static PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ptr)
{
User user = (User)ptr;
DM da;
DMDALocalInfo info;
PetscInt i;
Field *f;
const Field *x,*xdot;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
/* Get pointers to vector data */
ierr = DMDAVecGetArrayRead(da,X,(void*)&x);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(da,Xdot,(void*)&xdot);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/* Compute function over the locally owned part of the grid */
for (i=info.xs; i<info.xs+info.xm; i++) {
f[i][0] = xdot[i][0] + user->k[0]*x[i][0] - user->k[1]*x[i][1] - user->s[0];
f[i][1] = xdot[i][1] - user->k[0]*x[i][0] + user->k[1]*x[i][1] - user->s[1];
}
/* Restore vectors */
ierr = DMDAVecRestoreArrayRead(da,X,(void*)&x);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,Xdot,(void*)&xdot);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* IJacobian - Compute IJacobian = dF/dU + a dF/dUdot */
PetscErrorCode FormIJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat J, Mat Jpre, void *ctx)
{
User user = (User) ctx;
DM dm, cdm;
DMDALocalInfo info;
Vec C;
Field *u, *udot;
PetscScalar *x;
PetscInt i;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(dm, &info);CHKERRQ(ierr);
ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(dm, &C);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(dm, U, &u);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(dm, Udot, &udot);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(cdm, C, &x);CHKERRQ(ierr);
for (i = info.xs; i < info.xs+info.xm; ++i) {
if (i == 0) {
const PetscScalar hx = x[i+1] - x[i];
const PetscInt row = i, col[] = {i,i+1};
const PetscScalar dxx0 = PetscSqr(user->c)/hx,dxxR = -PetscSqr(user->c)/hx;
const PetscScalar vals[3][2][3] = {{{a*hx, 0,0},{0,0, 0}},
{{0,a*hx+dxx0,0},{0,dxxR,0}},
{{0,0, a*hx},{0,0, 0}}};
ierr = MatSetValuesBlocked(Jpre, 1, &row, 2, col, &vals[0][0][0], INSERT_VALUES);CHKERRQ(ierr);
} else if (i == info.mx-1) {
const PetscScalar hx = x[i+1] - x[i];
const PetscInt row = i, col[] = {i-1,i};
const PetscScalar dxxL = -PetscSqr(user->c)/hx, dxx0 = PetscSqr(user->c)/hx;
const PetscScalar vals[3][2][3] = {{{0,0, 0},{a*hx, 0,0}},
{{0,dxxL,0},{0,a*hx+dxx0,0}},
{{0,0, 0},{0,0, a*hx}}};
ierr = MatSetValuesBlocked(Jpre, 1, &row, 2, col, &vals[0][0][0], INSERT_VALUES);CHKERRQ(ierr);
} else {
const PetscScalar hx = x[i+1] - x[i];
const PetscInt row = i, col[] = {i-1,i,i+1};
const PetscScalar dxxL = -PetscSqr(user->c)/hx, dxx0 = 2.*PetscSqr(user->c)/hx,dxxR = -PetscSqr(user->c)/hx;
const PetscScalar vals[3][3][3] = {{{0,0, 0},{a*hx, 0,0},{0,0, 0}},
{{0,dxxL,0},{0,a*hx+dxx0,0},{0,dxxR,0}},
{{0,0, 0},{0,0, a*hx},{0,0, 0}}};
ierr = MatSetValuesBlocked(Jpre, 1, &row, 3, col, &vals[0][0][0], INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = DMDAVecRestoreArrayRead(dm, U, &u);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(dm, Udot, &udot);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(cdm, C, &x);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Jpre, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Jpre, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (J != Jpre) {
ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
{
PetscErrorCode ierr;
AppCtx *user=(AppCtx*)ctx;
DM cda;
DMDACoor2d **coors;
PetscScalar **p,**f,**pdot;
PetscInt i,j;
PetscInt xs,ys,xm,ym,M,N;
Vec localX,gc,localXdot;
PetscScalar p_adv1,p_adv2,p_diff;
PetscFunctionBeginUser;
ierr = DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
ierr = DMGetCoordinateDM(user->da,&cda);CHKERRQ(ierr);
ierr = DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
ierr = DMGetLocalVector(user->da,&localX);CHKERRQ(ierr);
ierr = DMGetLocalVector(user->da,&localXdot);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(user->da,Xdot,INSERT_VALUES,localXdot);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(user->da,Xdot,INSERT_VALUES,localXdot);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(user->da,&gc);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(cda,gc,&coors);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(user->da,localX,&p);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(user->da,localXdot,&pdot);CHKERRQ(ierr);
ierr = DMDAVecGetArray(user->da,F,&f);CHKERRQ(ierr);
PetscScalar diffuse1,gamma;
gamma = user->D*user->ws/(2*user->H);
diffuse1 = user->lambda*user->lambda*user->q/(user->lambda*gamma+1)*(1.0 - PetscExpScalar(-t*(gamma+1.0)/user->lambda));
user->disper_coe = user->ws*user->ws/(4*user->H*user->H)*diffuse1;
for (i=xs; i < xs+xm; i++) {
for (j=ys; j < ys+ym; j++) {
ierr = adv1(p,coors[j][i].y,i,j,M,&p_adv1,user);CHKERRQ(ierr);
ierr = adv2(p,coors[j][i].x,coors[j][i].y,i,j,N,&p_adv2,user);CHKERRQ(ierr);
ierr = diffuse(p,i,j,t,&p_diff,user);CHKERRQ(ierr);
f[j][i] = -p_adv1 - p_adv2 + p_diff - pdot[j][i];
}
}
ierr = DMDAVecRestoreArrayRead(user->da,localX,&p);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(user->da,localX,&pdot);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(user->da,&localX);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(user->da,&localXdot);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(user->da,F,&f);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(cda,gc,&coors);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ptr)
{
User user = (User)ptr;
DM da;
DMDALocalInfo info;
PetscInt i;
Field *x,*xdot,*f;
PetscReal hx;
Vec Xloc;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
hx = 1.0/(PetscReal)(info.mx-1);
/*
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 = DMGetLocalVector(da,&Xloc);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,X,INSERT_VALUES,Xloc);CHKERRQ(ierr);
/* Get pointers to vector data */
ierr = DMDAVecGetArrayRead(da,Xloc,&x);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(da,Xdot,&xdot);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/* Compute function over the locally owned part of the grid */
for (i=info.xs; i<info.xs+info.xm; i++) {
if (i == 0) {
f[i].u = hx * (x[i].u - user->uleft);
f[i].v = hx * (x[i].v - user->vleft);
} else if (i == info.mx-1) {
f[i].u = hx * (x[i].u - user->uright);
f[i].v = hx * (x[i].v - user->vright);
} else {
f[i].u = hx * xdot[i].u - user->alpha * (x[i-1].u - 2.*x[i].u + x[i+1].u) / hx;
f[i].v = hx * xdot[i].v - user->alpha * (x[i-1].v - 2.*x[i].v + x[i+1].v) / hx;
}
}
/* Restore vectors */
ierr = DMDAVecRestoreArrayRead(da,Xloc,&x);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,Xdot,&xdot);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&Xloc);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode FormIFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, void *ctx)
{
User user = (User) ctx;
DM dm, cdm;
DMDALocalInfo info;
Vec Uloc, C;
Field *u, *udot, *f;
PetscScalar *x;
PetscInt i;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(dm, &info);CHKERRQ(ierr);
ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(dm, &C);CHKERRQ(ierr);
ierr = DMGetLocalVector(dm, &Uloc);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(dm, U, INSERT_VALUES, Uloc);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(dm, U, INSERT_VALUES, Uloc);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(dm, Uloc, &u);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(dm, Udot, &udot);CHKERRQ(ierr);
ierr = DMDAVecGetArray(dm, F, &f);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(cdm, C, &x);CHKERRQ(ierr);
for (i = info.xs; i < info.xs+info.xm; ++i) {
if (i == 0) {
const PetscScalar hx = x[i+1] - x[i];
f[i].u = hx * udot[i].u;
f[i].v = hx * udot[i].v - PetscSqr(user->c) * (u[i+1].u - u[i].u) / hx;
f[i].th = hx * udot[i].th;
} else if (i == info.mx-1) {
const PetscScalar hx = x[i] - x[i-1];
f[i].u = hx * udot[i].u;
