Actual source code: ex11.c
2: static char help[] =
3: "This program demonstrates use of the SNES package to solve systems of\n\
4: nonlinear equations in parallel, using 2-dimensional distributed arrays.\n\
5: The 2-dim Bratu (SFI - solid fuel ignition) test problem is used, where\n\
6: analytic formation of the Jacobian is the default. \n\
7: \n\
8: Solves the linear systems via 2 level additive Schwarz \n\
9: \n\
10: The command line\n\
11: options are:\n\
12: -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
13: problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)\n\
14: -Mx <xg>, where <xg> = number of grid points in the x-direction on coarse grid\n\
15: -My <yg>, where <yg> = number of grid points in the y-direction on coarse grid\n\n";
17: /*
18: 1) Solid Fuel Ignition (SFI) problem. This problem is modeled by
19: the partial differential equation
20:
21: -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1 ,
22:
23: with boundary conditions
24:
25: u = 0 for x = 0, x = 1, y = 0, y = 1.
26:
27: A finite difference approximation with the usual 5-point stencil
28: is used to discretize the boundary value problem to obtain a nonlinear
29: system of equations.
31: The code has two cases for multilevel solver
32: I. the coarse grid Jacobian is computed in parallel
33: II. the coarse grid Jacobian is computed sequentially on each processor
34: in both cases the coarse problem is SOLVED redundantly.
36: */
38: #include petscsnes.h
39: #include petscda.h
40: #include petscmg.h
42: /* User-defined application contexts */
44: typedef struct {
45: PetscInt mx,my; /* number grid points in x and y direction */
46: Vec localX,localF; /* local vectors with ghost region */
47: DA da;
48: Vec x,b,r; /* global vectors */
49: Mat J; /* Jacobian on grid */
50: } GridCtx;
52: typedef struct {
53: double param; /* test problem parameter */
54: GridCtx fine;
55: GridCtx coarse;
56: KSP ksp_coarse;
57: KSP ksp_fine;
58: PetscInt ratio;
59: Mat R; /* restriction fine to coarse */
60: Vec Rscale;
61: PetscTruth redundant_build; /* build coarse matrix redundantly */
62: Vec localall; /* contains entire coarse vector on each processor in NATURAL order*/
63: VecScatter tolocalall; /* maps from parallel "global" coarse vector to localall */
64: VecScatter fromlocalall; /* maps from localall vector back to global coarse vector */
65: } AppCtx;
67: #define COARSE_LEVEL 0
68: #define FINE_LEVEL 1
74: /*
75: Mm_ratio - ration of grid lines between fine and coarse grids.
76: */
79: int main( int argc, char **argv )
80: {
81: SNES snes;
82: AppCtx user;
84: PetscInt its, N, n, Nx = PETSC_DECIDE, Ny = PETSC_DECIDE, nlocal,Nlocal;
85: PetscMPIInt size;
86: double bratu_lambda_max = 6.81, bratu_lambda_min = 0.;
87: KSP ksp;
88: PC pc;
90: /*
91: Initialize PETSc, note that default options in ex11options can be
92: overridden at the command line
93: */
94: PetscInitialize( &argc, &argv,"ex11options",help );
96: user.ratio = 2;
97: user.coarse.mx = 5; user.coarse.my = 5; user.param = 6.0;
98: PetscOptionsGetInt(PETSC_NULL,"-Mx",&user.coarse.mx,PETSC_NULL);
99: PetscOptionsGetInt(PETSC_NULL,"-My",&user.coarse.my,PETSC_NULL);
100: PetscOptionsGetInt(PETSC_NULL,"-ratio",&user.ratio,PETSC_NULL);
