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LinearElasticity.cc
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LinearElasticity.cc
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#include "LinearElasticity.h"
/*
Authors: Niels Aage, Erik Andreassen, Boyan Lazarov, August 2013
Disclaimer:
The authors reserves all rights but does not guaranty that the code is
free from errors. Furthermore, we shall not be liable in any event
caused by the use of the program.
*/
LinearElasticity::LinearElasticity(DM da_nodes) {
// Set pointers to null
K = NULL;
U = NULL;
RHS = NULL;
N = NULL;
ksp = NULL;
da_nodal;
// Parameters - to be changed on read of variables
nu = 0.3;
nlvls = 4;
PetscBool flg;
PetscOptionsGetInt(NULL, NULL, "-nlvls", &nlvls, &flg);
PetscOptionsGetReal(NULL, NULL, "-nu", &nu, &flg);
// Setup sitffness matrix, load vector and bcs (Dirichlet) for the design
// problem
SetUpLoadAndBC(da_nodes);
}
LinearElasticity::~LinearElasticity() {
// Deallocate
VecDestroy(&(U));
VecDestroy(&(RHS));
VecDestroy(&(N));
MatDestroy(&(K));
KSPDestroy(&(ksp));
if (da_nodal != NULL) {
DMDestroy(&(da_nodal));
}
}
PetscErrorCode LinearElasticity::SetUpLoadAndBC(DM da_nodes) {
PetscErrorCode ierr;
// Extract information from input DM and create one for the linear elasticity
// number of nodal dofs: (u,v,w)
PetscInt numnodaldof = 3;
// 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);
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] * dx;
xc[2] = 0.0;
xc[3] = ne[1] * dy;
xc[4] = 0.0;
xc[5] = ne[2] * dz;
}
// 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);
// Allocate matrix and the RHS and Solution vector and Dirichlet vector
ierr = DMCreateMatrix(da_nodal, &(K));
CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da_nodal, &(U));
CHKERRQ(ierr);
VecDuplicate(U, &(RHS));
VecDuplicate(U, &(N));
// Set the local stiffness matrix
PetscScalar X[8] = {0.0, dx, dx, 0.0, 0.0, dx, dx, 0.0};
PetscScalar Y[8] = {0.0, 0.0, dy, dy, 0.0, 0.0, dy, dy};
PetscScalar Z[8] = {0.0, 0.0, 0.0, 0.0, dz, dz, dz, dz};
// Compute the element stiffnes matrix - constant due to structured grid
Hex8Isoparametric(X, Y, Z, nu, false, KE);
// Set the RHS and Dirichlet vector
VecSet(N, 1.0);
VecSet(RHS, 0.0);
// Global coordinates and a pointer
Vec lcoor; // borrowed ref - do not destroy!