f[i].v = hx * udot[i].v - PetscSqr(user->c) * (u[i-1].u - u[i].u) / hx;
f[i].th = hx * udot[i].th;
} else {
const PetscScalar hx = x[i+1] - x[i];
f[i].u = hx * udot[i].u;
f[i].v = hx * udot[i].v - PetscSqr(user->c) * (u[i-1].u - 2.*u[i].u + u[i+1].u) / hx;
f[i].th = hx * udot[i].th;
}
}
ierr = DMDAVecRestoreArrayRead(dm, Uloc, &u);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(dm, Udot, &udot);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(dm, F, &f);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(cdm, C, &x);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(dm, &Uloc);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode SetCoordinates2d(DM da)
{
PetscErrorCode ierr;
PetscInt i,j,mstart,m,nstart,n;
Vec local,global;
DMDACoor2d **coors,**coorslocal;
DM cda;
PetscFunctionBeginUser;
ierr = DMDASetUniformCoordinates(da,0.0,1.0,0.0,1.0,0.0,1.0);CHKERRQ(ierr);
ierr = DMGetCoordinateDM(da,&cda);CHKERRQ(ierr);
ierr = DMGetCoordinates(da,&global);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(da,&local);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cda,global,&coors);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(cda,local,&coorslocal);CHKERRQ(ierr);
ierr = DMDAGetCorners(cda,&mstart,&nstart,0,&m,&n,0);CHKERRQ(ierr);
for (i=mstart; i<mstart+m; i++) {
for (j=nstart; j<nstart+n; j++) {
if (i % 2) {
coors[j][i].x = coorslocal[j][i-1].x + .1*(coorslocal[j][i+1].x - coorslocal[j][i-1].x);
}
if (j % 2) {
coors[j][i].y = coorslocal[j-1][i].y + .3*(coorslocal[j+1][i].y - coorslocal[j-1][i].y);
}
}
}
ierr = DMDAVecRestoreArray(cda,global,&coors);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(cda,local,&coorslocal);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(cda,global,INSERT_VALUES,local);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(cda,global,INSERT_VALUES,local);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode ini_bou(Vec X,AppCtx* user)
{
PetscErrorCode ierr;
DM cda;
DMDACoor2d **coors;
PetscScalar **p;
Vec gc;
PetscInt M,N,I,J;
PetscMPIInt rank;
PetscFunctionBeginUser;
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
user->dx = (user->xmax - user->xmin)/(M-1); user->dy = (user->ymax - user->ymin)/(N-1);
ierr = DMGetCoordinateDM(user->da,&cda);CHKERRQ(ierr);
ierr = DMGetCoordinates(user->da,&gc);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(cda,gc,&coors);CHKERRQ(ierr);
ierr = DMDAVecGetArray(user->da,X,&p);CHKERRQ(ierr);
/* Point mass at (mux,muy) */
ierr = PetscPrintf(PETSC_COMM_WORLD,"Original user->mux = %f, user->muy = %f\n",user->mux,user->muy);CHKERRQ(ierr);
ierr = DMDAGetLogicalCoordinate(user->da,user->mux,user->muy,0.0,&I,&J,NULL,&user->mux,&user->muy,NULL);CHKERRQ(ierr);
user->PM_min = user->Pmax*PetscSinScalar(user->mux);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Corrected user->mux = %f, user->muy = %f user->PM_min = %f,user->dx = %f\n",user->mux,user->muy,user->PM_min,user->dx);CHKERRQ(ierr);
if (I > -1 && J > -1) {
p[J][I] = 1.0;
}
ierr = DMDAVecRestoreArrayRead(cda,gc,&coors);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(user->da,X,&p);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode FormRHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ptr)
{
User user = (User)ptr;
DM da;
DMDALocalInfo info;
PetscInt i;
PetscReal hx;
Field *x,*f;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
hx = 1.0/(PetscReal)(info.mx-1);
/* Get pointers to vector data */
ierr = DMDAVecGetArrayRead(da,X,&x);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/* Compute function over the locally owned part of the grid */
for (i=info.xs; i<info.xs+info.xm; i++) {
PetscScalar u = x[i].u,v = x[i].v;
f[i].u = hx*(user->A + u*u*v - (user->B+1)*u);
f[i].v = hx*(user->B*u - u*u*v);
}
/* Restore vectors */
ierr = DMDAVecRestoreArrayRead(da,X,&x);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode SetCoordinates1d(DM da)
{
PetscErrorCode ierr;
PetscInt i,start,m;
Vec local,global;
PetscScalar *coors,*coorslocal;
DM cda;
PetscFunctionBeginUser;
ierr = DMDASetUniformCoordinates(da,0.0,1.0,0.0,1.0,0.0,1.0);CHKERRQ(ierr);
ierr = DMGetCoordinateDM(da,&cda);CHKERRQ(ierr);
ierr = DMGetCoordinates(da,&global);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(da,&local);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cda,global,&coors);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(cda,local,&coorslocal);CHKERRQ(ierr);
ierr = DMDAGetCorners(cda,&start,0,0,&m,0,0);CHKERRQ(ierr);
for (i=start; i<start+m; i++) {
if (i % 2) {
coors[i] = coorslocal[i-1] + .1*(coorslocal[i+1] - coorslocal[i-1]);
}
}
ierr = DMDAVecRestoreArray(cda,global,&coors);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(cda,local,&coorslocal);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(cda,global,INSERT_VALUES,local);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(cda,global,INSERT_VALUES,local);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode FormRHSFunction(TS ts, PetscReal t, Vec U, Vec F, void *ctx)
{
User user = (User) ctx;
DM dm, cdm;
DMDALocalInfo info;
Vec C;
Field *f;
const Field *u;
const PetscScalar *x;
PetscInt i;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(dm, &C);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(dm, &info);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(dm, U, &u);CHKERRQ(ierr);
ierr = DMDAVecGetArray(dm, F, &f);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cdm, C, &x);CHKERRQ(ierr);
for (i = info.xs; i < info.xs+info.xm; ++i) {
const PetscScalar hx = i+1 == info.xs+info.xm ? x[i] - x[i-1] : x[i+1] - x[i];
f[i].u = hx*(u[i].v);
f[i].v = -hx*(PetscSqr(user->gammaTilde)*u[i].u + (PetscSqr(user->gamma) / user->xi)*(u[i].th + log(u[i].v + 1)));
f[i].th = -hx*(u[i].v + 1)*(u[i].th + (1 + user->epsilon)*log(u[i].v + 1));
}
ierr = DMDAVecRestoreArrayRead(dm, U, &u);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(dm, F, &f);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(cdm, C, &x);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FormInitialSolution(TS ts, Vec U, void *ctx)
{
/* User user = (User) ctx; */
DM dm, cdm;
DMDALocalInfo info;
Vec C;
Field *u;
PetscScalar *x;
const PetscReal sigma = 1.0;
PetscInt i;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = TSGetDM(ts, &dm);
ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(dm, &C);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(dm, &info);CHKERRQ(ierr);
ierr = DMDAVecGetArray(dm, U, &u);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(cdm, C, &x);CHKERRQ(ierr);
for (i = info.xs; i < info.xs+info.xm; ++i) {
u[i].u = 1.5 * PetscExpScalar(-PetscSqr(x[i] - 10)/PetscSqr(sigma));
u[i].v = 0.0;
u[i].th = 0.0;
}
ierr = DMDAVecRestoreArray(dm, U, &u);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(cdm, C, &x);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
Use Lax-Wendroff method to evaluate F(u,t) = du/dt + a * du/dx
*/
PetscErrorCode IFunction_LaxWendroff(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void* ctx)
{
PetscErrorCode ierr;
AppCtx *appctx=(AppCtx*)ctx;
PetscInt mstart,mend,M,i,um;
DM da;
Vec Uold,localUold;
PetscScalar *uarray,*f,*uoldarray,h,RFlux,LFlux,lambda;
PetscReal dt,a;
PetscFunctionBegin;
ierr = TSGetTimeStep(ts,&dt);CHKERRQ(ierr);
ierr = TSGetSolution(ts,&Uold);CHKERRQ(ierr);
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&M,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&mstart,0,0,&um,0,0);CHKERRQ(ierr);
h = 1.0/M;
mend = mstart + um;
/* printf(" mstart %d, um %d\n",mstart,um); */
ierr = DMGetLocalVector(da,&localUold);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(da,Uold,INSERT_VALUES,localUold);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,Uold,INSERT_VALUES,localUold);CHKERRQ(ierr);