101: user.fine.mx = user.ratio*(user.coarse.mx-1)+1; user.fine.my = user.ratio*(user.coarse.my-1)+1;
103: PetscOptionsHasName(PETSC_NULL,"-redundant_build",&user.redundant_build);
104: if (user.redundant_build) {
105: PetscPrintf(PETSC_COMM_WORLD,"Building coarse Jacobian redundantly\n");
106: }
108: PetscPrintf(PETSC_COMM_WORLD,"Coarse grid size %D by %D\n",user.coarse.mx,user.coarse.my);
109: PetscPrintf(PETSC_COMM_WORLD,"Fine grid size %D by %D\n",user.fine.mx,user.fine.my);
111: PetscOptionsGetReal(PETSC_NULL,"-par",&user.param,PETSC_NULL);
112: if (user.param >= bratu_lambda_max || user.param < bratu_lambda_min) {
113: SETERRQ(1,"Lambda is out of range");
114: }
115: n = user.fine.mx*user.fine.my; N = user.coarse.mx*user.coarse.my;
117: MPI_Comm_size(PETSC_COMM_WORLD,&size);
118: PetscOptionsGetInt(PETSC_NULL,"-Nx",&Nx,PETSC_NULL);
119: PetscOptionsGetInt(PETSC_NULL,"-Ny",&Ny,PETSC_NULL);
121: /* Set up distributed array for fine grid */
122: DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,user.fine.mx,
123: user.fine.my,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&user.fine.da);
124: DACreateGlobalVector(user.fine.da,&user.fine.x);
125: VecDuplicate(user.fine.x,&user.fine.r);
126: VecDuplicate(user.fine.x,&user.fine.b);
127: VecGetLocalSize(user.fine.x,&nlocal);
128: DACreateLocalVector(user.fine.da,&user.fine.localX);
129: VecDuplicate(user.fine.localX,&user.fine.localF);
130: MatCreateMPIAIJ(PETSC_COMM_WORLD,nlocal,nlocal,n,n,5,PETSC_NULL,3,PETSC_NULL,&user.fine.J);
132: /* Set up distributed array for coarse grid */
133: DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,user.coarse.mx,
134: user.coarse.my,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&user.coarse.da);
135: DACreateGlobalVector(user.coarse.da,&user.coarse.x);
136: VecDuplicate(user.coarse.x,&user.coarse.b);
137: if (user.redundant_build) {
138: /* Create scatter from parallel global numbering to redundant with natural ordering */
139: DAGlobalToNaturalAllCreate(user.coarse.da,&user.tolocalall);
140: DANaturalAllToGlobalCreate(user.coarse.da,&user.fromlocalall);
141: VecCreateSeq(PETSC_COMM_SELF,N,&user.localall);
142: /* Create sequential matrix to hold entire coarse grid Jacobian on each processor */
143: MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,5,PETSC_NULL,&user.coarse.J);
144: } else {
145: VecGetLocalSize(user.coarse.x,&Nlocal);
146: DACreateLocalVector(user.coarse.da,&user.coarse.localX);
147: VecDuplicate(user.coarse.localX,&user.coarse.localF);
148: /* We will compute the coarse Jacobian in parallel */
149: MatCreateMPIAIJ(PETSC_COMM_WORLD,Nlocal,Nlocal,N,N,5,PETSC_NULL,3,PETSC_NULL,&user.coarse.J);
150: }
152: /* Create nonlinear solver */
153: SNESCreate(PETSC_COMM_WORLD,&snes);
155: /* provide user function and Jacobian */
156: SNESSetFunction(snes,user.fine.b,FormFunction,&user);
157: SNESSetJacobian(snes,user.fine.J,user.fine.J,FormJacobian,&user);
159: /* set two level additive Schwarz preconditioner */
160: SNESGetKSP(snes,&ksp);
161: KSPGetPC(ksp,&pc);
162: PCSetType(pc,PCMG);
163: PCMGSetLevels(pc,2,PETSC_NULL);
164: PCMGSetType(pc,PC_MG_ADDITIVE);
166: /* always solve the coarse problem redundantly with direct LU solver */