PetscScalar* lcoorp;
// Get local coordinates in local node numbering including ghosts
ierr = DMGetCoordinatesLocal(da_nodal, &lcoor);
CHKERRQ(ierr);
VecGetArray(lcoor, &lcoorp);
// Get local dof number
PetscInt nn;
VecGetSize(lcoor, &nn);
// Compute epsilon parameter for finding points in space:
PetscScalar epsi = PetscMin(dx * 0.05, PetscMin(dy * 0.05, dz * 0.05));
// Set the values:
// In this case: N = the wall at x=xmin is fully clamped
// RHS(z) = sin(pi*y/Ly) at x=xmax,z=zmin;
// OR
// RHS(z) = -0.1 at x=xmax,z=zmin;
PetscScalar LoadIntensity = -0.001;
for (PetscInt i = 0; i < nn; i++) {
// Make a wall with all dofs clamped
if (i % 3 == 0 && PetscAbsScalar(lcoorp[i] - xc[0]) < epsi) {
VecSetValueLocal(N, i, 0.0, INSERT_VALUES);
VecSetValueLocal(N, ++i, 0.0, INSERT_VALUES);
VecSetValueLocal(N, ++i, 0.0, INSERT_VALUES);
}
// Line load
if (i % 3 == 0 && PetscAbsScalar(lcoorp[i] - xc[1]) < epsi && PetscAbsScalar(lcoorp[i + 2] - xc[4]) < epsi) {
VecSetValueLocal(RHS, i + 2, LoadIntensity, INSERT_VALUES);
}
// Adjust the corners
if (i % 3 == 0 && PetscAbsScalar(lcoorp[i] - xc[1]) < epsi && PetscAbsScalar(lcoorp[i + 1] - xc[2]) < epsi &&
PetscAbsScalar(lcoorp[i + 2] - xc[4]) < epsi) {
VecSetValueLocal(RHS, i + 2, LoadIntensity / 2.0, INSERT_VALUES);
}
if (i % 3 == 0 && PetscAbsScalar(lcoorp[i] - xc[1]) < epsi && PetscAbsScalar(lcoorp[i + 1] - xc[3]) < epsi &&
PetscAbsScalar(lcoorp[i + 2] - xc[4]) < epsi) {
VecSetValueLocal(RHS, i + 2, LoadIntensity / 2.0, INSERT_VALUES);
}
}
VecAssemblyBegin(N);
VecAssemblyBegin(RHS);
VecAssemblyEnd(N);
VecAssemblyEnd(RHS);
VecRestoreArray(lcoor, &lcoorp);
return ierr;
}
PetscErrorCode LinearElasticity::SolveState(Vec xPhys, PetscScalar Emin, PetscScalar Emax, PetscScalar penal) {
PetscErrorCode ierr;
double t1, t2;
t1 = MPI_Wtime();
// Assemble the stiffness matrix
ierr = AssembleStiffnessMatrix(xPhys, Emin, Emax, penal);
CHKERRQ(ierr);
// Setup the solver
if (ksp == NULL) {
ierr = SetUpSolver();
CHKERRQ(ierr);
} else {
ierr = KSPSetOperators(ksp, K, K);
CHKERRQ(ierr);
KSPSetUp(ksp);
}
// Solve
ierr = KSPSolve(ksp, RHS, U);
CHKERRQ(ierr);
CHKERRQ(ierr);
// DEBUG
// Get iteration number and residual from KSP
PetscInt niter;
PetscScalar rnorm;
KSPGetIterationNumber(ksp, &niter);
KSPGetResidualNorm(ksp, &rnorm);
PetscReal RHSnorm;
ierr = VecNorm(RHS, NORM_2, &RHSnorm);
CHKERRQ(ierr);
rnorm = rnorm / RHSnorm;
t2 = MPI_Wtime();
PetscPrintf(PETSC_COMM_WORLD, "State solver: iter: %i, rerr.: %e, time: %f\n", niter, rnorm, t2 - t1);
return ierr;
}
PetscErrorCode LinearElasticity::ComputeObjectiveConstraints(PetscScalar* fx, PetscScalar* gx, Vec xPhys,
PetscScalar Emin, PetscScalar Emax, PetscScalar penal,
PetscScalar volfrac) {
// Error code
PetscErrorCode ierr;
// Solve state eqs
ierr = SolveState(xPhys, Emin, Emax, penal);
CHKERRQ(ierr);
// Get the FE mesh structure (from the nodal mesh)
PetscInt nel, nen;
const PetscInt* necon;
ierr = DMDAGetElements_3D(da_nodal, &nel, &nen, &necon);
CHKERRQ(ierr);
// Get pointer to the densities
PetscScalar* xp;
VecGetArray(xPhys, &xp);
// Get Solution
Vec Uloc;
DMCreateLocalVector(da_nodal, &Uloc);
DMGlobalToLocalBegin(da_nodal, U, INSERT_VALUES, Uloc);