/* Get pointers to vector data */
ierr = DMDAVecGetArrayRead(da,U,&uarray);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(da,localUold,&uoldarray);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/* advection -- finite volume (appctx->a < 0 -- can be relaxed?) */
lambda = dt/h;
a = appctx->a;
for (i=mstart; i<mend; i++) {
RFlux = 0.5 * a * (uoldarray[i+1] + uoldarray[i]) - a*a*0.5*lambda * (uoldarray[i+1] - uoldarray[i]);
LFlux = 0.5 * a * (uoldarray[i-1] + uoldarray[i]) - a*a*0.5*lambda * (uoldarray[i] - uoldarray[i-1]);
f[i] = uarray[i] - uoldarray[i] + lambda * (RFlux - LFlux);
}
/* Restore vectors */
ierr = DMDAVecRestoreArrayRead(da,U,&uarray);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,localUold,&uoldarray);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localUold);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
IJacobian - Compute IJacobian = dF/dU + a dF/dUdot
*/
PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat J,Mat Jpre,void *ptr)
{
User user = (User)ptr;
PetscErrorCode ierr;
DMDALocalInfo info;
PetscInt i;
PetscReal hx;
DM da;
Field *x,*xdot;
PetscFunctionBeginUser;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
hx = 1.0/(PetscReal)(info.mx-1);
/* Get pointers to vector data */
ierr = DMDAVecGetArrayRead(da,X,&x);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(da,Xdot,&xdot);CHKERRQ(ierr);
/* Compute function over the locally owned part of the grid */
for (i=info.xs; i<info.xs+info.xm; i++) {
if (i == 0 || i == info.mx-1) {
const PetscInt row = i,col = i;
const PetscScalar vals[2][2] = {{hx,0},{0,hx}};
ierr = MatSetValuesBlocked(Jpre,1,&row,1,&col,&vals[0][0],INSERT_VALUES);CHKERRQ(ierr);
} else {
const PetscInt row = i,col[] = {i-1,i,i+1};
const PetscScalar dxxL = -user->alpha/hx,dxx0 = 2.*user->alpha/hx,dxxR = -user->alpha/hx;
const PetscScalar vals[2][3][2] = {{{dxxL,0},{a *hx+dxx0,0},{dxxR,0}},
{{0,dxxL},{0,a*hx+dxx0},{0,dxxR}}};
ierr = MatSetValuesBlocked(Jpre,1,&row,3,col,&vals[0][0][0],INSERT_VALUES);CHKERRQ(ierr);
}
}
/* Restore vectors */
ierr = DMDAVecRestoreArrayRead(da,X,&x);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,Xdot,&xdot);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (J != Jpre) {
ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
/*
Use Lax-Friedrichs method to evaluate F(u,t) = du/dt + a * du/dx
See https://en.wikipedia.org/wiki/Lax%E2%80%93Friedrichs_method
*/
PetscErrorCode IFunction_LaxFriedrichs(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void* ctx)
{
PetscErrorCode ierr;
AppCtx *appctx=(AppCtx*)ctx;
PetscInt mstart,mend,M,i,um;
DM da;
Vec Uold,localUold;
PetscScalar *uarray,*f,*uoldarray,h,uave,c;
PetscReal dt;
PetscFunctionBegin;
ierr = TSGetTimeStep(ts,&dt);CHKERRQ(ierr);
ierr = TSGetSolution(ts,&Uold);CHKERRQ(ierr);
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&M,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&mstart,0,0,&um,0,0);CHKERRQ(ierr);
h = 1.0/M;
mend = mstart + um;
/* printf(" mstart %d, um %d\n",mstart,um); */
ierr = DMGetLocalVector(da,&localUold);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(da,Uold,INSERT_VALUES,localUold);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,Uold,INSERT_VALUES,localUold);CHKERRQ(ierr);
/* Get pointers to vector data */
ierr = DMDAVecGetArrayRead(da,U,&uarray);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(da,localUold,&uoldarray);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/* advection */
c = appctx->a*dt/h; /* Courant-Friedrichs-Lewy number (CFL number) */
for (i=mstart; i<mend; i++) {
uave = 0.5*(uoldarray[i-1] + uoldarray[i+1]);
f[i] = uarray[i] - uave + c*0.5*(uoldarray[i+1] - uoldarray[i-1]);
}
/* Restore vectors */
ierr = DMDAVecRestoreArrayRead(da,U,&uarray);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,localUold,&uoldarray);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localUold);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
FormFunction - Evaluates nonlinear function, F(x).
Input Parameters:
. ts - the TS context
. X - input vector
. ptr - optional user-defined context, as set by SNESSetFunction()
Output Parameter:
. F - function vector
*/
PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec F,void *ptr)
{
DM da;
PetscErrorCode ierr;
PetscInt i,Mx,xs,xm;
PetscReal hx,sx;
PetscScalar *x,*f;
Vec localX;
UserCtx *ctx = (UserCtx*)ptr;
PetscFunctionBegin;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localX);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
hx = 1.0/(PetscReal)Mx; sx = 1.0/(hx*hx);
/*
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(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
/*
Get pointers to vector data
*/
ierr = DMDAVecGetArrayRead(da,localX,&x);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/*
Get local grid boundaries
*/
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
/*
Compute function over the locally owned part of the grid
*/
for (i=xs; i<xs+xm; i++) {
f[i] = ctx->kappa*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
if (ctx->allencahn) f[i] += (x[i] - x[i]*x[i]*x[i]);
}
/*
Restore vectors
*/
ierr = DMDAVecRestoreArrayRead(da,localX,&x);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localX);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode FormRHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ptr)
{
User user = (User)ptr;
DM da;
Vec Xloc;
DMDALocalInfo info;
PetscInt i,j;
PetscReal hx;
Field *f;
const Field *x;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
hx = 1.0/(PetscReal)info.mx;
/*
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 = DMGetLocalVector(da,&Xloc);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,X,INSERT_VALUES,Xloc);CHKERRQ(ierr);
/* Get pointers to vector data */
ierr = DMDAVecGetArrayRead(da,Xloc,(void*)&x);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/* Compute function over the locally owned part of the grid */
for (i=info.xs; i<info.xs+info.xm; i++) {
const PetscReal *a = user->a;
PetscReal u0t[2];
u0t[0] = 1.0 - PetscPowRealInt(PetscSinReal(12*t),4);
u0t[1] = 0.0;
for (j=0; j<2; j++) {
if (i == 0) f[i][j] = a[j]/hx*(1./3*u0t[j] + 0.5*x[i][j] - x[i+1][j] + 1./6*x[i+2][j]);
else if (i == 1) f[i][j] = a[j]/hx*(-1./12*u0t[j] + 2./3*x[i-1][j] - 2./3*x[i+1][j] + 1./12*x[i+2][j]);
else if (i == info.mx-2) f[i][j] = a[j]/hx*(-1./6*x[i-2][j] + x[i-1][j] - 0.5*x[i][j] - 1./3*x[i+1][j]);
else if (i == info.mx-1) f[i][j] = a[j]/hx*(-x[i][j] + x[i-1][j]);
else f[i][j] = a[j]/hx*(-1./12*x[i-2][j] + 2./3*x[i-1][j] - 2./3*x[i+1][j] + 1./12*x[i+2][j]);
}
}
/* Restore vectors */
ierr = DMDAVecRestoreArrayRead(da,Xloc,(void*)&x);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&Xloc);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat J,Mat Jpre,void *ptr)
{
User user = (User)ptr;
PetscErrorCode ierr;
DMDALocalInfo info;
PetscInt i;
DM da;
const Field *x,*xdot;
PetscFunctionBeginUser;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
/* Get pointers to vector data */
ierr = DMDAVecGetArrayRead(da,X,(void*)&x);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(da,Xdot,(void*)&xdot);CHKERRQ(ierr);
/* Compute function over the locally owned part of the grid */
for (i=info.xs; i<info.xs+info.xm; i++) {
const PetscReal *k = user->k;
PetscScalar v[2][2];
v[0][0] = a + k[0]; v[0][1] = -k[1];
v[1][0] = -k[0]; v[1][1] = a+k[1];
ierr = MatSetValuesBlocked(Jpre,1,&i,1,&i,&v[0][0],INSERT_VALUES);CHKERRQ(ierr);
}
/* Restore vectors */
ierr = DMDAVecRestoreArrayRead(da,X,(void*)&x);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,Xdot,(void*)&xdot);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (J != Jpre) {
ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat J,Mat Jpre,void *ctx)
