/*
FormInitialGuess - Computes an initial approximation to the solution.
Input Parameters:
. user - user-defined application context
. X - vector
Output Parameters:
X - vector
*/
PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
{
PetscErrorCode ierr;
PetscInt i, j, k, mx = user->mx, my = user->my;
PetscInt xs, ys, xm, ym, gxm, gym, gxs, gys, xe, ye;
PetscReal hx = 1.0/(mx+1), hy = 1.0/(my+1), temp, val;
PetscFunctionBegin;
/* Get local mesh boundaries */
ierr = DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
ierr = DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);CHKERRQ(ierr);
/* Compute initial guess over locally owned part of mesh */
xe = xs+xm;
ye = ys+ym;
for (j=ys; j<ye; j++) { /* for (j=0; j<my; j++) */
temp = PetscMin(j+1,my-j)*hy;
for (i=xs; i<xe; i++) { /* for (i=0; i<mx; i++) */
k = (j-gys)*gxm + i-gxs;
val = PetscMin((PetscMin(i+1,mx-i))*hx,temp);
ierr = VecSetValuesLocal(X,1,&k,&val,ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = VecAssemblyBegin(X);CHKERRQ(ierr);
ierr = VecAssemblyEnd(X);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* Notice that this requires the previous momentum solution.
The element stiffness matrix for the identity in linear elements is
1 /2 1 1\
- |1 2 1|
12 \1 1 2/
no matter what the shape of the triangle. */
PetscErrorCode TaylorGalerkinStepIIMassEnergy(DM da, UserContext *user)
{
MPI_Comm comm;
Mat mat;
Vec rhs_m, rhs_e;
PetscScalar identity[9] = {0.16666666667, 0.08333333333, 0.08333333333,
0.08333333333, 0.16666666667, 0.08333333333,
0.08333333333, 0.08333333333, 0.16666666667};
PetscScalar *u_n, *v_n, *p_n, *t_n, *mu_n, *kappa_n;
PetscScalar *rho_n, *rho_u_n, *rho_v_n, *rho_e_n;
PetscScalar *u_phi, *v_phi;
PetscScalar *rho_u_np1, *rho_v_np1;
PetscInt idx[3];
PetscScalar psi_x[3], psi_y[3];
PetscScalar values_m[3];
PetscScalar values_e[3];
PetscScalar phi = user->phi;
PetscScalar mu, kappa, tau_xx, tau_xy, tau_yy, q_x, q_y;
PetscReal hx, hy, area;
KSP ksp;
const PetscInt *necon;
PetscInt j, k, e, ne, nc, mx, my;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = PetscObjectGetComm((PetscObject) da, &comm);CHKERRQ(ierr);
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da, &mat);CHKERRQ(ierr);
ierr = MatSetOption(mat,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &rhs_m);CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &rhs_e);CHKERRQ(ierr);
ierr = KSPCreate(comm, &ksp);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
hx = 1.0 / (PetscReal)(mx-1);
hy = 1.0 / (PetscReal)(my-1);
area = 0.5*hx*hy;
ierr = VecGetArray(user->sol_n.u, &u_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.v, &v_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.p, &p_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.t, &t_n);CHKERRQ(ierr);
ierr = VecGetArray(user->mu, &mu_n);CHKERRQ(ierr);
ierr = VecGetArray(user->kappa, &kappa_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.rho, &rho_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.rho_u, &rho_u_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.rho_v, &rho_v_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.rho_e, &rho_e_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.u, &u_phi);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.v, &v_phi);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_np1.rho_u, &rho_u_np1);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_np1.rho_v, &rho_v_np1);CHKERRQ(ierr);
ierr = DMDAGetElements(da, &ne, &nc, &necon);CHKERRQ(ierr);
for (e = 0; e < ne; e++) {
for (j = 0; j < 3; j++) {
idx[j] = necon[3*e+j];
values_m[j] = 0.0;
values_e[j] = 0.0;
}
/* Get basis function deriatives (we need the orientation of the element here) */
if (idx[1] > idx[0]) {
psi_x[0] = -hy; psi_x[1] = hy; psi_x[2] = 0.0;
psi_y[0] = -hx; psi_y[1] = 0.0; psi_y[2] = hx;
} else {
psi_x[0] = hy; psi_x[1] = -hy; psi_x[2] = 0.0;
psi_y[0] = hx; psi_y[1] = 0.0; psi_y[2] = -hx;
}
/* <\nabla\psi, F^*>: Divergence of the predicted convective fluxes */
