PetscErrorCode FormFunctionLocal(DMDALocalInfo *info, PetscReal **u,
PetscReal **F, Ctx *usr) {
PetscInt i, j;
const PetscReal e = usr->eps;
PetscReal x, y, uu, uxx, uyy, Wux, Wuy;
Wind W;
Spacings s;
getSpacings(info,&s);
for (j=info->ys; j<info->ys+info->ym; j++) {
y = -1.0 + j * s.hy;
for (i=info->xs; i<info->xs+info->xm; i++) {
x = -1.0 + i * s.hx;
if (i == info->mx-1) {
F[j][i] = u[j][i] - 1.0;
} else if (i == 0 || j == 0 || j == info->my-1) {
F[j][i] = u[j][i];
} else {
uu = u[j][i];
uxx = (u[j][i-1] - 2.0 * uu + u[j][i+1]) / s.hx2;
uyy = (u[j-1][i] - 2.0 * uu + u[j+1][i]) / s.hy2;
W = getWind(x,y);
Wux = W.x * (u[j][i+1] - u[j][i-1]) / (2.0 * s.hx);
Wuy = W.y * (u[j+1][i] - u[j-1][i]) / (2.0 * s.hy);
F[j][i] = - e * (uxx + uyy) + Wux + Wuy;
}
}
}
return 0;
}
PetscErrorCode FormJacobianLocal(DMDALocalInfo *info, PetscScalar ***u,
Mat J, Mat Jpre, Ctx *usr) {
PetscErrorCode ierr;
PetscInt i,j,q;
PetscReal v[5],diag,x,y;
const PetscReal e = usr->eps;
MatStencil col[5],row;
Spacings s;
Wind W;
getSpacings(info,&s);
diag = e * 2.0 * (1.0/s.hx2 + 1.0/s.hy2);
for (j=info->ys; j<info->ys+info->ym; j++) {
y = -1.0 + j * s.hy;
row.j = j;
col[0].j = j;
for (i=info->xs; i<info->xs+info->xm; i++) {
x = -1.0 + i * s.hx;
row.i = i;
col[0].i = i;
q = 1;
if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
v[0] = 1.0;
} else {
W = getWind(x,y);
v[0] = diag;
if (i-1 != 0) {
v[q] = - e / s.hx2 - W.x / (2.0 * s.hx);
col[q].j = j; col[q].i = i-1;
q++;
}
if (i+1 != info->mx-1) {
v[q] = - e / s.hx2 + W.x / (2.0 * s.hx);
col[q].j = j; col[q].i = i+1;
q++;
}
if (j-1 != 0) {
v[q] = - e / s.hy2 - W.y / (2.0 * s.hy);
col[q].j = j-1; col[q].i = i;
q++;
}
if (j+1 != info->my-1) {
v[q] = - e / s.hy2 + W.y / (2.0 * s.hy);
col[q].j = j+1; col[q].i = i;
q++;
}
}
ierr = MatSetValuesStencil(Jpre,1,&row,q,col,v,INSERT_VALUES); 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);
}
return 0;
}
//STARTFUNCTION
PetscErrorCode FormFunctionLocal(DMDALocalInfo *info, double ***u,
double ***F, Ctx *usr) {
PetscErrorCode ierr;
int i, j, k;
const double e = usr->eps;
double x, y, z, uu, uxx, uyy, uzz, Wux, Wuy, Wuz, ***af, ***ag;
Wind W;
Spacings s;
getSpacings(info,&s);
ierr = DMDAVecGetArray(usr->da, usr->f, &af);
CHKERRQ(ierr);
ierr = DMDAVecGetArray(usr->da, usr->g, &ag);
CHKERRQ(ierr);
for (k=info->zs; k<info->zs+info->zm; k++) {
z = -1.0 + k * s.hz;
for (j=info->ys; j<info->ys+info->ym; j++) {
y = -1.0 + j * s.hy;
for (i=info->xs; i<info->xs+info->xm; i++) {
x = -1.0 + i * s.hx;
if (i == info->mx-1) {
F[k][j][i] = u[k][j][i] - ag[k][j][i];
} else if (i == 0 || j == 0 || j == info->my-1) {
F[k][j][i] = u[k][j][i];
} else {
uu = u[k][j][i];
uxx = (u[k][j][i-1] - 2.0 * uu + u[k][j][i+1]) / s.hx2;
uyy = (u[k][j-1][i] - 2.0 * uu + u[k][j+1][i]) / s.hy2;
uzz = (u[k-1][j][i] - 2.0 * uu + u[k+1][j][i]) / s.hz2;
W = getWind(x,y,z);
if (usr->upwind) {
Wux = (W.x > 0) ? uu - u[k][j][i-1]
: u[k][j][i+1] - uu;
Wux *= W.x / s.hx;
Wuy = (W.y > 0) ? uu - u[k][j-1][i]
: u[k][j+1][i] - uu;
Wuy *= W.y / s.hy;
Wuz = (W.z > 0) ? uu - u[k-1][j][i]
: u[k+1][j][i] - uu;
Wuz *= W.z / s.hz;
} else {
Wux = W.x * (u[k][j][i+1] - u[k][j][i-1]) / (2.0*s.hx);
Wuy = W.y * (u[k][j+1][i] - u[k][j-1][i]) / (2.0*s.hy);
Wuz = W.z * (u[k+1][j][i] - u[k-1][j][i]) / (2.0*s.hz);
}
F[k][j][i] = - e * (uxx + uyy + uzz) + Wux + Wuy + Wuz
- af[k][j][i];
}
}