{
PetscErrorCode ierr;
AppCtx *user=(AppCtx*)ctx;
DM cda;
DMDACoor2d **coors;
PetscInt i,j;
PetscInt xs,ys,xm,ym,M,N;
Vec gc;
PetscScalar val[5],xi,yi;
MatStencil row,col[5];
PetscScalar c1,c3,c5,c1pos,c1neg,c3pos,c3neg;
PetscFunctionBeginUser;
ierr = DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
ierr = DMGetCoordinateDM(user->da,&cda);CHKERRQ(ierr);
ierr = DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(user->da,&gc);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(cda,gc,&coors);CHKERRQ(ierr);
for (i=xs; i < xs+xm; i++) {
for (j=ys; j < ys+ym; j++) {
PetscInt nc = 0;
xi = coors[j][i].x; yi = coors[j][i].y;
row.i = i; row.j = j;
c1 = (yi-user->ws)/user->dx;
c1pos = PetscMax(c1,0);
c1neg = PetscMin(c1,0);
c3 = (user->ws/(2.0*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(xi) - user->D*(yi - user->ws))/user->dy;
c3pos = PetscMax(c3,0);
c3neg = PetscMin(c3,0);
c5 = (PetscPowScalar((user->lambda*user->ws)/(2*user->H),2)*user->q*(1.0-PetscExpScalar(-t/user->lambda)))/(user->dy*user->dy);
col[nc].i = i-1; col[nc].j = j; val[nc++] = c1pos;
col[nc].i = i+1; col[nc].j = j; val[nc++] = -c1neg;
col[nc].i = i; col[nc].j = j-1; val[nc++] = c3pos + c5;
col[nc].i = i; col[nc].j = j+1; val[nc++] = -c3neg + c5;
col[nc].i = i; col[nc].j = j; val[nc++] = -c1pos + c1neg -c3pos + c3neg -2*c5 -a;
ierr = MatSetValuesStencil(Jpre,1,&row,nc,col,val,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = DMDAVecRestoreArrayRead(cda,gc,&coors);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (J != Jpre) {
ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
/*@C
DMDAGetLogicalCoordinate - Returns a the i,j,k logical coordinate for the closest mesh point to a x,y,z point in the coordinates of the DMDA
Collective on DMDA
Input Parameters:
+ da - the distributed array
- x,y,z - the physical coordinates
Output Parameters:
+ II, JJ, KK - the logical coordinate (-1 on processes that do not contain that point)
- X, Y, Z, - (optional) the coordinates of the located grid point
Level: advanced
Notes:
All processors that share the DMDA must call this with the same coordinate value
.keywords: distributed array, get, processor subset
@*/
PetscErrorCode DMDAGetLogicalCoordinate(DM da,PetscScalar x,PetscScalar y,PetscScalar z,PetscInt *II,PetscInt *JJ,PetscInt *KK,PetscScalar *X,PetscScalar *Y,PetscScalar *Z)
{
PetscErrorCode ierr;
Vec coors;
DM dacoors;
DMDACoor2d **c;
PetscInt i,j,xs,xm,ys,ym;
PetscReal d,D = PETSC_MAX_REAL,Dv;
PetscMPIInt rank,root;
PetscFunctionBegin;
if (da->dim == 1) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Cannot get point from 1d DMDA");
if (da->dim == 3) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Cannot get point from 3d DMDA");
*II = -1;
*JJ = -1;
ierr = DMGetCoordinateDM(da,&dacoors);CHKERRQ(ierr);
ierr = DMDAGetCorners(dacoors,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
ierr = DMGetCoordinates(da,&coors);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(dacoors,coors,&c);CHKERRQ(ierr);
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
d = PetscSqrtReal(PetscRealPart( (c[j][i].x - x)*(c[j][i].x - x) + (c[j][i].y - y)*(c[j][i].y - y) ));
if (d < D) {
D = d;
*II = i;
*JJ = j;
}
}
}
ierr = MPI_Allreduce(&D,&Dv,1,MPIU_REAL,MPI_MIN,PetscObjectComm((PetscObject)da));CHKERRQ(ierr);
if (D != Dv) {
*II = -1;
*JJ = -1;
rank = 0;
} else {
*X = c[*JJ][*II].x;
*Y = c[*JJ][*II].y;
ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)da),&rank);CHKERRQ(ierr);
rank++;
}
ierr = MPI_Allreduce(&rank,&root,1,MPI_INT,MPI_SUM,PetscObjectComm((PetscObject)da));CHKERRQ(ierr);
root--;
ierr = MPI_Bcast(X,1,MPIU_SCALAR,root,PetscObjectComm((PetscObject)da));CHKERRQ(ierr);
ierr = MPI_Bcast(Y,1,MPIU_SCALAR,root,PetscObjectComm((PetscObject)da));CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(dacoors,coors,&c);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FormIFunction(TS ts,PetscReal ptime,Vec X,Vec Xdot,Vec F,void *user)
{
DMDALocalInfo info;
Field **u,**udot,**fu;
PetscErrorCode ierr;
Vec localX;
DM da;
PetscFunctionBeginUser;
ierr = TSGetDM(ts,(DM*)&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(da,localX,&u);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(da,Xdot,&udot);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&fu);CHKERRQ(ierr);
ierr = FormIFunctionLocal(&info,ptime,u,udot,fu,(AppCtx*)user);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,localX,&u);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,Xdot,&udot);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&fu);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localX);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
TrueSolution() computes the true solution for the PDE
Input Parameter:
u - uninitialized solution vector (global)
appctx - user-defined application context
Output Parameter:
u - vector with solution at initial time (global)
*/
PetscErrorCode TrueSolution(TS ts, PetscReal t, Vec u,AppCtx *appctx)
{
PetscScalar *s;
const PetscScalar *xg;
PetscErrorCode ierr;
PetscInt i,xs,xn;
ierr = DMDAVecGetArray(appctx->da,u,&s);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(appctx->da,appctx->SEMop.grid,(void*)&xg);CHKERRQ(ierr);
ierr = DMDAGetCorners(appctx->da,&xs,NULL,NULL,&xn,NULL,NULL);CHKERRQ(ierr);
for (i=xs; i<xs+xn; i++) {
s[i]=2.0*appctx->param.mu*PETSC_PI*PetscSinScalar(PETSC_PI*xg[i])*PetscExpReal(-appctx->param.mu*PETSC_PI*PETSC_PI*t)/(2.0+PetscCosScalar(PETSC_PI*xg[i])*PetscExpReal(-appctx->param.mu*PETSC_PI*PETSC_PI*t));
}
ierr = DMDAVecRestoreArray(appctx->da,u,&s);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(appctx->da,appctx->SEMop.grid,(void*)&xg);CHKERRQ(ierr);
return 0;
}
/*
Matrix free operation of 1d Laplacian and Grad for GLL spectral elements
*/
PetscErrorCode MatMult_Laplacian(Mat A,Vec x,Vec y)
{
AppCtx *appctx;
PetscErrorCode ierr;
PetscReal **temp,vv;
PetscInt i,j,xs,xn;
Vec xlocal,ylocal;
const PetscScalar *xl;
PetscScalar *yl;
PetscBLASInt _One = 1,n;
PetscScalar _DOne = 1;
ierr = MatShellGetContext(A,&appctx);CHKERRQ(ierr);
ierr = DMGetLocalVector(appctx->da,&xlocal);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(appctx->da,x,INSERT_VALUES,xlocal);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(appctx->da,x,INSERT_VALUES,xlocal);CHKERRQ(ierr);
ierr = DMGetLocalVector(appctx->da,&ylocal);CHKERRQ(ierr);
ierr = VecSet(ylocal,0.0);CHKERRQ(ierr);
ierr = PetscGLLElementLaplacianCreate(&appctx->SEMop.gll,&temp);CHKERRQ(ierr);
for (i=0; i<appctx->param.N; i++) {
vv =-appctx->param.mu*2.0/appctx->param.Le;
for (j=0; j<appctx->param.N; j++) temp[i][j]=temp[i][j]*vv;
}
ierr = DMDAVecGetArrayRead(appctx->da,xlocal,(void*)&xl);CHKERRQ(ierr);
ierr = DMDAVecGetArray(appctx->da,ylocal,&yl);CHKERRQ(ierr);
ierr = DMDAGetCorners(appctx->da,&xs,NULL,NULL,&xn,NULL,NULL);CHKERRQ(ierr);
ierr = PetscBLASIntCast(appctx->param.N,&n);CHKERRQ(ierr);
for (j=xs; j<xs+xn; j += appctx->param.N-1) {
PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&_DOne,&temp[0][0],&n,&xl[j],&_One,&_DOne,&yl[j],&_One));
}
ierr = DMDAVecRestoreArrayRead(appctx->da,xlocal,(void*)&xl);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(appctx->da,ylocal,&yl);CHKERRQ(ierr);
ierr = PetscGLLElementLaplacianDestroy(&appctx->SEMop.gll,&temp);CHKERRQ(ierr);
ierr = VecSet(y,0.0);CHKERRQ(ierr);
ierr = DMLocalToGlobalBegin(appctx->da,ylocal,ADD_VALUES,y);CHKERRQ(ierr);
ierr = DMLocalToGlobalEnd(appctx->da,ylocal,ADD_VALUES,y);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(appctx->da,&xlocal);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(appctx->da,&ylocal);CHKERRQ(ierr);
ierr = VecPointwiseDivide(y,y,appctx->SEMop.mass);CHKERRQ(ierr);
return 0;
}
/*
FormJacobian - Evaluates Jacobian matrix.