for (j = 0; j < 3; j++) {
values_m[j] += (psi_x[j]*(phi*rho_u_np1[idx[j]] + rho_u_n[idx[j]]) + psi_y[j]*(rho_v_np1[idx[j]] + rho_v_n[idx[j]]))/3.0;
values_e[j] += values_m[j]*((rho_e_n[idx[j]] + p_n[idx[j]]) / rho_n[idx[j]]);
}
/* -<\nabla\psi, F^n_v>: Divergence of the viscous fluxes */
for (j = 0; j < 3; j++) {
/* \tau_{xx} = 2/3 \mu(T) (2 {\partial u\over\partial x} - {\partial v\over\partial y}) */
/* \tau_{xy} = \mu(T) ( {\partial u\over\partial y} + {\partial v\over\partial x}) */
/* \tau_{yy} = 2/3 \mu(T) (2 {\partial v\over\partial y} - {\partial u\over\partial x}) */
/* q_x = -\kappa(T) {\partial T\over\partial x} */
/* q_y = -\kappa(T) {\partial T\over\partial y} */
/* above code commeted out - causing ininitialized variables. */
q_x =0; q_y =0;
mu = 0.0;
kappa = 0.0;
tau_xx = 0.0;
tau_xy = 0.0;
tau_yy = 0.0;
for (k = 0; k < 3; k++) {
mu += mu_n[idx[k]];
kappa += kappa_n[idx[k]];
tau_xx += 2.0*psi_x[k]*u_n[idx[k]] - psi_y[k]*v_n[idx[k]];
tau_xy += psi_y[k]*u_n[idx[k]] + psi_x[k]*v_n[idx[k]];
tau_yy += 2.0*psi_y[k]*v_n[idx[k]] - psi_x[k]*u_n[idx[k]];
q_x += psi_x[k]*t_n[idx[k]];
q_y += psi_y[k]*t_n[idx[k]];
}
mu /= 3.0;
kappa /= 3.0;
tau_xx *= (2.0/3.0)*mu;
tau_xy *= mu;
tau_yy *= (2.0/3.0)*mu;
values_e[j] -= area*(psi_x[j]*(u_phi[e]*tau_xx + v_phi[e]*tau_xy + q_x) + psi_y[j]*(u_phi[e]*tau_xy + v_phi[e]*tau_yy + q_y));
}
/* Accumulate to global structures */
ierr = VecSetValuesLocal(rhs_m, 3, idx, values_m, ADD_VALUES);CHKERRQ(ierr);
ierr = VecSetValuesLocal(rhs_e, 3, idx, values_e, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesLocal(mat, 3, idx, 3, idx, identity, ADD_VALUES);CHKERRQ(ierr);
}
ierr = DMDARestoreElements(da, &ne, &nc, &necon);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.u, &u_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.v, &v_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.p, &p_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.t, &t_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->mu, &mu_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->kappa, &kappa_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.rho, &rho_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.rho_u, &rho_u_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.rho_v, &rho_v_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.rho_e, &rho_e_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.u, &u_phi);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.v, &v_phi);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_np1.rho_u, &rho_u_np1);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_np1.rho_v, &rho_v_np1);CHKERRQ(ierr);
ierr = VecAssemblyBegin(rhs_m);CHKERRQ(ierr);
ierr = VecAssemblyBegin(rhs_e);CHKERRQ(ierr);
ierr = MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecAssemblyEnd(rhs_m);CHKERRQ(ierr);
ierr = VecAssemblyEnd(rhs_e);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecScale(rhs_m, user->dt);CHKERRQ(ierr);
ierr = VecScale(rhs_e, user->dt);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp, mat, mat, DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPSolve(ksp, rhs_m, user->sol_np1.rho);CHKERRQ(ierr);
ierr = KSPSolve(ksp, rhs_e, user->sol_np1.rho_e);CHKERRQ(ierr);
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = MatDestroy(&mat);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da, &rhs_m);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da, &rhs_e);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
The element stiffness matrix for the identity in linear elements is
1 /2 1 1\
- |1 2 1|
12 \1 1 2/
no matter what the shape of the triangle. */
PetscErrorCode TaylorGalerkinStepIIMomentum(DM da, UserContext *user)
{
MPI_Comm comm;
KSP ksp;
Mat mat;
Vec rhs_u, rhs_v;
PetscScalar identity[9] = {0.16666666667, 0.08333333333, 0.08333333333,
0.08333333333, 0.16666666667, 0.08333333333,
0.08333333333, 0.08333333333, 0.16666666667};
PetscScalar *u_n, *v_n, *mu_n;
PetscScalar *u_phi, *v_phi;
