69   subroutine FormFunction(snes, X, F, ctx, ierr)  argument
76     type(AppCtx) ctx
103     PetscCall(FormFunctionLocal(lx_v, lf_v, ctx, ierr))
112     PetscCall(PetscLogFlops(11.0d0*ctx%ym*ctx%xm, ierr))
139     type(AppCtx), pointer:: ctx
149     PetscCallA(SNESGetApplicationContext(snes, ctx, ierr))
160     PetscCallA(InitialGuessLocal(ctx, lx_v, ierr))
184   subroutine InitialGuessLocal(ctx, x, ierr)  argument
186     type(AppCtx) ctx  local
187     PetscScalar x(ctx%xs:ctx%xe, ctx%ys:ctx%ye)
199     hx = one/(ctx%mx - 1)
200     hy = one/(ctx%my - 1)
201     temp1 = ctx%lambda/(ctx%lambda + one)
203     do j = ctx%ys, ctx%ye
204       temp = min(j - 1, ctx%my - j)*hy
205       do i = ctx%xs, ctx%xe
206         if (i == 1 .or. j == 1 .or. i == ctx%mx .or. j == ctx%my) then
209           x(i, j) = temp1*sqrt(min(hx*min(i - 1, ctx%mx - i), temp))
231   subroutine FormFunctionLocal(x, f, ctx, ierr)  argument
233     type(AppCtx) ctx  local
234     PetscScalar x(ctx%gxs:ctx%gxe, ctx%gys:ctx%gye)
235     PetscScalar f(ctx%xs:ctx%xe, ctx%ys:ctx%ye)
245     hx = one/(ctx%mx - 1)
246     hy = one/(ctx%my - 1)
247     sc = hx*hy*ctx%lambda
253     do j = ctx%ys, ctx%ye
254       do i = ctx%xs, ctx%xe
255         if (i == 1 .or. j == 1 .or. i == ctx%mx .or. j == ctx%my) then
310   subroutine FormJacobian(snes, X, jac, jac_prec, ctx, ierr)  argument
315     type(AppCtx) ctx
337     PetscCallA(FormJacobianLocal(lx_v, jac_prec, ctx, ierr))
397   subroutine FormJacobianLocal(x, jac_prec, ctx, ierr)  argument
399     type(AppCtx) ctx  local
400     PetscScalar x(ctx%gxs:ctx%gxe, ctx%gys:ctx%gye)
415     hx = one/(ctx%mx - 1)
416     hy = one/(ctx%my - 1)
433     do j = ctx%ys, ctx%ye
434       row = (j - ctx%gys)*ctx%gxm + ctx%xs - ctx%gxs - 1
435       do i = ctx%xs, ctx%xe
438         if (i == 1 .or. j == 1 .or. i == ctx%mx .or. j == ctx%my) then
446           v(3) = two*(hydhx + hxdhy) - sc*ctx%lambda*exp(x(i, j))
449           col(1) = row - ctx%gxm
453           col(5) = row + ctx%gxm
488   type(AppCtx) ctx
495   PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD, ctx%rank, ierr))
500   ctx%lambda = 6.0
503 …PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS, PETSC_NULL_CHARACTER, '-par', ctx%lambda, flg, …
504 …PetscCheckA(ctx%lambda < lambda_max .and. ctx%lambda > lambda_min, PETSC_COMM_SELF, PETSC_ERR_USER…
523 …PetscCallA(DMDAGetInfo(da, PETSC_NULL_INTEGER, ctx%mx, ctx%my, PETSC_NULL_INTEGER, PETSC_NULL_INTE…
536 …PetscCallA(DMDAGetCorners(da, ctx%xs, ctx%ys, PETSC_NULL_INTEGER, ctx%xm, ctx%ym, PETSC_NULL_INTEG…
537 …PetscCallA(DMDAGetGhostCorners(da, ctx%gxs, ctx%gys, PETSC_NULL_INTEGER, ctx%gxm, ctx%gym, PETSC_N…
541   ctx%xs = ctx%xs + 1
542   ctx%ys = ctx%ys + 1
543   ctx%gxs = ctx%gxs + 1
544   ctx%gys = ctx%gys + 1
546   ctx%ye = ctx%ys + ctx%ym - 1
547   ctx%xe = ctx%xs + ctx%xm - 1
548   ctx%gye = ctx%gys + ctx%gym - 1
549   ctx%gxe = ctx%gxs + ctx%gxm - 1
551   PetscCallA(SNESSetApplicationContext(snes, ctx, ierr))
554   PetscCallA(SNESSetFunction(snes, r, FormFunction, ctx, ierr))
584     PetscCallA(SNESSetJacobian(snes, J, J, FormJacobian, ctx, ierr))
605   if (ctx%rank == 0) then