167: PetscOptionsSetValue("-coarse_pc_type","redundant");
168: PetscOptionsSetValue("-coarse_redundant_pc_type","lu");
170: /* Create coarse level */
171: PCMGGetCoarseSolve(pc,&user.ksp_coarse);
172: KSPSetOptionsPrefix(user.ksp_coarse,"coarse_");
173: KSPSetFromOptions(user.ksp_coarse);
174: KSPSetOperators(user.ksp_coarse,user.coarse.J,user.coarse.J,DIFFERENT_NONZERO_PATTERN);
175: PCMGSetX(pc,COARSE_LEVEL,user.coarse.x);
176: PCMGSetRhs(pc,COARSE_LEVEL,user.coarse.b);
177: if (user.redundant_build) {
178: PC rpc;
179: KSPGetPC(user.ksp_coarse,&rpc);
180: PCRedundantSetScatter(rpc,user.tolocalall,user.fromlocalall);
181: }
183: /* Create fine level */
184: PCMGGetSmoother(pc,FINE_LEVEL,&user.ksp_fine);
185: KSPSetOptionsPrefix(user.ksp_fine,"fine_");
186: KSPSetFromOptions(user.ksp_fine);
187: KSPSetOperators(user.ksp_fine,user.fine.J,user.fine.J,DIFFERENT_NONZERO_PATTERN);
188: PCMGSetR(pc,FINE_LEVEL,user.fine.r);
189: PCMGSetResidual(pc,FINE_LEVEL,PCMGDefaultResidual,user.fine.J);
191: /* Create interpolation between the levels */
192: FormInterpolation(&user);
193: PCMGSetInterpolate(pc,FINE_LEVEL,user.R);
194: PCMGSetRestriction(pc,FINE_LEVEL,user.R);
196: /* Set options, then solve nonlinear system */
197: SNESSetFromOptions(snes);
198: FormInitialGuess1(&user,user.fine.x);
199: SNESSolve(snes,PETSC_NULL,user.fine.x);
200: SNESGetIterationNumber(snes,&its);
201: PetscPrintf(PETSC_COMM_WORLD,"Number of Newton iterations = %D\n", its );
203: /* Free data structures */
204: if (user.redundant_build) {
205: VecScatterDestroy(user.tolocalall);
206: VecScatterDestroy(user.fromlocalall);
207: VecDestroy(user.localall);
208: } else {
209: VecDestroy(user.coarse.localX);
210: VecDestroy(user.coarse.localF);
211: }
213: MatDestroy(user.fine.J);
214: VecDestroy(user.fine.x);
215: VecDestroy(user.fine.r);
216: VecDestroy(user.fine.b);
217: DADestroy(user.fine.da);
218: VecDestroy(user.fine.localX);
219: VecDestroy(user.fine.localF);
221: MatDestroy(user.coarse.J);
222: VecDestroy(user.coarse.x);
223: VecDestroy(user.coarse.b);
224: DADestroy(user.coarse.da);
226: SNESDestroy(snes);
227: MatDestroy(user.R);
228: VecDestroy(user.Rscale);
229: PetscFinalize();
231: return 0;
232: }/* -------------------- Form initial approximation ----------------- */
235: PetscErrorCode FormInitialGuess1(AppCtx *user,Vec X)
236: {
237: PetscInt i, j, row, mx, my, xs, ys, xm, ym, Xm, Ym, Xs, Ys;
239: double one = 1.0, lambda, temp1, temp, hx, hy, hxdhy, hydhx,sc;
240: PetscScalar *x;
241: Vec localX = user->fine.localX;
243: mx = user->fine.mx; my = user->fine.my; lambda = user->param;
244: hx = one/(double)(mx-1); hy = one/(double)(my-1);
245: sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
247: temp1 = lambda/(lambda + one);
249: /* Get ghost points */
250: DAGetCorners(user->fine.da,&xs,&ys,0,&xm,&ym,0);
251: DAGetGhostCorners(user->fine.da,&Xs,&Ys,0,&Xm,&Ym,0);
252: VecGetArray(localX,&x);
254: /* Compute initial guess */
255: for (j=ys; j<ys+ym; j++) {
256: temp = (double)(PetscMin(j,my-j-1))*hy;
257: for (i=xs; i<xs+xm; i++) {
258: row = i - Xs + (j - Ys)*Xm;
259: if (i == 0 || j == 0 || i == mx-1 || j == my-1 ) {
260: x[row] = 0.0;
261: continue;
262: }