PetscScalar *rho_u_phi, *rho_v_phi;
PetscInt idx[3];
PetscScalar values_u[3];
PetscScalar values_v[3];
PetscScalar psi_x[3], psi_y[3];
PetscScalar mu, tau_xx, tau_xy, tau_yy;
PetscReal hx, hy, area;
const PetscInt *necon;
PetscInt j, k, e, ne, nc, mx, my;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = PetscObjectGetComm((PetscObject) da, &comm);CHKERRQ(ierr);
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da, &mat);CHKERRQ(ierr);
ierr = MatSetOption(mat,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &rhs_u);CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &rhs_v);CHKERRQ(ierr);
ierr = KSPCreate(comm, &ksp);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
hx = 1.0 / (PetscReal)(mx-1);
hy = 1.0 / (PetscReal)(my-1);
area = 0.5*hx*hy;
ierr = VecGetArray(user->sol_n.u, &u_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_n.v, &v_n);CHKERRQ(ierr);
ierr = VecGetArray(user->mu, &mu_n);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.u, &u_phi);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.v, &v_phi);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.rho_u, &rho_u_phi);CHKERRQ(ierr);
ierr = VecGetArray(user->sol_phi.rho_v, &rho_v_phi);CHKERRQ(ierr);
ierr = DMDAGetElements(da, &ne, &nc, &necon);CHKERRQ(ierr);
for (e = 0; e < ne; e++) {
for (j = 0; j < 3; j++) {
idx[j] = necon[3*e+j];
values_u[j] = 0.0;
values_v[j] = 0.0;
}
/* Get basis function deriatives (we need the orientation of the element here) */
if (idx[1] > idx[0]) {
psi_x[0] = -hy; psi_x[1] = hy; psi_x[2] = 0.0;
psi_y[0] = -hx; psi_y[1] = 0.0; psi_y[2] = hx;
} else {
psi_x[0] = hy; psi_x[1] = -hy; psi_x[2] = 0.0;
psi_y[0] = hx; psi_y[1] = 0.0; psi_y[2] = -hx;
}
/* <\nabla\psi, F^{n+\phi}_e>: Divergence of the element-averaged convective fluxes */
for (j = 0; j < 3; j++) {
values_u[j] += psi_x[j]*rho_u_phi[e]*u_phi[e] + psi_y[j]*rho_u_phi[e]*v_phi[e];
values_v[j] += psi_x[j]*rho_v_phi[e]*u_phi[e] + psi_y[j]*rho_v_phi[e]*v_phi[e];
}
/* -<\nabla\psi, F^n_v>: Divergence of the viscous fluxes */
for (j = 0; j < 3; j++) {
/* \tau_{xx} = 2/3 \mu(T) (2 {\partial u\over\partial x} - {\partial v\over\partial y}) */
/* \tau_{xy} = \mu(T) ( {\partial u\over\partial y} + {\partial v\over\partial x}) */
/* \tau_{yy} = 2/3 \mu(T) (2 {\partial v\over\partial y} - {\partial u\over\partial x}) */
mu = 0.0;
tau_xx = 0.0;
tau_xy = 0.0;
tau_yy = 0.0;
for (k = 0; k < 3; k++) {
mu += mu_n[idx[k]];
tau_xx += 2.0*psi_x[k]*u_n[idx[k]] - psi_y[k]*v_n[idx[k]];
tau_xy += psi_y[k]*u_n[idx[k]] + psi_x[k]*v_n[idx[k]];
tau_yy += 2.0*psi_y[k]*v_n[idx[k]] - psi_x[k]*u_n[idx[k]];
}
mu /= 3.0;
tau_xx *= (2.0/3.0)*mu;
tau_xy *= mu;
tau_yy *= (2.0/3.0)*mu;
values_u[j] -= area*(psi_x[j]*tau_xx + psi_y[j]*tau_xy);
values_v[j] -= area*(psi_x[j]*tau_xy + psi_y[j]*tau_yy);
}
/* Accumulate to global structures */
ierr = VecSetValuesLocal(rhs_u, 3, idx, values_u, ADD_VALUES);CHKERRQ(ierr);
ierr = VecSetValuesLocal(rhs_v, 3, idx, values_v, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesLocal(mat, 3, idx, 3, idx, identity, ADD_VALUES);CHKERRQ(ierr);
}
ierr = DMDARestoreElements(da, &ne, &nc, &necon);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.u, &u_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_n.v, &v_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->mu, &mu_n);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.u, &u_phi);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.v, &v_phi);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.rho_u, &rho_u_phi);CHKERRQ(ierr);
ierr = VecRestoreArray(user->sol_phi.rho_v, &rho_v_phi);CHKERRQ(ierr);
ierr = VecAssemblyBegin(rhs_u);CHKERRQ(ierr);
ierr = VecAssemblyBegin(rhs_v);CHKERRQ(ierr);
ierr = MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecAssemblyEnd(rhs_u);CHKERRQ(ierr);
ierr = VecAssemblyEnd(rhs_v);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecScale(rhs_u,user->dt);CHKERRQ(ierr);
