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); }