DMGlobalToLocalEnd(da_nodal, U, INSERT_VALUES, Uloc);
// get pointer to local vector
PetscScalar* up;
VecGetArray(Uloc, &up);
// Edof array
PetscInt edof[24];
fx[0] = 0.0;
// Loop over elements
for (PetscInt i = 0; i < nel; i++) {
// loop over element nodes
for (PetscInt j = 0; j < nen; j++) {
// Get local dofs
for (PetscInt k = 0; k < 3; k++) {
edof[j * 3 + k] = 3 * necon[i * nen + j] + k;
}
}
// Use SIMP for stiffness interpolation
PetscScalar uKu = 0.0;
for (PetscInt k = 0; k < 24; k++) {
for (PetscInt h = 0; h < 24; h++) {
uKu += up[edof[k]] * KE[k * 24 + h] * up[edof[h]];
}
}
// Add to objective
fx[0] += (Emin + PetscPowScalar(xp[i], penal) * (Emax - Emin)) * uKu;
}
// Allreduce fx[0]
PetscScalar tmp = fx[0];
fx[0] = 0.0;
MPI_Allreduce(&tmp, &(fx[0]), 1, MPIU_SCALAR, MPI_SUM, PETSC_COMM_WORLD);
// Compute volume constraint gx[0]
PetscInt neltot;
VecGetSize(xPhys, &neltot);
gx[0] = 0;
VecSum(xPhys, &(gx[0]));
gx[0] = gx[0] / (((PetscScalar)neltot)) - volfrac;
VecRestoreArray(xPhys, &xp);
VecRestoreArray(Uloc, &up);
VecDestroy(&Uloc);
return (ierr);
}
PetscErrorCode LinearElasticity::ComputeSensitivities(Vec dfdx, Vec dgdx, Vec xPhys, PetscScalar Emin, PetscScalar Emax,
PetscScalar penal, PetscScalar volfrac) {
PetscErrorCode ierr;
// Get the FE mesh structure (from the nodal mesh)
PetscInt nel, nen;
const PetscInt* necon;
ierr = DMDAGetElements_3D(da_nodal, &nel, &nen, &necon);
CHKERRQ(ierr);
// Get pointer to the densities
PetscScalar* xp;
VecGetArray(xPhys, &xp);
// Get Solution
Vec Uloc;
DMCreateLocalVector(da_nodal, &Uloc);
DMGlobalToLocalBegin(da_nodal, U, INSERT_VALUES, Uloc);
DMGlobalToLocalEnd(da_nodal, U, INSERT_VALUES, Uloc);
// get pointer to local vector
PetscScalar* up;
VecGetArray(Uloc, &up);
// Get dfdx
PetscScalar* df;
VecGetArray(dfdx, &df);
// Edof array
PetscInt edof[24];
// Loop over elements
for (PetscInt i = 0; i < nel; i++) {
// loop over element nodes
for (PetscInt j = 0; j < nen; j++) {
// Get local dofs
for (PetscInt k = 0; k < 3; k++) {
edof[j * 3 + k] = 3 * necon[i * nen + j] + k;
}
}
// Use SIMP for stiffness interpolation
PetscScalar uKu = 0.0;
for (PetscInt k = 0; k < 24; k++) {
for (PetscInt h = 0; h < 24; h++) {
uKu += up[edof[k]] * KE[k * 24 + h] * up[edof[h]];
}
}
// Set the Senstivity
df[i] = -1.0 * penal * PetscPowScalar(xp[i], penal - 1) * (Emax - Emin) * uKu;
}
// Compute volume constraint gx[0]
PetscInt neltot;
VecGetSize(xPhys, &neltot);
VecSet(dgdx, 1.0 / (((PetscScalar)neltot)));
VecRestoreArray(xPhys, &xp);
VecRestoreArray(Uloc, &up);
VecRestoreArray(dfdx, &df);
VecDestroy(&Uloc);
return (ierr);
}
PetscErrorCode LinearElasticity::ComputeObjectiveConstraintsSensitivities(PetscScalar* fx, PetscScalar* gx, Vec dfdx,
Vec dgdx, Vec xPhys, PetscScalar Emin,
PetscScalar Emax, PetscScalar penal,
PetscScalar volfrac) {
// Errorcode
PetscErrorCode ierr;
// Solve state eqs
ierr = SolveState(xPhys, Emin, Emax, penal);
CHKERRQ(ierr);
// Get the FE mesh structure (from the nodal mesh)
PetscInt nel, nen;
const PetscInt* necon;
ierr = DMDAGetElements_3D(da_nodal, &nel, &nen, &necon);
CHKERRQ(ierr);
// DMDAGetElements(da_nodes,&nel,&nen,&necon); // Still issue with elemtype
// change !