ierr = VecScale(rhs_v,user->dt);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp, mat, mat, DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPSolve(ksp, rhs_u, user->sol_np1.rho_u);CHKERRQ(ierr);
ierr = KSPSolve(ksp, rhs_v, user->sol_np1.rho_v);CHKERRQ(ierr);
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = MatDestroy(&mat);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da, &rhs_u);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da, &rhs_v);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode SetInitialGuess(Vec X,AppCtx *user)
{
PetscErrorCode ierr;
PetscInt n,i,Mda;
PetscScalar *xx,*cv_p,*wv_p,*eta_p;
PetscViewer view_out;
/* needed for the void growth case */
PetscScalar xmid,cv_v=1.0,cv_m=user->Sv*user->cv0,eta_v=1.0,eta_m=0.0,h,lambda;
PetscInt nele,nen,idx[2];
const PetscInt *ele;
PetscScalar x[2];
Vec coords;
const PetscScalar *_coords;
PetscScalar xwidth = user->xmax - user->xmin;
PetscFunctionBeginUser;
ierr = VecGetLocalSize(X,&n);CHKERRQ(ierr);
ierr = DMDAGetInfo(user->da2,NULL,&Mda,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(user->da2,&coords);CHKERRQ(ierr);
ierr = VecGetArrayRead(coords,&_coords);CHKERRQ(ierr);
if (user->periodic) h = (user->xmax-user->xmin)/Mda;
else h = (user->xmax-user->xmin)/(Mda-1.0);
xmid = (user->xmax + user->xmin)/2.0;
lambda = 4.0*h;
ierr = DMDAGetElements(user->da2,&nele,&nen,&ele);CHKERRQ(ierr);
for (i=0; i < nele; i++) {
idx[0] = ele[2*i]; idx[1] = ele[2*i+1];
x[0] = _coords[idx[0]];
x[1] = _coords[idx[1]];
PetscInt k;
PetscScalar vals_DDcv[2],vals_cv[2],vals_eta[2],s,hhr,r;
for (k=0; k < 2; k++) {
s = PetscAbs(x[k] - xmid);
if (s <= xwidth*(5.0/64.0)) {
vals_cv[k] = cv_v;
vals_eta[k] = eta_v;
vals_DDcv[k] = 0.0;
} else if (s> xwidth*(5.0/64.0) && s<= xwidth*(7.0/64.0)) {
/*r = (s - xwidth*(6.0/64.0))/(0.5*lambda);*/
r = (s - xwidth*(6.0/64.0))/(xwidth/64.0);
hhr = 0.25*(-r*r*r + 3*r + 2);
vals_cv[k] = cv_m + (1.0 - hhr)*(cv_v - cv_m);
vals_eta[k] = eta_m + (1.0 - hhr)*(eta_v - eta_m);
vals_DDcv[k] = (cv_v - cv_m)*r*6.0/(lambda*lambda);
} else {
vals_cv[k] = cv_m;
vals_eta[k] = eta_m;
vals_DDcv[k] = 0.0;
}
}
ierr = VecSetValuesLocal(user->cv,2,idx,vals_cv,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecSetValuesLocal(user->eta,2,idx,vals_eta,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecSetValuesLocal(user->work2,2,idx,vals_DDcv,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = DMDARestoreElements(user->da2,&nele,&nen,&ele);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(coords,&_coords);CHKERRQ(ierr);
ierr = VecAssemblyBegin(user->cv);CHKERRQ(ierr);
ierr = VecAssemblyEnd(user->cv);CHKERRQ(ierr);
ierr = VecAssemblyBegin(user->eta);CHKERRQ(ierr);
ierr = VecAssemblyEnd(user->eta);CHKERRQ(ierr);
ierr = VecAssemblyBegin(user->work2);CHKERRQ(ierr);
ierr = VecAssemblyEnd(user->work2);CHKERRQ(ierr);
ierr = DPsi(user);CHKERRQ(ierr);
ierr = VecCopy(user->DPsiv,user->wv);CHKERRQ(ierr);
ierr = VecAXPY(user->wv,-2.0*user->kav,user->work2);CHKERRQ(ierr);
ierr = VecGetArray(X,&xx);CHKERRQ(ierr);
ierr = VecGetArray(user->wv,&wv_p);CHKERRQ(ierr);
ierr = VecGetArray(user->cv,&cv_p);CHKERRQ(ierr);
ierr = VecGetArray(user->eta,&eta_p);CHKERRQ(ierr);
for (i=0; i<n/3; i++) {
xx[3*i] =wv_p[i];
xx[3*i+1]=cv_p[i];
xx[3*i+2]=eta_p[i];
}
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_initial",FILE_MODE_WRITE,&view_out);CHKERRQ(ierr);
ierr = VecView(user->wv,view_out);CHKERRQ(ierr);
ierr = VecView(user->cv,view_out);CHKERRQ(ierr);
ierr = VecView(user->eta,view_out);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&view_out);CHKERRQ(ierr);
ierr = VecRestoreArray(X,&xx);CHKERRQ(ierr);
ierr = VecRestoreArray(user->wv,&wv_p);CHKERRQ(ierr);
ierr = VecRestoreArray(user->cv,&cv_p);CHKERRQ(ierr);
ierr = VecRestoreArray(user->eta,&eta_p);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
PetscMPIInt rank;
PetscInt i,N,ng,*gindices,rstart,rend,M;
PetscScalar one = 1.0;
Vec x;
PetscInitialize(&argc,&argv,(char *)0,help);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
/*
Create a parallel vector.
