| 1 | /* ------------------------------------------------------------------------
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| 2 |
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| 3 | Solid Fuel Ignition (SFI) problem. This problem is modeled by
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| 4 | the partial differential equation
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| 5 |
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| 6 | -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
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| 7 |
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| 8 | with boundary conditions
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| 9 |
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| 10 | u = 0 for x = 0, x = 1, y = 0, y = 1.
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| 11 |
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| 12 | A finite difference approximation with the usual 5-point stencil
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| 13 | is used to discretize the boundary value problem to obtain a nonlinear
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| 14 | system of equations.
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| 15 | ------------------------------------------------------------------------- */
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| 16 |
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| 17 | #include "petsc.h"
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| 18 |
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| 19 | typedef struct {
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| 20 | PassiveReal param; /* test problem parameter */
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| 21 | } AppCtx;
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| 22 |
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| 23 | /* ------------------------------------------------------------------- */
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| 24 | #undef __FUNCT__
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| 25 | #define __FUNCT__ "FormFunctionLocal"
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| 26 | /*
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| 27 | FormFunctionLocal - Evaluates nonlinear function, F(x) on local process patch
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| 28 | */
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| 29 | PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
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| 30 | {
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| 31 | PetscErrorCode ierr;
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| 32 | PetscInt i,j;
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| 33 | PetscReal lambda,hx,hy,hxdhy,hydhx,sc;
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| 34 | PetscScalar u,uxx,uyy;
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| 35 |
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| 36 | PetscFunctionBegin;
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| 37 |
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| 38 | lambda = user->param;
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| 39 | hx = 1.0/(PetscReal)(info->mx-1);
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| 40 | hy = 1.0/(PetscReal)(info->my-1);
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| 41 | sc = hx*hy*lambda;
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| 42 | hxdhy = hx/hy;
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| 43 | hydhx = hy/hx;
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| 44 |
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| 45 | /*
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| 46 | Compute function over the locally owned part of the grid
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| 47 | */
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| 48 | for (j=info->ys; j<info->ys+info->ym; j++) {
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| 49 | for (i=info->xs; i<info->xs+info->xm; i++) {
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| 50 | if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
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| 51 | f[j][i] = 2.0*(hydhx+hxdhy)*x[j][i];
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| 52 | ierr = PetscLogFlops(3.0);CHKERRQ(ierr);
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| 53 | } else {
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| 54 | f[j][i] = FormFunctionPt(x[j][i],x[j-1][i],x[j+1][i],x[j][i-1],x[j][i+1],hxdhy,hyhdx,sc);
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| 55 | ierr = PetscLogFlops(11.0);CHKERRQ(ierr);
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| 56 | }
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| 57 | }
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| 58 | }
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| 59 | PetscFunctionReturn(0);
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| 60 | }
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| 61 |
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| 62 | PetscScalar FormFunctionPt(PetscScalar C,PetscScalar S,PetscScalar N,PetscScalar W,PetscScalar E,PetscReal hxdhy,PetscReal hydhx,PetscReal sc) {
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| 63 | PetscScalar uxx,uyy;
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| 64 |
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| 65 | uxx = (2.0*C - W - E)*hydhx;
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| 66 | uyy = (2.0*C - S - N)*hxdhy;
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| 67 | return (uxx + uyy - sc*PetscExpScalar(C));
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| 68 | }
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