Input Parameters:
. snes - the SNES context
. x - input vector
. dummy - optional user-defined context (not used here)
Output Parameters:
. jac - Jacobian matrix
. B - optionally different preconditioning matrix
. flag - flag indicating matrix structure
*/
PetscErrorCode FormJacobian(SNES snes,Vec x,Mat jac,Mat B,void *ctx)
{
PetscScalar *xx,A[3];
PetscErrorCode ierr;
PetscInt i,M,xs,xm;
DM da = (DM) ctx;
MatStencil row,cols[3];
PetscReal h;
PetscFunctionBeginUser;
/*
Get pointer to vector data
*/
ierr = DMDAVecGetArrayRead(da,x,&xx);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
/*
Get range of locally owned matrix
*/
ierr = DMDAGetInfo(da,NULL,&M,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = MatZeroEntries(jac);CHKERRQ(ierr);
h = 1.0/M;
/* because of periodic boundary conditions we can simply loop over all local nodes and access to the left and right */
for (i=xs; i<xs+xm; i++) {
row.i = i;
cols[0].i = i - 1;
cols[1].i = i;
cols[2].i = i + 1;
A[0] = A[2] = 1.0/(h*h); A[1] = -2.0/(h*h);
ierr = MatSetValuesStencil(jac,1,&row,3,cols,A,ADD_VALUES);CHKERRQ(ierr);
}
ierr = DMDAVecRestoreArrayRead(da,x,&xx);CHKERRQ(ierr);
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
IFunction - Evaluates nonlinear function, F(U).
Input Parameters:
. ts - the TS context
. U - input vector
. ptr - optional user-defined context, as set by SNESSetFunction()
Output Parameter:
. F - function vector
*/
PetscErrorCode IFunction(TS ts,PetscReal ftime,Vec U,Vec Udot,Vec F,void *ptr)
{
AppCtx *appctx = (AppCtx*)ptr;
DM da;
PetscErrorCode ierr;
PetscInt i,Mx,xs,xm;
PetscReal hx,sx;
PetscScalar rho,c,rhoxx,cxx,cx,rhox,kcxrhox;
Field *u,*f,*udot;
Vec localU;
PetscFunctionBegin;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localU);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
/*
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(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
/*
Get pointers to vector data
*/
ierr = DMDAVecGetArrayRead(da,localU,&u);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(da,Udot,&udot);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/*
Get local grid boundaries
*/
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
if (!xs) {
f[0].rho = udot[0].rho; /* u[0].rho - 0.0; */
f[0].c = udot[0].c; /* u[0].c - 1.0; */
xs++;
xm--;
}
if (xs+xm == Mx) {
f[Mx-1].rho = udot[Mx-1].rho; /* u[Mx-1].rho - 1.0; */
f[Mx-1].c = udot[Mx-1].c; /* u[Mx-1].c - 0.0; */
xm--;
}
/*
Compute function over the locally owned part of the grid
*/
for (i=xs; i<xs+xm; i++) {
rho = u[i].rho;
rhoxx = (-2.0*rho + u[i-1].rho + u[i+1].rho)*sx;
c = u[i].c;
cxx = (-2.0*c + u[i-1].c + u[i+1].c)*sx;
if (!appctx->upwind) {
rhox = .5*(u[i+1].rho - u[i-1].rho)/hx;
cx = .5*(u[i+1].c - u[i-1].c)/hx;
kcxrhox = appctx->kappa*(cxx*rho + cx*rhox);
} else {
kcxrhox = appctx->kappa*((u[i+1].c - u[i].c)*u[i+1].rho - (u[i].c - u[i-1].c)*u[i].rho)*sx;
}
f[i].rho = udot[i].rho - appctx->epsilon*rhoxx + kcxrhox - appctx->mu*PetscAbsScalar(rho)*(1.0 - rho)*PetscMax(0,PetscRealPart(c - appctx->cstar)) + appctx->beta*rho;
f[i].c = udot[i].c - appctx->delta*cxx + appctx->lambda*c + appctx->alpha*rho*c/(appctx->gamma + c);
}
/*
Restore vectors
*/
ierr = DMDAVecRestoreArrayRead(da,localU,&u);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,Udot,&udot);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localU);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode NonlinearGS(SNES snes, Vec X, Vec B, void *ctx)
{
DMDALocalInfo info;
Field **x,**b;
PetscErrorCode ierr;
Vec localX, localB;
DM da;
PetscInt xints,xinte,yints,yinte,i,j,k,l;
PetscInt max_its,tot_its;
PetscInt sweeps;
PetscReal rtol,atol,stol;
PetscReal hx,hy,dhx,dhy,hxdhy,hydhx;
PetscReal grashof,prandtl,lid;
PetscScalar u,uxx,uyy,vx,vy,avx,avy,vxp,vxm,vyp,vym;
PetscScalar fu, fv, fomega, ftemp;
PetscScalar dfudu;
PetscScalar dfvdv;
PetscScalar dfodu, dfodv, dfodo;
PetscScalar dftdu, dftdv, dftdt;
PetscScalar yu=0, yv=0, yo=0, yt=0;
PetscScalar bjiu, bjiv, bjiomega, bjitemp;
PetscBool ptconverged;
PetscReal pfnorm,pfnorm0,pynorm,pxnorm;
AppCtx *user = (AppCtx*)ctx;
PetscFunctionBeginUser;
grashof = user->grashof;
prandtl = user->prandtl;
lid = user->lidvelocity;
tot_its = 0;
ierr = SNESNGSGetTolerances(snes,&rtol,&atol,&stol,&max_its);CHKERRQ(ierr);
ierr = SNESNGSGetSweeps(snes,&sweeps);CHKERRQ(ierr);
ierr = SNESGetDM(snes,(DM*)&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localX);CHKERRQ(ierr);
if (B) {
ierr = DMGetLocalVector(da,&localB);CHKERRQ(ierr);
}
/*
Scatter ghost points to local vector, using the 2-step process
DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
*/
ierr = DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
if (B) {
ierr = DMGlobalToLocalBegin(da,B,INSERT_VALUES,localB);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,B,INSERT_VALUES,localB);CHKERRQ(ierr);
}
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,localX,&x);CHKERRQ(ierr);
if (B) {
ierr = DMDAVecGetArrayRead(da,localB,&b);CHKERRQ(ierr);
}
/* looks like a combination of the formfunction / formjacobian routines */
dhx = (PetscReal)(info.mx-1);dhy = (PetscReal)(info.my-1);
hx = 1.0/dhx; hy = 1.0/dhy;
hxdhy = hx*dhy; hydhx = hy*dhx;
xints = info.xs; xinte = info.xs+info.xm; yints = info.ys; yinte = info.ys+info.ym;
/* Set the boundary conditions on the momentum equations */
/* Test whether we are on the bottom edge of the global array */
if (yints == 0) {
j = 0;
yints = yints + 1;
/* bottom edge */
for (i=info.xs; i<info.xs+info.xm; i++) {
if (B) {
bjiu = b[j][i].u;
bjiv = b[j][i].v;
} else {
bjiu = 0.0;
bjiv = 0.0;
}
x[j][i].u = 0.0 + bjiu;
x[j][i].v = 0.0 + bjiv;
}
}
/* Test whether we are on the top edge of the global array */
if (yinte == info.my) {
j = info.my - 1;
yinte = yinte - 1;
/* top edge */
for (i=info.xs; i<info.xs+info.xm; i++) {
if (B) {
bjiu = b[j][i].u;
bjiv = b[j][i].v;
} else {