- In this case, we specify the size of each processor's local
portion, and PETSc computes the global size. Alternatively,
PETSc could determine the vector's distribution if we specify
just the global size.
*/
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,rank+1,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecGetSize(x,&N);CHKERRQ(ierr);
ierr = VecSet(x,one);CHKERRQ(ierr);
/*
Set the local to global ordering for the vector. Each processor
generates a list of the global indices for each local index. Note that
the local indices are just whatever is convenient for a particular application.
In this case we treat the vector as lying on a one dimensional grid and
have one ghost point on each end of the blocks owned by each processor.
*/
ierr = VecGetSize(x,&M);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(x,&rstart,&rend);CHKERRQ(ierr);
ng = rend - rstart + 2;
ierr = PetscMalloc(ng*sizeof(PetscInt),&gindices);CHKERRQ(ierr);
gindices[0] = rstart - 1;
for (i=0; i<ng-1; i++) {
gindices[i+1] = gindices[i] + 1;
}
/* map the first and last point as periodic */
if (gindices[0] == -1) gindices[0] = M - 1;
if (gindices[ng-1] == M) gindices[ng-1] = 0;
{
ISLocalToGlobalMapping ltog;
ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,ng,gindices,PETSC_COPY_VALUES,<og);CHKERRQ(ierr);
ierr = VecSetLocalToGlobalMapping(x,ltog);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingDestroy(<og);CHKERRQ(ierr);
}
ierr = PetscFree(gindices);CHKERRQ(ierr);
/*
Set the vector elements.
- In this case set the values using the local ordering
- Each processor can contribute any vector entries,
regardless of which processor "owns" them; any nonlocal
contributions will be transferred to the appropriate processor
during the assembly process.
- In this example, the flag ADD_VALUES indicates that all
contributions will be added together.
*/
for (i=0; i<ng; i++) {
ierr = VecSetValuesLocal(x,1,&i,&one,ADD_VALUES);CHKERRQ(ierr);
}
/*
Assemble vector, using the 2-step process:
VecAssemblyBegin(), VecAssemblyEnd()
Computations can be done while messages are in transition
by placing code between these two statements.
*/
ierr = VecAssemblyBegin(x);CHKERRQ(ierr);
ierr = VecAssemblyEnd(x);CHKERRQ(ierr);
/*
View the vector; then destroy it.
*/
ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
/*
FormFunctionGradient - Evaluates the function and corresponding gradient.
Input Parameters:
tao - the Tao context
X - the input vector
ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
Output Parameters:
f - the newly evaluated function
G - the newly evaluated gradient
*/
PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f,Vec G,void *ptr){
AppCtx *user = (AppCtx *)ptr;
PetscErrorCode ierr;
PetscInt i,j,k,ind;
PetscInt xe,ye,xsm,ysm,xep,yep;
PetscInt xs, ys, xm, ym, gxm, gym, gxs, gys;
PetscInt mx = user->mx, my = user->my;
PetscReal three = 3.0, zero = 0.0, *x, floc, cdiv3 = user->param/three;
PetscReal p5 = 0.5, area, val, flin, fquad;
PetscReal v,vb,vl,vr,vt,dvdx,dvdy;
PetscReal hx = 1.0/(user->mx + 1);
PetscReal hy = 1.0/(user->my + 1);
Vec localX = user->localX;
PetscFunctionBegin;
/* Initialize */
flin = fquad = zero;
ierr = VecSet(G, zero);CHKERRQ(ierr);
/*
Scatter ghost points to local vector,using the 2-step process
DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
By placing code between these two statements, computations can be
done while messages are in transition.