}
}
ierr = DMDAVecRestoreArray(usr->da, usr->f, &af);
CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(usr->da, usr->g, &ag);
CHKERRQ(ierr);
return 0;
}
PetscErrorCode formUexFG(DMDALocalInfo *info, Ctx *usr, Vec uex) {
PetscErrorCode ierr;
int i, j, k;
Spacings s;
const double E = PETSC_PI / 2.0, F = 2.0 * PETSC_PI,
lam2 = E*E + F*F; // lambda = sqrt(17.0) * PETSC_PI / 2.0
double x, y, z, QQ, UU, ***auex, ***af, ***ag;
getSpacings(info,&s);
ierr = DMDAVecGetArray(usr->da, uex, &auex);
CHKERRQ(ierr);
ierr = DMDAVecGetArray(usr->da, usr->f, &af);
CHKERRQ(ierr);
ierr = DMDAVecGetArray(usr->da, usr->g, &ag);
CHKERRQ(ierr);
for (k=info->zs; k<info->zs+info->zm; k++) {
z = -1.0 + k * s.hz;
for (j=info->ys; j<info->ys+info->ym; j++) {
y = -1.0 + j * s.hy;
QQ = sin(E*(y+1.0)) * sin(F*(z+1.0));
for (i=info->xs; i<info->xs+info->xm; i++) {
x = -1.0 + i * s.hx;
UU = exp((x+1)/usr->eps) - 1.0;
UU /= exp(2.0/usr->eps) - 1.0;
auex[k][j][i] = UU * QQ;
af[k][j][i] = usr->eps * lam2 * auex[k][j][i];
if (i == info->mx-1)
ag[k][j][i] = QQ;
else
ag[k][j][i] = 0.0;
}
}
}
ierr = DMDAVecRestoreArray(usr->da, uex, &auex);
CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(usr->da, usr->f, &af);
CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(usr->da, usr->g, &ag);
CHKERRQ(ierr);
return 0;
}
PetscErrorCode FormJacobianLocal(DMDALocalInfo *info, PetscScalar ***u,
Mat J, Mat Jpre, Ctx *usr) {
PetscErrorCode ierr;
int i,j,k,q;
double v[7],diag,x,y,z;
const double e = usr->eps;
MatStencil col[7],row;
Spacings s;
Wind W;
getSpacings(info,&s);
diag = e * 2.0 * (1.0/s.hx2 + 1.0/s.hy2 + 1.0/s.hz2);
for (k=info->zs; k<info->zs+info->zm; k++) {
z = -1.0 + k * s.hz;
row.k = k;
col[0].k = k;
for (j=info->ys; j<info->ys+info->ym; j++) {
y = -1.0 + j * s.hy;
row.j = j;
col[0].j = j;
for (i=info->xs; i<info->xs+info->xm; i++) {
x = -1.0 + i * s.hx;
row.i = i;
col[0].i = i;
if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
v[0] = 1.0;
q = 1;
} else {
W = getWind(x,y,z);
v[0] = diag;
if (usr->upwind) {
v[0] += (W.x / s.hx) * ((W.x > 0.0) ? 1.0 : -1.0);
v[0] += (W.y / s.hy) * ((W.y > 0.0) ? 1.0 : -1.0);
v[0] += (W.z / s.hz) * ((W.z > 0.0) ? 1.0 : -1.0);
}
v[1] = - e / s.hz2;
if (usr->upwind) {
if (W.z > 0.0)
v[q] -= W.z / s.hz;
} else
v[q] -= W.z / (2.0 * s.hz);
col[1].k = k-1;
col[1].j = j;
col[1].i = i;
v[2] = - e / s.hz2;
if (usr->upwind) {
if (W.z <= 0.0)
v[q] += W.z / s.hz;
} else
v[q] += W.z / (2.0 * s.hz);
col[2].k = k+1;
col[2].j = j;
col[2].i = i;
q = 3;
if (i-1 != 0) {
v[q] = - e / s.hx2;
if (usr->upwind) {
if (W.x > 0.0)
v[q] -= W.x / s.hx;
} else
v[q] -= W.x / (2.0 * s.hx);
col[q].k = k;
col[q].j = j;
col[q].i = i-1;
q++;
}
if (i+1 != info->mx-1) {
v[q] = - e / s.hx2;
if (usr->upwind) {
if (W.x <= 0.0)
v[q] += W.x / s.hx;
} else
v[q] += W.x / (2.0 * s.hx);
col[q].k = k;
col[q].j = j;
col[q].i = i+1;
q++;
}
if (j-1 != 0) {
v[q] = - e / s.hy2;
if (usr->upwind) {
if (W.y > 0.0)
v[q] -= W.y / s.hy;
} else
v[q] -= W.y / (2.0 * s.hy);
col[q].k = k;
col[q].j = j-1;
col[q].i = i;
q++;
}
if (j+1 != info->my-1) {
v[q] = - e / s.hy2;
if (usr->upwind) {
if (W.y <= 0.0)
v[q] += W.y / s.hy;
} else
v[q] += W.y / (2.0 * s.hy);
col[q].k = k;
col[q].j = j+1;
col[q].i = i;
q++;
}
}
ierr = MatSetValuesStencil(Jpre,1,&row,q,col,v,INSERT_VALUES);
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);
}
return 0;
}
