the dx, dy, dz
dx = lcoorp[3 * necon[0 * nen + 1] + 0] - lcoorp[3 * necon[0 * nen + 0] + 0];
dy = lcoorp[3 * necon[0 * nen + 2] + 1] - lcoorp[3 * necon[0 * nen + 1] + 1];
dz = lcoorp[3 * necon[0 * nen + 4] + 2] - lcoorp[3 * necon[0 * nen + 0] + 2];
VecRestoreArray(lcoor, &lcoorp);
// ELement volume
elemVol = dx * dy * dz;
nn[0] = M;
nn[1] = N;
nn[2] = P;
ne[0] = nn[0] - 1;
ne[1] = nn[1] - 1;
ne[2] = nn[2] - 1;
xc[0] = 0.0;
xc[1] = ne[0] * M;
xc[2] = 0.0;
xc[3] = ne[1] * N;
xc[4] = 0.0;
xc[5] = ne[2] * P;
}
// Create the nodal mesh
DMDACreate3d(PETSC_COMM_WORLD, bx, by, bz, stype, nn[0], nn[1], nn[2], PETSC_DECIDE, PETSC_DECIDE, PETSC_DECIDE,
numnodaldof, stencilwidth, 0, 0, 0, &(da_nodal));
// Initialize
DMSetFromOptions(da_nodal);
DMSetUp(da_nodal);
// Set the coordinates
DMDASetUniformCoordinates(da_nodal, xc[0], xc[1], xc[2], xc[3], xc[4], xc[5]);
// Set the element type to Q1: Otherwise calls to GetElements will change to
// P1 ! STILL DOESN*T WORK !!!!
DMDASetElementType(da_nodal, DMDA_ELEMENT_Q1);
// Create the element mesh
// find the geometric partitioning of the nodal mesh, so the element mesh will
// coincide
PetscInt md, nd, pd;
DMDAGetInfo(da_nodal, NULL, NULL, NULL, NULL, &md, &nd, &pd, NULL, NULL, NULL, NULL, NULL, NULL);
PetscInt* Lx = new PetscInt[md];
PetscInt* Ly = new PetscInt[nd];
PetscInt* Lz = new PetscInt[pd];
// get number of nodes for each partition
const PetscInt *LxCorrect, *LyCorrect, *LzCorrect;
DMDAGetOwnershipRanges(da_nodal, &LxCorrect, &LyCorrect, &LzCorrect);
// subtract one from the lower left corner
for (int i = 0; i < md; i++) {
Lx[i] = LxCorrect[i];
if (i == 0) {
Lx[i] = Lx[i] - 1;
}
}
for (int i = 0; i < nd; i++) {
Ly[i] = LyCorrect[i];
if (i == 0) {
Ly[i] = Ly[i] - 1;
}
}
for (int i = 0; i < pd; i++) {
Lz[i] = LzCorrect[i];
if (i == 0) {
Lz[i] = Lz[i] - 1;
}
}
PetscInt overlap = 0;
// Create the element grid:
DMDACreate3d(PETSC_COMM_WORLD, bx, by, bz, stype, nn[0] - 1, nn[1] - 1, nn[2] - 1, md, nd, pd, 1, overlap, Lx, Ly,
Lz, &(da_element));
// Initialize
DMSetFromOptions(da_element);
DMSetUp(da_element);
delete[] Lx;
delete[] Ly;
delete[] Lz;
PDEFilterMatrix(dx, dy, dz, R, KF, TF);
// create the stiffness matrix
DMCreateMatrix(da_nodal, &(K));
// create RHS
DMCreateGlobalVector(da_nodal, &(RHS));
DMCreateGlobalVector(da_element, &(X));
VecDuplicate(RHS, &U);
// Create T matrix
{
PetscInt m;
PetscInt n;
// PetscInt M;
// PetscInt N;
// m,M extract it from RHS
// n,N extract it from X
VecGetLocalSize(RHS, &m);
VecGetLocalSize(X, &n);
MatCreateAIJ(PETSC_COMM_WORLD, m, n, PETSC_DETERMINE, PETSC_DETERMINE, 8, NULL, 7, NULL, &T);
ISLocalToGlobalMapping rmapping;
ISLocalToGlobalMapping cmapping;