*/
ierr = DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);CHKERRQ(ierr);
/* Get pointer to vector data */
ierr = VecGetArray(localX,&x);CHKERRQ(ierr);
/* Get local mesh boundaries */
ierr = DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
ierr = DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);CHKERRQ(ierr);
/* Set local loop dimensions */
xe = xs+xm;
ye = ys+ym;
if (xs == 0) xsm = xs-1;
else xsm = xs;
if (ys == 0) ysm = ys-1;
else ysm = ys;
if (xe == mx) xep = xe+1;
else xep = xe;
if (ye == my) yep = ye+1;
else yep = ye;
/* Compute local gradient contributions over the lower triangular elements */
for (j=ysm; j<ye; j++) { /* for (j=-1; j<my; j++) */
for (i=xsm; i<xe; i++) { /* for (i=-1; i<mx; i++) */
k = (j-gys)*gxm + i-gxs;
v = zero;
vr = zero;
vt = zero;
if (i >= 0 && j >= 0) v = x[k];
if (i < mx-1 && j > -1) vr = x[k+1];
if (i > -1 && j < my-1) vt = x[k+gxm];
dvdx = (vr-v)/hx;
dvdy = (vt-v)/hy;
if (i != -1 && j != -1) {
ind = k; val = - dvdx/hx - dvdy/hy - cdiv3;
ierr = VecSetValuesLocal(G,1,&k,&val,ADD_VALUES);CHKERRQ(ierr);
}
if (i != mx-1 && j != -1) {
ind = k+1; val = dvdx/hx - cdiv3;
ierr = VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);CHKERRQ(ierr);
}
if (i != -1 && j != my-1) {
ind = k+gxm; val = dvdy/hy - cdiv3;
ierr = VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);CHKERRQ(ierr);
}
fquad += dvdx*dvdx + dvdy*dvdy;
flin -= cdiv3 * (v + vr + vt);
}
}
/* Compute local gradient contributions over the upper triangular elements */
for (j=ys; j<yep; j++) { /* for (j=0; j<=my; j++) */
for (i=xs; i<xep; i++) { /* for (i=0; i<=mx; i++) */
k = (j-gys)*gxm + i-gxs;
vb = zero;
vl = zero;
v = zero;
if (i < mx && j > 0) vb = x[k-gxm];
if (i > 0 && j < my) vl = x[k-1];
if (i < mx && j < my) v = x[k];
dvdx = (v-vl)/hx;
dvdy = (v-vb)/hy;
if (i != mx && j != 0) {
ind = k-gxm; val = - dvdy/hy - cdiv3;
ierr = VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);CHKERRQ(ierr);
}
if (i != 0 && j != my) {
ind = k-1; val = - dvdx/hx - cdiv3;
ierr = VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);CHKERRQ(ierr);
}
if (i != mx && j != my) {
ind = k; val = dvdx/hx + dvdy/hy - cdiv3;
ierr = VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);CHKERRQ(ierr);
}
fquad += dvdx*dvdx + dvdy*dvdy;
flin -= cdiv3 * (vb + vl + v);
}
}
/* Restore vector */
ierr = VecRestoreArray(localX,&x);CHKERRQ(ierr);
/* Assemble gradient vector */
ierr = VecAssemblyBegin(G);CHKERRQ(ierr);
ierr = VecAssemblyEnd(G);CHKERRQ(ierr);
/* Scale the gradient */
area = p5*hx*hy;
floc = area * (p5 * fquad + flin);
ierr = VecScale(G, area);CHKERRQ(ierr);
/* Sum function contributions from all processes */
ierr = (PetscErrorCode)MPI_Allreduce((void*)&floc,(void*)f,1,MPIU_REAL,MPIU_SUM,MPI_COMM_WORLD);CHKERRQ(ierr);
ierr=PetscLogFlops((ye-ysm)*(xe-xsm)*20+(xep-xs)*(yep-ys)*16);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode MatISGetMPIXAIJ_IS(Mat mat, MatReuse reuse, Mat *M)
{
Mat_IS *matis = (Mat_IS*)(mat->data);
/* info on mat */
/* ISLocalToGlobalMapping rmapping,cmapping; */
PetscInt bs,rows,cols;
PetscInt lrows,lcols;
PetscInt local_rows,local_cols;
PetscBool isdense,issbaij,issbaij_red;
/* values insertion */
PetscScalar *array;
PetscInt *local_indices,*global_indices;
/* work */
PetscInt i,j,index_row;
PetscErrorCode ierr;
PetscFunctionBegin;
/* MISSING CHECKS
- rectangular case not covered (it is not allowed by MATIS)
*/
/* get info from mat */
/* ierr = MatGetLocalToGlobalMapping(mat,&rmapping,&cmapping);CHKERRQ(ierr); */
ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
ierr = MatGetSize(matis->A,&local_rows,&local_cols);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)matis->A,MATSEQDENSE,&isdense);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)matis->A,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
/* work */
ierr = PetscMalloc1(local_rows,&local_indices);CHKERRQ(ierr);
for (i=0;i<local_rows;i++) local_indices[i]=i;
/* map indices of local mat to global values */
ierr = PetscMalloc(PetscMax(local_cols,local_rows)*sizeof(*global_indices),&global_indices);CHKERRQ(ierr);
/* ierr = ISLocalToGlobalMappingApply(rmapping,local_rows,local_indices,global_indices);CHKERRQ(ierr); */
ierr = ISLocalToGlobalMappingApply(matis->mapping,local_rows,local_indices,global_indices);CHKERRQ(ierr);
if (issbaij) {
ierr = MatGetRowUpperTriangular(matis->A);CHKERRQ(ierr);
}
if (reuse == MAT_INITIAL_MATRIX) {
Mat new_mat;
MatType new_mat_type;
Vec vec_dnz,vec_onz;
PetscScalar *my_dnz,*my_onz;
PetscInt *dnz,*onz,*mat_ranges,*row_ownership;
PetscInt index_col,owner;
PetscMPIInt nsubdomains;
/* determining new matrix type */
ierr = MPI_Allreduce(&issbaij,&issbaij_red,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
if (issbaij_red) {
new_mat_type = MATSBAIJ;
} else {
if (bs>1) {
new_mat_type = MATBAIJ;
} else {
new_mat_type = MATAIJ;
}
}
ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&nsubdomains);CHKERRQ(ierr);
ierr = MatCreate(PetscObjectComm((PetscObject)mat),&new_mat);CHKERRQ(ierr);
ierr = MatSetSizes(new_mat,PETSC_DECIDE,PETSC_DECIDE,rows,cols);CHKERRQ(ierr);
ierr = MatSetBlockSize(new_mat,bs);CHKERRQ(ierr);
ierr = MatSetType(new_mat,new_mat_type);CHKERRQ(ierr);
ierr = MatSetUp(new_mat);CHKERRQ(ierr);
ierr = MatGetLocalSize(new_mat,&lrows,&lcols);CHKERRQ(ierr);
/*
preallocation
*/
ierr = MatPreallocateInitialize(PetscObjectComm((PetscObject)new_mat),lrows,lcols,dnz,onz);CHKERRQ(ierr);
/*
Some vectors are needed to sum up properly on shared interface dofs.