// Get pointer to the densities
PetscScalar* xp;
VecGetArray(xPhys, &xp);
// Get Solution
Vec Uloc;
DMCreateLocalVector(da_nodal, &Uloc);
DMGlobalToLocalBegin(da_nodal, U, INSERT_VALUES, Uloc);
DMGlobalToLocalEnd(da_nodal, U, INSERT_VALUES, Uloc);
// get pointer to local vector
PetscScalar* up;
VecGetArray(Uloc, &up);
// Get dfdx
PetscScalar* df;
VecGetArray(dfdx, &df);
// Edof array
PetscInt edof[24];
fx[0] = 0.0;
// Loop over elements
for (PetscInt i = 0; i < nel; i++) {
// loop over element nodes
for (PetscInt j = 0; j < nen; j++) {
// Get local dofs
for (PetscInt k = 0; k < 3; k++) {
edof[j * 3 + k] = 3 * necon[i * nen + j] + k;
}
}
// Use SIMP for stiffness interpolation
PetscScalar uKu = 0.0;
for (PetscInt k = 0; k < 24; k++) {
for (PetscInt h = 0; h < 24; h++) {
uKu += up[edof[k]] * KE[k * 24 + h] * up[edof[h]];
}
}
// Add to objective
fx[0] += (Emin + PetscPowScalar(xp[i], penal) * (Emax - Emin)) * uKu;
// Set the Senstivity
df[i] = -1.0 * penal * PetscPowScalar(xp[i], penal - 1) * (Emax - Emin) * uKu;
}
// Allreduce fx[0]
PetscScalar tmp = fx[0];
fx[0] = 0.0;
MPI_Allreduce(&tmp, &(fx[0]), 1, MPIU_SCALAR, MPI_SUM, PETSC_COMM_WORLD);
// Compute volume constraint gx[0]
PetscInt neltot;
VecGetSize(xPhys, &neltot);
gx[0] = 0;
VecSum(xPhys, &(gx[0]));
gx[0] = gx[0] / (((PetscScalar)neltot)) - volfrac;
VecSet(dgdx, 1.0 / (((PetscScalar)neltot)));
VecRestoreArray(xPhys, &xp);
VecRestoreArray(Uloc, &up);
VecRestoreArray(dfdx, &df);
VecDestroy(&Uloc);
return (ierr);
}
PetscErrorCode LinearElasticity::WriteRestartFiles() {
PetscErrorCode ierr = 0;
// Only dump data if correct allocater has been used
if (!restart) {
return -1;
}
// Choose previous set of restart files
if (flip) {
flip = PETSC_FALSE;
} else {
flip = PETSC_TRUE;
}
// Open viewers for writing
PetscViewer view; // vectors
if (!flip) {
PetscViewerBinaryOpen(PETSC_COMM_WORLD, filename00.c_str(), FILE_MODE_WRITE, &view);
} else if (flip) {
PetscViewerBinaryOpen(PETSC_COMM_WORLD, filename01.c_str(), FILE_MODE_WRITE, &view);
}
// Write vectors
VecView(U, view);
// Clean up
PetscViewerDestroy(&view);
return ierr;
}
//##################################################################
//##################################################################
//##################################################################
// ######################## PRIVATE ################################
//##################################################################
//##################################################################