DMGetLocalToGlobalMapping(da_nodal, &rmapping);
DMGetLocalToGlobalMapping(da_element, &cmapping);
MatSetLocalToGlobalMapping(T, rmapping, cmapping);
}
MatAssemble();
SetUpSolver();
// test
PetscRandom rctx;
PetscRandomCreate(PETSC_COMM_WORLD, &rctx);
PetscRandomSetType(rctx, PETSCRAND48);
VecSetRandom(X, rctx);
PetscRandomDestroy(&rctx);
PetscPrintf(PETSC_COMM_WORLD,"Calling FilterProject\n");
FilterProject(X, X);
Gradients(X, X);
//
PetscPrintf(PETSC_COMM_WORLD, "Done setting up the PDEFilter\n");
}
PetscErrorCode PDEFilt::FilterProject(Vec OX, Vec FX) {
// PetscPrintf(PETSC_COMM_WORLD,"Inside FilterProject\n");
PetscErrorCode ierr;
double t1, t2;
PetscScalar rnorm;
PetscInt niter;
t1 = MPI_Wtime();
ierr = MatMult(T, OX, RHS);
CHKERRQ(ierr);
ierr = VecCopy(RHS, U);
CHKERRQ(ierr);
ierr = VecScale(RHS, elemVol);
CHKERRQ(ierr);
ierr = KSPSolve(ksp, RHS, U);
CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp, &niter);
CHKERRQ(ierr);
ierr = KSPGetResidualNorm(ksp, &rnorm);
CHKERRQ(ierr);
ierr = MatMultTranspose(T, U, FX);
CHKERRQ(ierr);
t2 = MPI_Wtime();
PetscPrintf(PETSC_COMM_WORLD, "PDEFilter solver: iter: %i, rerr.: %e, time: %f\n", niter, rnorm, t2 - t1);
return ierr;
}
PetscErrorCode PDEFilt::Gradients(Vec OS, Vec FS) { return FilterProject(OS, FS); }
PDEFilt::~PDEFilt() { Free(); }
PetscErrorCode PDEFilt::Free() {
PetscErrorCode ierr;
KSPDestroy(&ksp);
VecDestroy(&RHS);
VecDestroy(&X);
VecDestroy(&U);
MatDestroy(&T);
MatDestroy(&K);
ierr = DMDestroy(&da_nodal);
CHKERRQ(ierr);
ierr = DMDestroy(&da_element);
CHKERRQ(ierr);
return ierr;
}
void PDEFilt::MatAssemble() {
// Get the FE mesh structure (from the nodal mesh)
PetscInt nel, nen;
const PetscInt* necon;
DMDAGetElements_3D(da_nodal, &nel, &nen, &necon);
MatZeroEntries(K);
MatZeroEntries(T);
PetscInt* edof = new PetscInt[8];
for (PetscInt i = 0; i < nel; i++) {
// loop over element nodes
for (PetscInt j = 0; j < nen; j++) {
edof[j] = necon[i * nen + j];
}
MatSetValuesLocal(K, 8, edof, 8, edof, KF, ADD_VALUES);
// assemble the T matrix
MatSetValuesLocal(T, 8, edof, 1, &i, TF, ADD_VALUES);
}
MatAssemblyBegin(K, MAT_FINAL_ASSEMBLY);
MatAssemblyBegin(T, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(K, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(T, MAT_FINAL_ASSEMBLY);
delete[] edof;
}
PetscErrorCode PDEFilt::SetUpSolver() {
// make sure ksp is not allocated before
PetscErrorCode ierr;
PC pc;
// The fine grid Krylov method
KSPCreate(PETSC_COMM_WORLD, &ksp);
ierr = KSPSetType(ksp, KSPFGMRES); // KSPCG, KSPGMRES
PetscInt restart = 20;
ierr = KSPGMRESSetRestart(ksp, restart);
PetscScalar rtol = 1.0e-8;
PetscScalar atol = 1.0e-50;
PetscScalar dtol = 1.0e3;