Preallocation macros cannot do the job.
Note that preallocation is not exact, since it overestimates nonzeros
*/
ierr = MatCreateVecs(new_mat,NULL,&vec_dnz);CHKERRQ(ierr);
/* ierr = VecSetLocalToGlobalMapping(vec_dnz,rmapping);CHKERRQ(ierr); */
ierr = VecSetLocalToGlobalMapping(vec_dnz,matis->mapping);CHKERRQ(ierr);
ierr = VecDuplicate(vec_dnz,&vec_onz);CHKERRQ(ierr);
/* All processes need to compute entire row ownership */
ierr = PetscMalloc1(rows,&row_ownership);CHKERRQ(ierr);
ierr = MatGetOwnershipRanges(new_mat,(const PetscInt**)&mat_ranges);CHKERRQ(ierr);
for (i=0;i<nsubdomains;i++) {
for (j=mat_ranges[i];j<mat_ranges[i+1];j++) {
row_ownership[j]=i;
}
}
/*
my_dnz and my_onz contains exact contribution to preallocation from each local mat
then, they will be summed up properly. This way, preallocation is always sufficient
*/
ierr = PetscMalloc1(local_rows,&my_dnz);CHKERRQ(ierr);
ierr = PetscMalloc1(local_rows,&my_onz);CHKERRQ(ierr);
ierr = PetscMemzero(my_dnz,local_rows*sizeof(*my_dnz));CHKERRQ(ierr);
ierr = PetscMemzero(my_onz,local_rows*sizeof(*my_onz));CHKERRQ(ierr);
/* preallocation as a MATAIJ */
if (isdense) { /* special case for dense local matrices */
for (i=0;i<local_rows;i++) {
index_row = global_indices[i];
for (j=i;j<local_rows;j++) {
owner = row_ownership[index_row];
index_col = global_indices[j];
if (index_col > mat_ranges[owner]-1 && index_col < mat_ranges[owner+1] ) { /* diag block */
my_dnz[i] += 1.0;
} else { /* offdiag block */
my_onz[i] += 1.0;
}
/* same as before, interchanging rows and cols */
if (i != j) {
owner = row_ownership[index_col];
if (index_row > mat_ranges[owner]-1 && index_row < mat_ranges[owner+1] ) {
my_dnz[j] += 1.0;
} else {
my_onz[j] += 1.0;
}
}
}
}
} else {
for (i=0;i<local_rows;i++) {
PetscInt ncols;
const PetscInt *cols;
index_row = global_indices[i];
ierr = MatGetRow(matis->A,i,&ncols,&cols,NULL);CHKERRQ(ierr);
for (j=0;j<ncols;j++) {
owner = row_ownership[index_row];
index_col = global_indices[cols[j]];
if (index_col > mat_ranges[owner]-1 && index_col < mat_ranges[owner+1] ) { /* diag block */
my_dnz[i] += 1.0;
} else { /* offdiag block */
my_onz[i] += 1.0;
}
/* same as before, interchanging rows and cols */
if (issbaij) {
owner = row_ownership[index_col];
if (index_row > mat_ranges[owner]-1 && index_row < mat_ranges[owner+1] ) {
my_dnz[j] += 1.0;
} else {
my_onz[j] += 1.0;
}
}
}
ierr = MatRestoreRow(matis->A,i,&ncols,&cols,NULL);CHKERRQ(ierr);
}
}
ierr = VecSet(vec_dnz,0.0);CHKERRQ(ierr);
ierr = VecSet(vec_onz,0.0);CHKERRQ(ierr);
if (local_rows) { /* multilevel guard */
ierr = VecSetValuesLocal(vec_dnz,local_rows,local_indices,my_dnz,ADD_VALUES);CHKERRQ(ierr);
ierr = VecSetValuesLocal(vec_onz,local_rows,local_indices,my_onz,ADD_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(vec_dnz);CHKERRQ(ierr);
ierr = VecAssemblyBegin(vec_onz);CHKERRQ(ierr);
ierr = VecAssemblyEnd(vec_dnz);CHKERRQ(ierr);
ierr = VecAssemblyEnd(vec_onz);CHKERRQ(ierr);
ierr = PetscFree(my_dnz);CHKERRQ(ierr);
ierr = PetscFree(my_onz);CHKERRQ(ierr);
ierr = PetscFree(row_ownership);CHKERRQ(ierr);
/* set computed preallocation in dnz and onz */
ierr = VecGetArray(vec_dnz,&array);CHKERRQ(ierr);