bjiu = 0.0;
bjiv = 0.0;
}
x[j][i].u = lid + bjiu;
x[j][i].v = bjiv;
}
}
/* Test whether we are on the left edge of the global array */
if (xints == 0) {
i = 0;
xints = xints + 1;
/* left edge */
for (j=info.ys; j<info.ys+info.ym; j++) {
if (B) {
bjiu = b[j][i].u;
bjiv = b[j][i].v;
} else {
bjiu = 0.0;
bjiv = 0.0;
}
x[j][i].u = 0.0 + bjiu;
x[j][i].v = 0.0 + bjiv;
}
}
/* Test whether we are on the right edge of the global array */
if (xinte == info.mx) {
i = info.mx - 1;
xinte = xinte - 1;
/* right edge */
for (j=info.ys; j<info.ys+info.ym; j++) {
if (B) {
bjiu = b[j][i].u;
bjiv = b[j][i].v;
} else {
bjiu = 0.0;
bjiv = 0.0;
}
x[j][i].u = 0.0 + bjiu;
x[j][i].v = 0.0 + bjiv;
}
}
for (k=0; k < sweeps; k++) {
for (j=info.ys; j<info.ys + info.ym; j++) {
for (i=info.xs; i<info.xs + info.xm; i++) {
ptconverged = PETSC_FALSE;
pfnorm0 = 0.0;
pfnorm = 0.0;
fu = 0.0;
fv = 0.0;
fomega = 0.0;
ftemp = 0.0;
for (l = 0; l < max_its && !ptconverged; l++) {
if (B) {
bjiu = b[j][i].u;
bjiv = b[j][i].v;
bjiomega = b[j][i].omega;
bjitemp = b[j][i].temp;
} else {
bjiu = 0.0;
bjiv = 0.0;
bjiomega = 0.0;
bjitemp = 0.0;
}
if (i != 0 && i != info.mx - 1 && j != 0 && j != info.my-1) {
/* U velocity */
u = x[j][i].u;
uxx = (2.0*u - x[j][i-1].u - x[j][i+1].u)*hydhx;
uyy = (2.0*u - x[j-1][i].u - x[j+1][i].u)*hxdhy;
fu = uxx + uyy - .5*(x[j+1][i].omega-x[j-1][i].omega)*hx - bjiu;
dfudu = 2.0*(hydhx + hxdhy);
/* V velocity */
u = x[j][i].v;
uxx = (2.0*u - x[j][i-1].v - x[j][i+1].v)*hydhx;
uyy = (2.0*u - x[j-1][i].v - x[j+1][i].v)*hxdhy;
fv = uxx + uyy + .5*(x[j][i+1].omega-x[j][i-1].omega)*hy - bjiv;
dfvdv = 2.0*(hydhx + hxdhy);
/*
convective coefficients for upwinding
*/
vx = x[j][i].u; avx = PetscAbsScalar(vx);
vxp = .5*(vx+avx); vxm = .5*(vx-avx);
vy = x[j][i].v; avy = PetscAbsScalar(vy);
vyp = .5*(vy+avy); vym = .5*(vy-avy);
/* Omega */
u = x[j][i].omega;
uxx = (2.0*u - x[j][i-1].omega - x[j][i+1].omega)*hydhx;
uyy = (2.0*u - x[j-1][i].omega - x[j+1][i].omega)*hxdhy;
fomega = uxx + uyy + (vxp*(u - x[j][i-1].omega) + vxm*(x[j][i+1].omega - u))*hy +
(vyp*(u - x[j-1][i].omega) + vym*(x[j+1][i].omega - u))*hx -
.5*grashof*(x[j][i+1].temp - x[j][i-1].temp)*hy - bjiomega;
/* convective coefficient derivatives */
dfodo = 2.0*(hydhx + hxdhy) + ((vxp - vxm)*hy + (vyp - vym)*hx);
if (PetscRealPart(vx) > 0.0) dfodu = (u - x[j][i-1].omega)*hy;
else dfodu = (x[j][i+1].omega - u)*hy;
if (PetscRealPart(vy) > 0.0) dfodv = (u - x[j-1][i].omega)*hx;
else dfodv = (x[j+1][i].omega - u)*hx;
/* Temperature */
u = x[j][i].temp;
uxx = (2.0*u - x[j][i-1].temp - x[j][i+1].temp)*hydhx;
uyy = (2.0*u - x[j-1][i].temp - x[j+1][i].temp)*hxdhy;
ftemp = uxx + uyy + prandtl*((vxp*(u - x[j][i-1].temp) + vxm*(x[j][i+1].temp - u))*hy +
(vyp*(u - x[j-1][i].temp) + vym*(x[j+1][i].temp - u))*hx) - bjitemp;
dftdt = 2.0*(hydhx + hxdhy) + prandtl*((vxp - vxm)*hy + (vyp - vym)*hx);
if (PetscRealPart(vx) > 0.0) dftdu = prandtl*(u - x[j][i-1].temp)*hy;
else dftdu = prandtl*(x[j][i+1].temp - u)*hy;
if (PetscRealPart(vy) > 0.0) dftdv = prandtl*(u - x[j-1][i].temp)*hx;
else dftdv = prandtl*(x[j+1][i].temp - u)*hx;
/* invert the system:
[ dfu / du 0 0 0 ][yu] = [fu]
[ 0 dfv / dv 0 0 ][yv] [fv]
[ dfo / du dfo / dv dfo / do 0 ][yo] [fo]
[ dft / du dft / dv 0 dft / dt ][yt] [ft]
by simple back-substitution
*/
yu = fu / dfudu;
yv = fv / dfvdv;
yo = fomega / dfodo;
yt = ftemp / dftdt;
yo = (fomega - (dfodu*yu + dfodv*yv)) / dfodo;
yt = (ftemp - (dftdu*yu + dftdv*yv)) / dftdt;
x[j][i].u = x[j][i].u - yu;
x[j][i].v = x[j][i].v - yv;
x[j][i].temp = x[j][i].temp - yt;
x[j][i].omega = x[j][i].omega - yo;
}
if (i == 0) {
fomega = x[j][i].omega - (x[j][i+1].v - x[j][i].v)*dhx - bjiomega;
ftemp = x[j][i].temp - bjitemp;
yo = fomega;
yt = ftemp;
x[j][i].omega = x[j][i].omega - fomega;
x[j][i].temp = x[j][i].temp - ftemp;
}
if (i == info.mx - 1) {
fomega = x[j][i].omega - (x[j][i].v - x[j][i-1].v)*dhx - bjiomega;
ftemp = x[j][i].temp - (PetscReal)(grashof>0) - bjitemp;
yo = fomega;
yt = ftemp;
x[j][i].omega = x[j][i].omega - fomega;
x[j][i].temp = x[j][i].temp - ftemp;
}
if (j == 0) {
fomega = x[j][i].omega + (x[j+1][i].u - x[j][i].u)*dhy - bjiomega;
ftemp = x[j][i].temp-x[j+1][i].temp - bjitemp;
yo = fomega;
yt = ftemp;
x[j][i].omega = x[j][i].omega - fomega;
x[j][i].temp = x[j][i].temp - ftemp;
}
if (j == info.my - 1) {
fomega = x[j][i].omega + (x[j][i].u - x[j-1][i].u)*dhy - bjiomega;
ftemp = x[j][i].temp-x[j-1][i].temp - bjitemp;
yo = fomega;
yt = ftemp;
x[j][i].omega = x[j][i].omega - fomega;
x[j][i].temp = x[j][i].temp - ftemp;
}
tot_its++;
pfnorm = PetscRealPart(fu*fu + fv*fv + fomega*fomega + ftemp*ftemp);
pfnorm = PetscSqrtReal(pfnorm);
pynorm = PetscRealPart(yu*yu + yv*yv + yo*yo + yt*yt);
pfnorm = PetscSqrtReal(pynorm);
pxnorm = PetscRealPart(x[j][i].u*x[j][i].u + x[j][i].v*x[j][i].v + x[j][i].omega*x[j][i].omega + x[j][i].temp*x[j][i].temp);
pxnorm = PetscSqrtReal(pxnorm);
if (l == 0) pfnorm0 = pfnorm;
if (rtol*pfnorm0 > pfnorm ||
atol > pfnorm ||
pxnorm*stol > pynorm) ptconverged = PETSC_TRUE;
}
}
}
}
ierr = DMDAVecRestoreArray(da,localX,&x);CHKERRQ(ierr);
if (B) {
ierr = DMDAVecRestoreArrayRead(da,localB,&b);CHKERRQ(ierr);
}
ierr = DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X);CHKERRQ(ierr);
ierr = DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X);CHKERRQ(ierr);
ierr = PetscLogFlops(tot_its*(84.0 + 41.0 + 26.0));CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localX);CHKERRQ(ierr);
if (B) {
ierr = DMRestoreLocalVector(da,&localB);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat BB,void *ctx)
{
AppCtx *appctx = (AppCtx*)ctx; /* user-defined application context */
DM da;
PetscErrorCode ierr;
PetscInt i,j,Mx,My,xs,ys,xm,ym;
PetscReal hx,hy,sx,sy;
PetscScalar uc,vc;
Field **u;
Vec localU;
MatStencil stencil[6],rowstencil;
PetscScalar entries[6];