PetscInt maxitsGlobal = 60;
ierr = KSPSetTolerances(ksp, rtol, atol, dtol, maxitsGlobal);
PetscBool initialGuessNonzero;
PetscOptionsGetBool(NULL,NULL,"-ksp_initial_guess_nonzero",&initialGuessNonzero,NULL);
if (initialGuessNonzero){
ierr = KSPSetInitialGuessNonzero(ksp, PETSC_TRUE);
} else {
ierr = KSPSetInitialGuessNonzero(ksp, PETSC_FALSE);
}
KSPSetOperators(ksp, K, K); // ,SAME_PRECONDITIONER is now set in the prec
// preconditioner
KSPGetPC(ksp, &pc);
PCSetType(pc, PCMG);
// Set solver from options
KSPSetFromOptions(ksp);
// Get the prec again - check if it has changed
KSPGetPC(ksp, &pc);
ierr = PCSetReusePreconditioner(pc, PETSC_TRUE);
CHKERRQ(ierr);
// Flag for pcmg pc
PetscBool pcmg_flag = PETSC_TRUE;
PetscObjectTypeCompare((PetscObject)pc, PCMG, &pcmg_flag);
// Only if PCMG is used
if (pcmg_flag) {
// DMs for grid hierachy
DM *da_list, *daclist;
Mat R;
PetscMalloc(sizeof(DM) * nlvls, &da_list);
for (PetscInt k = 0; k < nlvls; k++)
da_list[k] = NULL;
PetscMalloc(sizeof(DM) * nlvls, &daclist);
for (PetscInt k = 0; k < nlvls; k++)
daclist[k] = NULL;
// Set 0 to the finest level
daclist[0] = da_nodal;
// Coordinates
PetscReal xmin = xc[0], xmax = xc[1], ymin = xc[2], ymax = xc[3], zmin = xc[4], zmax = xc[5];
// Set up the coarse meshes
ierr = DMCoarsenHierarchy(da_nodal, nlvls - 1, &daclist[1]);
CHKERRQ(ierr);
for (PetscInt k = 0; k < nlvls; k++) {
// NOTE: finest grid is nlevels - 1: PCMG MUST USE THIS ORDER ???
da_list[k] = daclist[nlvls - 1 - k];
DMDASetUniformCoordinates(da_list[k], xmin, xmax, ymin, ymax, zmin, zmax);
}
// the PCMG specific options
PCMGSetLevels(pc, nlvls, NULL);
PCMGSetType(pc, PC_MG_MULTIPLICATIVE); // Default
PCMGSetCycleType(pc, PC_MG_CYCLE_V);
PCMGSetGalerkin(pc, PC_MG_GALERKIN_BOTH);
for (PetscInt k = 1; k < nlvls; k++) {
DMCreateInterpolation(da_list[k - 1], da_list[k], &R, NULL);
PCMGSetInterpolation(pc, k, R);
MatDestroy(&R);
}
for (PetscInt k = 1; k < nlvls; k++) { // 0 level should be dealocated in the destructor
DMDestroy(&daclist[k]);
}
PetscFree(da_list);
PetscFree(daclist);
// AVOID THE DEFAULT FOR THE MG PART
{
// SET the coarse grid solver:
// i.e. get a pointer to the ksp and change its settings
KSP cksp;
PCMGGetCoarseSolve(pc, &cksp);
// The solver
ierr = KSPSetType(cksp, KSPGMRES); // KSPCG, KSPFGMRES
// PetscInt restarts[nlvls] = {10, 1 , 1}; // coarse .... fine
restart = 10;
ierr = KSPGMRESSetRestart(cksp, restart);
rtol = 1.0e-8;
atol = 1.0e-50;
dtol = 1e3;
PetscInt maxits = 10;
ierr = KSPSetTolerances(cksp, rtol, atol, dtol, maxits);
// The preconditioner
PC cpc;
KSPGetPC(cksp, &cpc);
// PCSetType(cpc,PCSOR); // PCSOR, PCSPAI (NEEDS TO BE COMPILED), PCJACOBI