PetscErrorCode LinearElasticity::AssembleStiffnessMatrix(Vec xPhys, PetscScalar Emin, PetscScalar Emax,
PetscScalar penal) {
PetscErrorCode ierr;
// Get the FE mesh structure (from the nodal mesh)
PetscInt nel, nen;
const PetscInt* necon;
ierr = DMDAGetElements_3D(da_nodal, &nel, &nen, &necon);
CHKERRQ(ierr);
// Get pointer to the densities
PetscScalar* xp;
VecGetArray(xPhys, &xp);
// Zero the matrix
MatZeroEntries(K);
// Edof array
PetscInt edof[24];
PetscScalar ke[24 * 24];
// Loop over elements
for (PetscInt i = 0; i < nel; i++) {
// loop over element nodes
for (PetscInt j = 0; j < nen; j++) {
// Get local dofs
for (PetscInt k = 0; k < 3; k++) {
edof[j * 3 + k] = 3 * necon[i * nen + j] + k;
}
}
// Use SIMP for stiffness interpolation
PetscScalar dens = Emin + PetscPowScalar(xp[i], penal) * (Emax - Emin);
for (PetscInt k = 0; k < 24 * 24; k++) {
ke[k] = KE[k] * dens;
}
// Add values to the sparse matrix
ierr = MatSetValuesLocal(K, 24, edof, 24, edof, ke, ADD_VALUES);
CHKERRQ(ierr);
}
MatAssemblyBegin(K, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(K, MAT_FINAL_ASSEMBLY);
// Impose the dirichlet conditions, i.e. K = N'*K*N - (N-I)
// 1.: K = N'*K*N
MatDiagonalScale(K, N, N);
// 2. Add ones, i.e. K = K + NI, NI = I - N
Vec NI;
VecDuplicate(N, &NI);
VecSet(NI, 1.0);
VecAXPY(NI, -1.0, N);
MatDiagonalSet(K, NI, ADD_VALUES);
// Zero out possible loads in the RHS that coincide
// with Dirichlet conditions
VecPointwiseMult(RHS, RHS, N);
VecDestroy(&NI);
VecRestoreArray(xPhys, &xp);
DMDARestoreElements(da_nodal, &nel, &nen, &necon);
return ierr;
}
PetscErrorCode LinearElasticity::SetUpSolver() {
PetscErrorCode ierr;
// CHECK FOR RESTART POINT
restart = PETSC_TRUE;
flip = PETSC_TRUE;
PetscBool flg, onlyDesign;
onlyDesign = PETSC_FALSE;
char filenameChar[PETSC_MAX_PATH_LEN];
PetscOptionsGetBool(NULL, NULL, "-restart", &restart, &flg);
PetscOptionsGetBool(NULL, NULL, "-onlyLoadDesign", &onlyDesign,
&flg); // DONT READ DESIGN IF THIS IS TRUE
// READ THE RESTART FILE INTO THE SOLUTION VECTOR(S)
if (restart) {
// THE FILES FOR WRITING RESTARTS
std::string filenameWorkdir = "./";
PetscOptionsGetString(NULL, NULL, "-workdir", filenameChar, sizeof(filenameChar), &flg);
if (flg) {
filenameWorkdir = "";
filenameWorkdir.append(filenameChar);
}
filename00 = filenameWorkdir;
filename01 = filenameWorkdir;
filename00.append("/RestartSol00.dat");
filename01.append("/RestartSol01.dat");
// CHECK FOR SOLUTION AND READ TO STATE VECTOR(s)
if (!onlyDesign) {
// Where to read the restart point from
std::string restartFileVec = ""; // NO RESTART FILE !!!!!