for (i=0; i<lrows; i++) dnz[i] = (PetscInt)PetscRealPart(array[i]);
ierr = VecRestoreArray(vec_dnz,&array);CHKERRQ(ierr);
ierr = VecGetArray(vec_onz,&array);CHKERRQ(ierr);
for (i=0;i<lrows;i++) onz[i] = (PetscInt)PetscRealPart(array[i]);
ierr = VecRestoreArray(vec_onz,&array);CHKERRQ(ierr);
ierr = VecDestroy(&vec_dnz);CHKERRQ(ierr);
ierr = VecDestroy(&vec_onz);CHKERRQ(ierr);
/* Resize preallocation if overestimated */
for (i=0;i<lrows;i++) {
dnz[i] = PetscMin(dnz[i],lcols);
onz[i] = PetscMin(onz[i],cols-lcols);
}
/* set preallocation */
ierr = MatMPIAIJSetPreallocation(new_mat,0,dnz,0,onz);CHKERRQ(ierr);
for (i=0;i<lrows/bs;i++) {
dnz[i] = dnz[i*bs]/bs;
onz[i] = onz[i*bs]/bs;
}
ierr = MatMPIBAIJSetPreallocation(new_mat,bs,0,dnz,0,onz);CHKERRQ(ierr);
for (i=0;i<lrows/bs;i++) {
dnz[i] = dnz[i]-i;
}
ierr = MatMPISBAIJSetPreallocation(new_mat,bs,0,dnz,0,onz);CHKERRQ(ierr);
ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
*M = new_mat;
} else {
PetscInt mbs,mrows,mcols;
/* some checks */
ierr = MatGetBlockSize(*M,&mbs);CHKERRQ(ierr);
ierr = MatGetSize(*M,&mrows,&mcols);CHKERRQ(ierr);
if (mrows != rows) {
SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix. Wrong number of rows (%d != %d)",rows,mrows);
}
if (mrows != rows) {
SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix. Wrong number of cols (%d != %d)",cols,mcols);
}
if (mbs != bs) {
SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix. Wrong block size (%d != %d)",bs,mbs);
}
ierr = MatZeroEntries(*M);CHKERRQ(ierr);
}
/* set local to global mappings */
/* ierr = MatSetLocalToGlobalMapping(*M,rmapping,cmapping);CHKERRQ(ierr); */
/* Set values */
if (isdense) { /* special case for dense local matrices */
ierr = MatSetOption(*M,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
ierr = MatDenseGetArray(matis->A,&array);CHKERRQ(ierr);
ierr = MatSetValues(*M,local_rows,global_indices,local_cols,global_indices,array,ADD_VALUES);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(matis->A,&array);CHKERRQ(ierr);
ierr = PetscFree(local_indices);CHKERRQ(ierr);
ierr = PetscFree(global_indices);CHKERRQ(ierr);
} else { /* very basic values insertion for all other matrix types */
ierr = PetscFree(local_indices);CHKERRQ(ierr);
for (i=0;i<local_rows;i++) {
ierr = MatGetRow(matis->A,i,&j,(const PetscInt**)&local_indices,(const PetscScalar**)&array);CHKERRQ(ierr);
/* ierr = MatSetValuesLocal(*M,1,&i,j,local_indices,array,ADD_VALUES);CHKERRQ(ierr); */
ierr = ISLocalToGlobalMappingApply(matis->mapping,j,local_indices,global_indices);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingApply(matis->mapping,1,&i,&index_row);CHKERRQ(ierr);
ierr = MatSetValues(*M,1,&index_row,j,global_indices,array,ADD_VALUES);CHKERRQ(ierr);
ierr = MatRestoreRow(matis->A,i,&j,(const PetscInt**)&local_indices,(const PetscScalar**)&array);CHKERRQ(ierr);
}
ierr = PetscFree(global_indices);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(*M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(*M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (isdense) {
ierr = MatSetOption(*M,MAT_ROW_ORIENTED,PETSC_TRUE);CHKERRQ(ierr);
}
if (issbaij) {
ierr = MatRestoreRowUpperTriangular(matis->A);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