PCSetType(cpc, PCJACOBI);
// Set smoothers on all levels (except for coarse grid):
for (PetscInt k = 1; k < nlvls; k++) {
KSP dksp;
PCMGGetSmoother(pc, k, &dksp);
PC dpc;
KSPGetPC(dksp, &dpc);
ierr = KSPSetType(dksp,
KSPGMRES); // KSPCG, KSPGMRES, KSPCHEBYSHEV (VERY GOOD FOR SPD)
restart = 1;
ierr = KSPGMRESSetRestart(dksp, restart);
ierr = KSPSetTolerances(dksp, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT,
restart); // NOTE maxitr=restart;
PCSetType(dpc, PCJACOBI); // PCJACOBI, PCSOR for KSPCHEBYSHEV very good
}
}
}
// // Write check to screen:
// // Check the overall Krylov solver
// KSPType ksptype;
// KSPGetType(ksp,&ksptype);
// PCType pctype;
// PCGetType(pc,&pctype);
// PetscInt mmax;
// KSPGetTolerances(ksp,NULL,NULL,NULL,&mmax);
// PetscPrintf(PETSC_COMM_WORLD,"##############################################################\n");
// PetscPrintf(PETSC_COMM_WORLD,"################# Linear solver
// settings #####################\n"); PetscPrintf(PETSC_COMM_WORLD,"#
// Main solver: %s, prec.: %s, maxiter.: %i \n",ksptype,pctype,mmax);
//
// // Only if pcmg is used
// if (pcmg_flag){
// // Check the smoothers and coarse grid solver:
// for (PetscInt k=0;k<nlvls;k++){
// KSP dksp;
// PC dpc;
// KSPType dksptype;
// PCMGGetSmoother(pc,k,&dksp);
// KSPGetType(dksp,&dksptype);
// KSPGetPC(dksp,&dpc);
// PCType dpctype;
// PCGetType(dpc,&dpctype);
// PetscInt mmax;
// KSPGetTolerances(dksp,NULL,NULL,NULL,&mmax);
// PetscPrintf(PETSC_COMM_WORLD,"# Level %i smoother:
// %s, prec.: %s, sweep: %i
// \n",k,dksptype,dpctype,mmax);
// }
// }
// PetscPrintf(PETSC_COMM_WORLD,"##############################################################\n");
return 0;
}
PetscErrorCode PDEFilt::DMDAGetElements_3D(DM dm, PetscInt* nel, PetscInt* nen, const PetscInt* e[]) {
DM_DA* da = (DM_DA*)dm->data;
PetscInt i, xs, xe, Xs, Xe;
PetscInt j, ys, ye, Ys, Ye;
PetscInt k, zs, ze, Zs, Ze;
PetscInt cnt = 0, cell[8], ns = 1, nn = 8;
PetscInt c;
if (!da->e) {
if (da->elementtype == DMDA_ELEMENT_Q1) {
ns = 1;
nn = 8;
}
DMDAGetCorners(dm, &xs, &ys, &zs, &xe, &ye, &ze);
DMDAGetGhostCorners(dm, &Xs, &Ys, &Zs, &Xe, &Ye, &Ze);
xe += xs;
Xe += Xs;
if (xs != Xs)
xs -= 1;
ye += ys;
Ye += Ys;
if (ys != Ys)
ys -= 1;
ze += zs;
Ze += Zs;
if (zs != Zs)
zs -= 1;
da->ne = ns * (xe - xs - 1) * (ye - ys - 1) * (ze - zs - 1);
PetscMalloc((1 + nn * da->ne) * sizeof(PetscInt), &da->e);
for (k = zs; k < ze - 1; k++) {
for (j = ys; j < ye - 1; j++) {
for (i = xs; i < xe - 1; i++) {
cell[0] = (i - Xs) + (j - Ys) * (Xe - Xs) + (k - Zs) * (Xe - Xs) * (Ye - Ys);
cell[1] = (i - Xs + 1) + (j - Ys) * (Xe - Xs) + (k - Zs) * (Xe - Xs) * (Ye - Ys);
