PetscErrorCode FormPsiAndExactSoln(DM da) {
ObsCtx *user;
PetscErrorCode ierr;
DMDALocalInfo info;
PetscInt i,j;
DM coordDA;
Vec coordinates;
DMDACoor2d **coords;
PetscReal **psi, **uexact, r;
const PetscReal afree = 0.69797, A = 0.68026, B = 0.47152;
PetscFunctionBeginUser;
ierr = DMGetApplicationContext(da,&user);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info); CHKERRQ(ierr);
ierr = DMGetCoordinateDM(da, &coordDA);CHKERRQ(ierr);
ierr = DMGetCoordinates(da, &coordinates);CHKERRQ(ierr);
ierr = DMDAVecGetArray(coordDA, coordinates, &coords);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da, user->psi, &psi);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da, user->uexact, &uexact);CHKERRQ(ierr);
for (j=info.ys; j<info.ys+info.ym; j++) {
for (i=info.xs; i<info.xs+info.xm; i++) {
r = PetscSqrtReal(PetscPowScalarInt(coords[j][i].x,2) + PetscPowScalarInt(coords[j][i].y,2));
if (r <= 1.0) psi[j][i] = PetscSqrtReal(1.0 - r * r);
else psi[j][i] = -1.0;
if (r <= afree) uexact[j][i] = psi[j][i]; /* on the obstacle */
else uexact[j][i] = - A * PetscLogReal(r) + B; /* solves the laplace eqn */
}
}
ierr = DMDAVecRestoreArray(da, user->psi, &psi);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da, user->uexact, &uexact);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(coordDA, coordinates, &coords);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,Userctx *user)
{
PetscErrorCode ierr;
PetscScalar *r;
const PetscScalar *u;
PetscInt idx;
Vec Xgen,Xnet;
PetscScalar *xgen;
PetscInt i;
PetscFunctionBegin;
ierr = DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);CHKERRQ(ierr);
ierr = DMCompositeScatter(user->dmpgrid,U,Xgen,Xnet);CHKERRQ(ierr);
ierr = VecGetArray(Xgen,&xgen);CHKERRQ(ierr);
ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
ierr = VecGetArray(R,&r);CHKERRQ(ierr);
r[0] = 0.;
idx = 0;
for (i=0;i<ngen;i++) {
r[0] += PetscPowScalarInt(PetscMax(0.,PetscMax(xgen[idx+3]/(2.*PETSC_PI)-user->freq_u,user->freq_l-xgen[idx+3]/(2.*PETSC_PI))),user->pow);
idx += 9;
}
ierr = VecRestoreArray(R,&r);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
ierr = DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode calcfluxa(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar emma, PetscScalar *flux) /* this function is not currently called upon */
{
PetscScalar emm = 0.001;
PetscFunctionBeginUser;
*flux = SIG*(-emm*(PetscPowScalarInt(airtemp,4))); /* calculates flux usinge Stefan-Boltzmann relation */
PetscFunctionReturn(0);
}
static PetscErrorCode DRDYFunction(TS ts,PetscReal t,Vec U,Vec *drdy,AppCtx *ctx)
{
PetscErrorCode ierr;
PetscScalar *ry;
const PetscScalar *u;
PetscFunctionBegin;
ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
ierr = VecGetArray(drdy[0],&ry);CHKERRQ(ierr);
ry[0] = ctx->c*ctx->beta*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta-1);CHKERRQ(ierr);
ierr = VecRestoreArray(drdy[0],&ry);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,AppCtx *ctx)
{
PetscErrorCode ierr;
PetscScalar *r;
const PetscScalar *u;
PetscFunctionBegin;
ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
ierr = VecGetArray(R,&r);CHKERRQ(ierr);
r[0] = ctx->c*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta);CHKERRQ(ierr);
ierr = VecRestoreArray(R,&r);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode DRDUJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDU,Mat B,AppCtx *ctx)
{
PetscErrorCode ierr;
PetscScalar ru[1];
const PetscScalar *u;
PetscInt row[] = {0},col[] = {0};
PetscFunctionBegin;
ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
ru[0] = ctx->c*ctx->beta*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta-1);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
ierr = MatSetValues(DRDU,1,row,1,col,ru,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(DRDU,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(DRDU,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode calcfluxs(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar emma, PetscScalar fract, PetscScalar cloudTemp, PetscScalar *flux)
{
PetscFunctionBeginUser;
*flux = SIG*((EMMSFC*emma*PetscPowScalarInt(airtemp,4)) + (EMMSFC*fract*(1 - emma)*PetscPowScalarInt(cloudTemp,4)) - (EMMSFC*PetscPowScalarInt(sfctemp,4))); /* calculates flux using Stefan-Boltzmann relation */
PetscFunctionReturn(0);
}