PetscFunctionBegin;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localU);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
hx = 2.50/(PetscReal)(Mx); sx = 1.0/(hx*hx);
hy = 2.50/(PetscReal)(My); sy = 1.0/(hy*hy);
/*
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(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
/*
Get pointers to vector data
*/
ierr = DMDAVecGetArrayRead(da,localU,&u);CHKERRQ(ierr);
/*
Get local grid boundaries
*/
ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
stencil[0].k = 0;
stencil[1].k = 0;
stencil[2].k = 0;
stencil[3].k = 0;
stencil[4].k = 0;
stencil[5].k = 0;
rowstencil.k = 0;
/*
Compute function over the locally owned part of the grid
*/
for (j=ys; j<ys+ym; j++) {
stencil[0].j = j-1;
stencil[1].j = j+1;
stencil[2].j = j;
stencil[3].j = j;
stencil[4].j = j;
stencil[5].j = j;
rowstencil.k = 0; rowstencil.j = j;
for (i=xs; i<xs+xm; i++) {
uc = u[j][i].u;
vc = u[j][i].v;
/* uxx = (-2.0*uc + u[j][i-1].u + u[j][i+1].u)*sx;
uyy = (-2.0*uc + u[j-1][i].u + u[j+1][i].u)*sy;
vxx = (-2.0*vc + u[j][i-1].v + u[j][i+1].v)*sx;
vyy = (-2.0*vc + u[j-1][i].v + u[j+1][i].v)*sy;
f[j][i].u = appctx->D1*(uxx + uyy) - uc*vc*vc + appctx->gamma*(1.0 - uc);*/
stencil[0].i = i; stencil[0].c = 0; entries[0] = appctx->D1*sy;
stencil[1].i = i; stencil[1].c = 0; entries[1] = appctx->D1*sy;
stencil[2].i = i-1; stencil[2].c = 0; entries[2] = appctx->D1*sx;
stencil[3].i = i+1; stencil[3].c = 0; entries[3] = appctx->D1*sx;
stencil[4].i = i; stencil[4].c = 0; entries[4] = -2.0*appctx->D1*(sx + sy) - vc*vc - appctx->gamma;
stencil[5].i = i; stencil[5].c = 1; entries[5] = -2.0*uc*vc;
rowstencil.i = i; rowstencil.c = 0;
ierr = MatSetValuesStencil(A,1,&rowstencil,6,stencil,entries,INSERT_VALUES);CHKERRQ(ierr);
stencil[0].c = 1; entries[0] = appctx->D2*sy;
stencil[1].c = 1; entries[1] = appctx->D2*sy;
stencil[2].c = 1; entries[2] = appctx->D2*sx;
stencil[3].c = 1; entries[3] = appctx->D2*sx;
stencil[4].c = 1; entries[4] = -2.0*appctx->D2*(sx + sy) + 2.0*uc*vc - appctx->gamma - appctx->kappa;
stencil[5].c = 0; entries[5] = vc*vc;
rowstencil.c = 1;
ierr = MatSetValuesStencil(A,1,&rowstencil,6,stencil,entries,INSERT_VALUES);CHKERRQ(ierr);
/* f[j][i].v = appctx->D2*(vxx + vyy) + uc*vc*vc - (appctx->gamma + appctx->kappa)*vc; */
}
}
/*
Restore vectors
*/
ierr = PetscLogFlops(19*xm*ym);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,localU,&u);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localU);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
RHSFunction - Evaluates nonlinear function, F(x).
Input Parameters:
. ts - the TS context
. X - input vector
. ptr - optional user-defined context, as set by TSSetRHSFunction()
Output Parameter:
. F - function vector
*/
PetscErrorCode RHSFunction(TS ts,PetscReal ftime,Vec U,Vec F,void *ptr)
{
AppCtx *appctx = (AppCtx*)ptr;
DM da;
PetscErrorCode ierr;
PetscInt i,j,Mx,My,xs,ys,xm,ym;
PetscReal hx,hy,sx,sy;
PetscScalar uc,uxx,uyy,vc,vxx,vyy;
Field **u,**f;
Vec localU;
PetscFunctionBegin;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localU);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
hx = 2.50/(PetscReal)(Mx); sx = 1.0/(hx*hx);
hy = 2.50/(PetscReal)(My); sy = 1.0/(hy*hy);
/*
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(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
/*
Get pointers to vector data
*/
ierr = DMDAVecGetArrayRead(da,localU,&u);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/*
Get local grid boundaries
*/
ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
/*
Compute function over the locally owned part of the grid
*/
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
uc = u[j][i].u;
uxx = (-2.0*uc + u[j][i-1].u + u[j][i+1].u)*sx;
uyy = (-2.0*uc + u[j-1][i].u + u[j+1][i].u)*sy;
vc = u[j][i].v;
vxx = (-2.0*vc + u[j][i-1].v + u[j][i+1].v)*sx;
vyy = (-2.0*vc + u[j-1][i].v + u[j+1][i].v)*sy;
f[j][i].u = appctx->D1*(uxx + uyy) - uc*vc*vc + appctx->gamma*(1.0 - uc);
f[j][i].v = appctx->D2*(vxx + vyy) + uc*vc*vc - (appctx->gamma + appctx->kappa)*vc;
}
}
ierr = PetscLogFlops(16*xm*ym);CHKERRQ(ierr);
/*
Restore vectors
*/
ierr = DMDAVecRestoreArrayRead(da,localU,&u);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localU);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
FormJacobian - Evaluates Jacobian matrix.
Input Parameters:
. snes - the SNES context
. x - input vector
. dummy - optional user-defined context (not used here)
Output Parameters:
. jac - Jacobian matrix
. B - optionally different preconditioning matrix
. flag - flag indicating matrix structure
*/
PetscErrorCode FormJacobian(SNES snes,Vec x,Mat jac,Mat B,void *ctx)
{
ApplicationCtx *user = (ApplicationCtx*) ctx;
PetscScalar *xx,d,A[3];
PetscErrorCode ierr;
PetscInt i,j[3],M,xs,xm;
DM da = user->da;
PetscFunctionBeginUser;
/*
Get pointer to vector data
*/
ierr = DMDAVecGetArrayRead(da,x,&xx);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
/*
Get range of locally owned matrix
*/
ierr = DMDAGetInfo(da,NULL,&M,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
/*
Determine starting and ending local indices for interior grid points.
Set Jacobian entries for boundary points.
*/
if (xs == 0) { /* left boundary */
i = 0; A[0] = 1.0;
ierr = MatSetValues(jac,1,&i,1,&i,A,INSERT_VALUES);CHKERRQ(ierr);
xs++;xm--;
}
if (xs+xm == M) { /* right boundary */
i = M-1;
A[0] = 1.0;
ierr = MatSetValues(jac,1,&i,1,&i,A,INSERT_VALUES);CHKERRQ(ierr);
xm--;
}
/*
Interior grid points
- Note that in this case we set all elements for a particular
row at once.
*/
d = 1.0/(user->h*user->h);
for (i=xs; i<xs+xm; i++) {
j[0] = i - 1; j[1] = i; j[2] = i + 1;
A[0] = A[2] = d; A[1] = -2.0*d + 2.0*xx[i];
ierr = MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);CHKERRQ(ierr);
}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd().
By placing code between these two statements, computations can be
done while messages are in transition.
Also, restore vector.