cell[2] = (i - Xs + 1) + (j - Ys + 1) * (Xe - Xs) + (k - Zs) * (Xe - Xs) * (Ye - Ys);
cell[3] = (i - Xs) + (j - Ys + 1) * (Xe - Xs) + (k - Zs) * (Xe - Xs) * (Ye - Ys);
cell[4] = (i - Xs) + (j - Ys) * (Xe - Xs) + (k - Zs + 1) * (Xe - Xs) * (Ye - Ys);
cell[5] = (i - Xs + 1) + (j - Ys) * (Xe - Xs) + (k - Zs + 1) * (Xe - Xs) * (Ye - Ys);
cell[6] = (i - Xs + 1) + (j - Ys + 1) * (Xe - Xs) + (k - Zs + 1) * (Xe - Xs) * (Ye - Ys);
cell[7] = (i - Xs) + (j - Ys + 1) * (Xe - Xs) + (k - Zs + 1) * (Xe - Xs) * (Ye - Ys);
if (da->elementtype == DMDA_ELEMENT_Q1) {
for (c = 0; c < ns * nn; c++)
da->e[cnt++] = cell[c];
}
}
}
}
}
*nel = da->ne;
*nen = nn;
*e = da->e;
return (0);
}
void PDEFilt::PDEFilterMatrix(PetscScalar dx, PetscScalar dy, PetscScalar dz, PetscScalar RR, PetscScalar* KK,
PetscScalar* T) {
PetscScalar t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t15, t16, t18, t22, t23, t27, t28, t32, t36, t37, t41,
t45, t49, t53;
t3 = 1.0 / dx / dy;
t4 = 1 / dz;
t5 = RR * RR;
t6 = dx * dx;
t7 = t5 * t6;
t8 = dy * dy;
t9 = t7 * t8;
t10 = 3.0 * t9;
t11 = dz * dz;
t12 = t7 * t11;
t13 = 3.0 * t12;
t15 = t5 * t8 * t11;
t16 = 3.0 * t15;
t18 = t6 * t8 * t11;
t22 = t3 * t4 * (t10 + t13 + t16 + t18) / 27.0;
t23 = 6.0 * t15;
t27 = t3 * t4 * (t10 + t13 - t23 + t18) / 54.0;
t28 = 6.0 * t12;
t32 = t3 * t4 * (t10 - t28 - t23 + t18) / 108.0;
t36 = t3 * t4 * (t10 - t28 + t16 + t18) / 54.0;
t37 = 6.0 * t9;
t41 = t3 * t4 * (t37 - t13 - t16 - t18) / 54.0;
t45 = t3 * t4 * (t37 - t13 + t23 - t18) / 108.0;
t49 = t3 * t4 * (t37 + t28 + t23 - t18) / 216.0;
t53 = t3 * t4 * (t37 + t28 - t16 - t18) / 108.0;
KK[0] = t22;
KK[1] = t27;
KK[2] = t32;
KK[3] = t36;
KK[4] = -t41;
KK[5] = -t45;
KK[6] = -t49;
KK[7] = -t53;
KK[8] = t27;
KK[9] = t22;
KK[10] = t36;
KK[11] = t32;
KK[12] = -t45;
KK[13] = -t41;
KK[14] = -t53;
KK[15] = -t49;
KK[16] = t32;
KK[17] = t36;
KK[18] = t22;
KK[19] = t27;
KK[20] = -t49;
KK[21] = -t53;
KK[22] = -t41;
KK[23] = -t45;
KK[24] = t36;
KK[25] = t32;
KK[26] = t27;
KK[27] = t22;
KK[28] = -t53;
KK[29] = -t49;
KK[30] = -t45;
KK[31] = -t41;
KK[32] = -t41;
KK[33] = -t45;
KK[34] = -t49;
KK[35] = -t53;
KK[36] = t22;
KK[37] = t27;
KK[38] = t32;
KK[39] = t36;
KK[40] = -t45;
KK[41] = -t41;
KK[42] = -t53;
KK[43] = -t49;
KK[44] = t27;
KK[45] = t22;
KK[46] = t36;
KK[47] = t32;
KK[48] = -t49;
KK[49] = -t53;
KK[50] = -t41;
KK[51] = -t45;
KK[52] = t32;
KK[53] = t36;
KK[54] = t22;
KK[55] = t27;
KK[56] = -t53;
KK[57] = -t49;
KK[58] = -t45;
KK[59] = -t41;
KK[60] = t36;
KK[61] = t32;
KK[62] = t27;
KK[63] = t22;
PetscScalar vol = 1.0;
T[0] = 0.125 * vol;
T[1] = 0.125 * vol;
T[2] = 0.125 * vol;
T[3] = 0.125 * vol;
T[4] = 0.125 * vol;
T[5] = 0.125 * vol;
T[6] = 0.125 * vol;
T[7] = 0.125 * vol;
}