// GET FILENAME
PetscOptionsGetString(NULL, NULL, "-restartFileVecSol", filenameChar, sizeof(filenameChar), &flg);
if (flg) {
restartFileVec.append(filenameChar);
}
// PRINT TO SCREEN
PetscPrintf(PETSC_COMM_WORLD,
"# Restarting with solution (State Vector) from "
"(-restartFileVecSol): %s \n",
restartFileVec.c_str());
// Check if files exist:
PetscBool vecFile = fexists(restartFileVec);
if (!vecFile) {
PetscPrintf(PETSC_COMM_WORLD, "File: %s NOT FOUND \n", restartFileVec.c_str());
}
// READ
if (vecFile) {
PetscViewer view;
// Open the data files
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD, restartFileVec.c_str(), FILE_MODE_READ, &view);
VecLoad(U, view);
PetscViewerDestroy(&view);
}
}
}
PC pc;
// The fine grid Krylov method
KSPCreate(PETSC_COMM_WORLD, &(ksp));
// SET THE DEFAULT SOLVER PARAMETERS
// The fine grid solver settings
PetscScalar rtol = 1.0e-5;
PetscScalar atol = 1.0e-50;
PetscScalar dtol = 1.0e5;
PetscInt restart = 100;
PetscInt maxitsGlobal = 200;
// Coarsegrid solver
PetscScalar coarse_rtol = 1.0e-8;
PetscScalar coarse_atol = 1.0e-50;
PetscScalar coarse_dtol = 1e5;
PetscInt coarse_maxits = 30;
PetscInt coarse_restart = 30;
// Number of smoothening iterations per up/down smooth_sweeps
PetscInt smooth_sweeps = 4;
// Set up the solver
ierr = KSPSetType(ksp, KSPFGMRES); // KSPCG, KSPGMRES
CHKERRQ(ierr);
ierr = KSPGMRESSetRestart(ksp, restart);
CHKERRQ(ierr);
ierr = KSPSetTolerances(ksp, rtol, atol, dtol, maxitsGlobal);
CHKERRQ(ierr);
ierr = KSPSetInitialGuessNonzero(ksp, PETSC_TRUE);
CHKERRQ(ierr);
ierr = KSPSetOperators(ksp, K, K);
CHKERRQ(ierr);
// The preconditinoer
KSPGetPC(ksp, &pc);
// Make PCMG the default solver
PCSetType(pc, PCMG);
// Set solver from options
KSPSetFromOptions(ksp);
// Get the prec again - check if it has changed
KSPGetPC(ksp, &pc);
// 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
DMCoarsenHierarchy(da_nodal, nlvls - 1, &daclist[1]);
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];
// THIS SHOULD NOT BE NECESSARY
DMDASetUniformCoordinates(da_list[k], xmin, xmax, ymin, ymax, zmin, zmax);
}
// the PCMG specific options
PCMGSetLevels(pc, nlvls, NULL);
PCMGSetType(pc, PC_MG_MULTIPLICATIVE); // Default
ierr = PCMGSetCycleType(pc, PC_MG_CYCLE_V);
CHKERRQ(ierr);
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);
}
// tidy up
for (PetscInt k = 1; k < nlvls; k++) { // DO NOT DESTROY LEVEL 0
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
ierr = KSPGMRESSetRestart(cksp, coarse_restart);
// ierr = KSPSetType(cksp,KSPCG);
ierr = KSPSetTolerances(cksp, coarse_rtol, coarse_atol, coarse_dtol, coarse_maxits);
// The preconditioner
PC cpc;
KSPGetPC(cksp, &cpc);
PCSetType(cpc, PCSOR); // PCGAMG, PCSOR, PCSPAI (NEEDS TO BE COMPILED), 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)
ierr = KSPGMRESSetRestart(dksp, smooth_sweeps);
// ierr = KSPSetType(dksp,KSPCHEBYSHEV);