*/
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,x,&xx);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
//------------------------------------------------------------------------------
int main(int argc, char *argv[])
{
PetscErrorCode ierr;
DM da;
Vec ug, ul;
PetscInt i, ibeg, nloc, nx=200;
const PetscInt sw = 3, ndof = 1; // stencil width
PetscMPIInt rank, size;
double cfl = 0.4;
ierr = PetscInitialize(&argc, &argv, (char*)0, help); CHKERRQ(ierr);
MPI_Comm_rank(PETSC_COMM_WORLD, &rank);
MPI_Comm_size(PETSC_COMM_WORLD, &size);
ierr = DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, nx, ndof, sw, NULL, &da); CHKERRQ(ierr);
ierr = DMSetFromOptions(da); CHKERRQ(ierr);
ierr = DMSetUp(da); CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &ug); CHKERRQ(ierr);
ierr = DMDAGetCorners(da, &ibeg, 0, 0, &nloc, 0, 0); CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&nx,0,0,0,0,0,0,0,0,0,0,0); CHKERRQ(ierr);
PetscReal dx = (xmax - xmin) / (PetscReal)(nx);
PetscPrintf(PETSC_COMM_WORLD,"nx = %d, dx = %e\n", nx, dx);
for(i=ibeg; i<ibeg+nloc; ++i)
{
PetscReal x = xmin + i*dx;
PetscReal v = initcond(x);
ierr = VecSetValues(ug,1,&i,&v,INSERT_VALUES); CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(ug); CHKERRQ(ierr);
ierr = VecAssemblyEnd(ug); CHKERRQ(ierr);
savesol(nx, dx, ug);
// Get local view
ierr = DMGetLocalVector(da, &ul); CHKERRQ(ierr);
PetscInt il, nl;
ierr = DMDAGetGhostCorners(da,&il,0,0,&nl,0,0); CHKERRQ(ierr);
double res[nloc], uold[nloc];
double dt = cfl * dx;
double lam= dt/dx;
double tfinal = 2.0, t = 0.0;
while(t < tfinal)
{
if(t+dt > tfinal)
{
dt = tfinal - t;
lam = dt/dx;
}
for(int rk=0; rk<3; ++rk)
{
ierr = DMGlobalToLocalBegin(da, ug, INSERT_VALUES, ul); CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da, ug, INSERT_VALUES, ul); CHKERRQ(ierr);
PetscScalar *u;
ierr = DMDAVecGetArrayRead(da, ul, &u); CHKERRQ(ierr);
PetscScalar *unew;
ierr = DMDAVecGetArray(da, ug, &unew); CHKERRQ(ierr);
if(rk==0)
for(i=ibeg; i<ibeg+nloc; ++i) uold[i-ibeg] = u[i];
for(i=0; i<nloc; ++i)
res[i] = 0.0;
// Loop over faces and compute flux
for(i=0; i<nloc+1; ++i)
{
// face between j-1, j
int j = il+sw+i;
int jm1 = j-1;
int jm2 = j-2;
int jm3 = j-3;
int jp1 = j+1;
double uleft = weno5(u[jm3],u[jm2],u[jm1],u[j],u[jp1]);
double flux = uleft;
if(i==0)
{
res[i] -= flux;
}
else if(i==nloc)
{
res[i-1] += flux;
}
else
{
res[i] -= flux;
res[i-1] += flux;
}
}
// Update solution
for(i=ibeg; i<ibeg+nloc; ++i)
unew[i] = ark[rk]*uold[i-ibeg] + (1-ark[rk])*(u[i] - lam * res[i-ibeg]);
ierr = DMDAVecRestoreArrayRead(da, ul, &u); CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da, ug, &unew); CHKERRQ(ierr);
}
t += dt;
PetscPrintf(PETSC_COMM_WORLD,"t = %f\n", t);
}
savesol(nx, dx, ug);
// Destroy everything before finishing
ierr = DMDestroy(&da); CHKERRQ(ierr);
ierr = VecDestroy(&ug); CHKERRQ(ierr);
ierr = PetscFinalize(); CHKERRQ(ierr);
}
/*
This routine is not parallel
*/
PetscErrorCode MyMonitor(TS ts,PetscInt step,PetscReal time,Vec U,void *ptr)
{
UserCtx *ctx = (UserCtx*)ptr;
PetscDrawLG lg;
PetscErrorCode ierr;
PetscScalar *u;
PetscInt Mx,i,xs,xm,cnt;
PetscReal x,y,hx,pause,sx,len,max,xx[2],yy[2];
PetscDraw draw;
Vec localU;
DM da;
int colors[] = {PETSC_DRAW_YELLOW,PETSC_DRAW_RED,PETSC_DRAW_BLUE};
const char*const legend[] = {"-kappa (\\grad u,\\grad u)","(1 - u^2)^2"};
PetscDrawAxis axis;
PetscDrawViewPorts *ports;
PetscReal vbounds[] = {-1.1,1.1};
PetscFunctionBegin;
ierr = PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1,vbounds);CHKERRQ(ierr);
ierr = PetscViewerDrawResize(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1200,800);CHKERRQ(ierr);
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localU);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
hx = 1.0/(PetscReal)Mx; sx = 1.0/(hx*hx);
ierr = DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(da,localU,&u);CHKERRQ(ierr);
ierr = PetscViewerDrawGetDrawLG(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1,&lg);CHKERRQ(ierr);
ierr = PetscDrawLGGetDraw(lg,&draw);CHKERRQ(ierr);
ierr = PetscDrawCheckResizedWindow(draw);CHKERRQ(ierr);
if (!ctx->ports) {
ierr = PetscDrawViewPortsCreateRect(draw,1,3,&ctx->ports);CHKERRQ(ierr);
}
ports = ctx->ports;
ierr = PetscDrawLGGetAxis(lg,&axis);CHKERRQ(ierr);
ierr = PetscDrawLGReset(lg);CHKERRQ(ierr);
xx[0] = 0.0; xx[1] = 1.0; cnt = 2;
ierr = PetscOptionsGetRealArray(NULL,NULL,"-zoom",xx,&cnt,NULL);CHKERRQ(ierr);
xs = xx[0]/hx; xm = (xx[1] - xx[0])/hx;
/*
Plot the energies
*/
ierr = PetscDrawLGSetDimension(lg,1 + (ctx->allencahn ? 1 : 0));CHKERRQ(ierr);
ierr = PetscDrawLGSetColors(lg,colors+1);CHKERRQ(ierr);
ierr = PetscDrawViewPortsSet(ports,2);CHKERRQ(ierr);
x = hx*xs;
for (i=xs; i<xs+xm; i++) {
xx[0] = xx[1] = x;
yy[0] = PetscRealPart(.25*ctx->kappa*(u[i-1] - u[i+1])*(u[i-1] - u[i+1])*sx);
if (ctx->allencahn) yy[1] = .25*PetscRealPart((1. - u[i]*u[i])*(1. - u[i]*u[i]));
ierr = PetscDrawLGAddPoint(lg,xx,yy);CHKERRQ(ierr);
x += hx;
}
ierr = PetscDrawGetPause(draw,&pause);CHKERRQ(ierr);
ierr = PetscDrawSetPause(draw,0.0);CHKERRQ(ierr);
ierr = PetscDrawAxisSetLabels(axis,"Energy","","");CHKERRQ(ierr);
ierr = PetscDrawLGSetLegend(lg,legend);CHKERRQ(ierr);
ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);
/*
Plot the forces
*/
ierr = PetscDrawViewPortsSet(ports,1);CHKERRQ(ierr);
ierr = PetscDrawLGReset(lg);CHKERRQ(ierr);
x = xs*hx;;
max = 0.;
for (i=xs; i<xs+xm; i++) {
xx[0] = xx[1] = x;
yy[0] = PetscRealPart(ctx->kappa*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
max = PetscMax(max,PetscAbs(yy[0]));
if (ctx->allencahn) {
yy[1] = PetscRealPart(u[i] - u[i]*u[i]*u[i]);
max = PetscMax(max,PetscAbs(yy[1]));
}
ierr = PetscDrawLGAddPoint(lg,xx,yy);CHKERRQ(ierr);
x += hx;
}
ierr = PetscDrawAxisSetLabels(axis,"Right hand side","","");CHKERRQ(ierr);
ierr = PetscDrawLGSetLegend(lg,NULL);CHKERRQ(ierr);
ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);
/*
Plot the solution
*/
ierr = PetscDrawLGSetDimension(lg,1);CHKERRQ(ierr);
ierr = PetscDrawViewPortsSet(ports,0);CHKERRQ(ierr);
ierr = PetscDrawLGReset(lg);CHKERRQ(ierr);
x = hx*xs;
ierr = PetscDrawLGSetLimits(lg,x,x+(xm-1)*hx,-1.1,1.1);CHKERRQ(ierr);
ierr = PetscDrawLGSetColors(lg,colors);CHKERRQ(ierr);
for (i=xs; i<xs+xm; i++) {
xx[0] = x;
yy[0] = PetscRealPart(u[i]);
ierr = PetscDrawLGAddPoint(lg,xx,yy);CHKERRQ(ierr);
x += hx;
}
ierr = PetscDrawAxisSetLabels(axis,"Solution","","");CHKERRQ(ierr);
ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);
/*
Print the forces as arrows on the solution
*/
x = hx*xs;
cnt = xm/60;
cnt = (!cnt) ? 1 : cnt;
for (i=xs; i<xs+xm; i += cnt) {
y = PetscRealPart(u[i]);
len = .5*PetscRealPart(ctx->kappa*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max;
ierr = PetscDrawArrow(draw,x,y,x,y+len,PETSC_DRAW_RED);CHKERRQ(ierr);
if (ctx->allencahn) {
len = .5*PetscRealPart(u[i] - u[i]*u[i]*u[i])/max;
ierr = PetscDrawArrow(draw,x,y,x,y+len,PETSC_DRAW_BLUE);CHKERRQ(ierr);
}
x += cnt*hx;
}
ierr = DMDAVecRestoreArrayRead(da,localU,&x);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localU);CHKERRQ(ierr);
ierr = PetscDrawStringSetSize(draw,.2,.2);CHKERRQ(ierr);
ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
ierr = PetscDrawSetPause(draw,pause);CHKERRQ(ierr);
ierr = PetscDrawPause(draw);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