ierr = KSPSetTolerances(dksp, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT,
smooth_sweeps); // NOTE in the above maxitr=restart;
PCSetType(dpc, PCSOR); // 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 (ierr);
}
PetscErrorCode LinearElasticity::DMDAGetElements_3D(DM dm, PetscInt* nel, PetscInt* nen, const PetscInt* e[]) {
PetscErrorCode ierr;
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;
}
ierr = DMDAGetCorners(dm, &xs, &ys, &zs, &xe, &ye, &ze);
CHKERRQ(ierr);
ierr = DMDAGetGhostCorners(dm, &Xs, &Ys, &Zs, &Xe, &Ye, &Ze);
CHKERRQ(ierr);
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);
}
PetscInt LinearElasticity::Hex8Isoparametric(PetscScalar* X, PetscScalar* Y, PetscScalar* Z, PetscScalar nu,
PetscInt redInt, PetscScalar* ke) {
// HEX8_ISOPARAMETRIC - Computes HEX8 isoparametric element matrices
// The element stiffness matrix is computed as:
//
// ke = int(int(int(B^T*C*B,x),y),z)
//
// For an isoparameteric element this integral becomes:
//
// ke = int(int(int(B^T*C*B*det(J),xi=-1..1),eta=-1..1),zeta=-1..1)
//
// where B is the more complicated expression:
// B = [dx*alpha1 + dy*alpha2 + dz*alpha3]*N
// where
// dx = [invJ11 invJ12 invJ13]*[dxi deta dzeta]
// dy = [invJ21 invJ22 invJ23]*[dxi deta dzeta]
// dy = [invJ31 invJ32 invJ33]*[dxi deta dzeta]
//
// Remark: The elasticity modulus is left out in the below
// computations, because we multiply with it afterwards (the aim is
// topology optimization).
// Furthermore, this is not the most efficient code, but it is readable.
//
/////////////////////////////////////////////////////////////////////////////////
//////// INPUT:
// X, Y, Z = Vectors containing the coordinates of the eight nodes
// (x1,y1,z1,x2,y2,z2,...,x8,y8,z8). Where node 1 is in the
// lower left corner, and node 2 is the next node
// counterclockwise (looking in the negative z-dir). Finish the
// x-y-plane and then move in the positive z-dir.
// redInt = Reduced integration option boolean (here an integer).
// redInt == 0 (false): Full integration
// redInt == 1 (true): Reduced integration
// nu = Poisson's ratio.
//
//////// OUTPUT:
// ke = Element stiffness matrix. Needs to be multiplied with elasticity
// modulus
//
// Written 2013 at
// Department of Mechanical Engineering
// Technical University of Denmark (DTU).
/////////////////////////////////////////////////////////////////////////////////
//// COMPUTE ELEMENT STIFFNESS MATRIX
// Lame's parameters (with E=1.0):
PetscScalar lambda = nu / ((1.0 + nu) * (1.0 - 2.0 * nu));
PetscScalar mu = 1.0 / (2.0 * (1.0 + nu));
// Constitutive matrix
PetscScalar C[6][6] = {{lambda + 2.0 * mu, lambda, lambda, 0.0, 0.0, 0.0},
{lambda, lambda + 2.0 * mu, lambda, 0.0, 0.0, 0.0},
{lambda, lambda, lambda + 2.0 * mu, 0.0, 0.0, 0.0},
{0.0, 0.0, 0.0, mu, 0.0, 0.0},
{0.0, 0.0, 0.0, 0.0, mu, 0.0},
{0.0, 0.0, 0.0, 0.0, 0.0, mu}};
// Gauss points (GP) and weigths
// Two Gauss points in all directions (total of eight)
PetscScalar GP[2] = {-0.577350269189626, 0.577350269189626};
// Corresponding weights
PetscScalar W[2] = {1.0, 1.0};
// If reduced integration only use one GP
if (redInt) {
GP[0] = 0.0;
W[0] = 2.0;
}
// Matrices that help when we gather the strain-displacement matrix:
PetscScalar alpha1[6][3];
PetscScalar alpha2[6][3];
PetscScalar alpha3[6][3];
memset(alpha1, 0, sizeof(alpha1[0][0]) * 6 * 3); // zero out
memset(alpha2, 0, sizeof(alpha2[0][0]) * 6 * 3); // zero out
memset(alpha3, 0, sizeof(alpha3[0][0]) * 6 * 3); // zero out
alpha1[0][0] = 1.0;
alpha1[3][1] = 1.0;
alpha1[5][2] = 1.0;
alpha2[1][1] = 1.0;
alpha2[3][0] = 1.0;
alpha2[4][2] = 1.0;
alpha3[2][2] = 1.0;
alpha3[4][1] = 1.0;
alpha3[5][0] = 1.0;
PetscScalar dNdxi[8];
PetscScalar dNdeta[8];
PetscScalar dNdzeta[8];
PetscScalar J[3][3];
PetscScalar invJ[3][3];
PetscScalar beta[6][3];
PetscScalar B[6][24]; // Note: Small enough to be allocated on stack
PetscScalar* dN;
// Make sure the stiffness matrix is zeroed out:
memset(ke, 0, sizeof(ke[0]) * 24 * 24);
// Perform the numerical integration
for (PetscInt ii = 0; ii < 2 - redInt; ii++) {
for (PetscInt jj = 0; jj < 2 - redInt; jj++) {
for (PetscInt kk = 0; kk < 2 - redInt; kk++) {
// Integration point
PetscScalar xi = GP[ii];
PetscScalar eta = GP[jj];
PetscScalar zeta = GP[kk];
// Differentiated shape functions
DifferentiatedShapeFunctions(xi, eta, zeta, dNdxi, dNdeta, dNdzeta);
// Jacobian
J[0][0] = Dot(dNdxi, X, 8);
J[0][1] = Dot(dNdxi, Y, 8);
J[0][2] = Dot(dNdxi, Z, 8);
J[1][0] = Dot(dNdeta, X, 8);
J[1][1] = Dot(dNdeta, Y, 8);
J[1][2] = Dot(dNdeta, Z, 8);
J[2][0] = Dot(dNdzeta, X, 8);
J[2][1] = Dot(dNdzeta, Y, 8);
J[2][2] = Dot(dNdzeta, Z, 8);
// Inverse and determinant
PetscScalar detJ = Inverse3M(J, invJ);
// Weight factor at this point
PetscScalar weight = W[ii] * W[jj] * W[kk] * detJ;
// Strain-displacement matrix
memset(B, 0, sizeof(B[0][0]) * 6 * 24); // zero out
for (PetscInt ll = 0; ll < 3; ll++) {
// Add contributions from the different derivatives
if (ll == 0) {
dN = dNdxi;
}
if (ll == 1) {
dN = dNdeta;
}
if (ll == 2) {
dN = dNdzeta;
}
// Assemble strain operator
for (PetscInt i = 0; i < 6; i++) {
for (PetscInt j = 0; j < 3; j++) {
beta[i][j] =
invJ[0][ll] * alpha1[i][j] + invJ[1][ll] * alpha2[i][j] + invJ[2][ll] * alpha3[i][j];
}
}
// Add contributions to strain-displacement matrix
for (PetscInt i = 0; i < 6; i++) {
for (PetscInt j = 0; j < 24; j++) {
B[i][j] = B[i][j] + beta[i][j % 3] * dN[j / 3];
}
}
}
// Finally, add to the element matrix
for (PetscInt i = 0; i < 24; i++) {
for (PetscInt j = 0; j < 24; j++) {
for (PetscInt k = 0; k < 6; k++) {
for (PetscInt l = 0; l < 6; l++) {
ke[j + 24 * i] = ke[j + 24 * i] + weight * (B[k][i] * C[k][l] * B[l][j]);
}
}
}
}
}
}
}
return 0;
}
PetscScalar LinearElasticity::Dot(PetscScalar* v1, PetscScalar* v2, PetscInt l) {
// Function that returns the dot product of v1 and v2,