263: x[row] = temp1*sqrt( PetscMin( (double)(PetscMin(i,mx-i-1))*hx,temp) );
264: }
265: }
266: VecRestoreArray(localX,&x);
268: /* Insert values into global vector */
269: DALocalToGlobal(user->fine.da,localX,INSERT_VALUES,X);
270: return 0;
271: }
273: /* -------------------- Evaluate Function F(x) --------------------- */
276: PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ptr)
277: {
278: AppCtx *user = (AppCtx *) ptr;
279: PetscInt i, j, row, mx, my, xs, ys, xm, ym, Xs, Ys, Xm, Ym;
281: double two = 2.0, one = 1.0, lambda,hx, hy, hxdhy, hydhx,sc;
282: PetscScalar u, uxx, uyy, *x,*f;
283: Vec localX = user->fine.localX, localF = user->fine.localF;
285: mx = user->fine.mx; my = user->fine.my; lambda = user->param;
286: hx = one/(double)(mx-1); hy = one/(double)(my-1);
287: sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
289: /* Get ghost points */
290: DAGlobalToLocalBegin(user->fine.da,X,INSERT_VALUES,localX);
291: DAGlobalToLocalEnd(user->fine.da,X,INSERT_VALUES,localX);
292: DAGetCorners(user->fine.da,&xs,&ys,0,&xm,&ym,0);
293: DAGetGhostCorners(user->fine.da,&Xs,&Ys,0,&Xm,&Ym,0);
294: VecGetArray(localX,&x);
295: VecGetArray(localF,&f);
297: /* Evaluate function */
298: for (j=ys; j<ys+ym; j++) {
299: row = (j - Ys)*Xm + xs - Xs - 1;
300: for (i=xs; i<xs+xm; i++) {
301: row++;
302: if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
303: u = x[row];
304: uxx = (two*u - x[row-1] - x[row+1])*hydhx;
305: uyy = (two*u - x[row-Xm] - x[row+Xm])*hxdhy;
306: f[row] = uxx + uyy - sc*exp(u);
307: } else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)){
308: f[row] = .5*two*(hydhx + hxdhy)*x[row];
309: } else {
310: f[row] = .25*two*(hydhx + hxdhy)*x[row];
311: }
312: }
313: }
314: VecRestoreArray(localX,&x);
315: VecRestoreArray(localF,&f);
317: /* Insert values into global vector */
318: DALocalToGlobal(user->fine.da,localF,INSERT_VALUES,F);
319: PetscLogFlops(11*ym*xm);
320: return 0;
321: }
323: /*
324: Computes the part of the Jacobian associated with this processor
325: */
328: PetscErrorCode FormJacobian_Grid(AppCtx *user,GridCtx *grid,Vec X, Mat *J,Mat *B)
329: {
330: Mat jac = *J;
332: PetscInt i, j, row, mx, my, xs, ys, xm, ym, Xs, Ys, Xm, Ym, col[5], nloc, *ltog, grow;
333: PetscScalar two = 2.0, one = 1.0, lambda, v[5], hx, hy, hxdhy, hydhx, sc, *x, value;
334: Vec localX = grid->localX;
336: mx = grid->mx; my = grid->my; lambda = user->param;
337: hx = one/(double)(mx-1); hy = one/(double)(my-1);
338: sc = hx*hy; hxdhy = hx/hy; hydhx = hy/hx;
340: /* Get ghost points */
341: DAGlobalToLocalBegin(grid->da,X,INSERT_VALUES,localX);
342: DAGlobalToLocalEnd(grid->da,X,INSERT_VALUES,localX);
343: DAGetCorners(grid->da,&xs,&ys,0,&xm,&ym,0);
344: DAGetGhostCorners(grid->da,&Xs,&Ys,0,&Xm,&Ym,0);
345: DAGetGlobalIndices(grid->da,&nloc,<og);
346: VecGetArray(localX,&x);
348: /* Evaluate Jacobian of function */
349: for (j=ys; j<ys+ym; j++) {
350: row = (j - Ys)*Xm + xs - Xs - 1;
351: for (i=xs; i<xs+xm; i++) {
352: row++;
353: grow = ltog[row];
354: if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
355: v[0] = -hxdhy; col[0] = ltog[row - Xm];
356: v[1] = -hydhx; col[1] = ltog[row - 1];
357: v[2] = two*(hydhx + hxdhy) - sc*lambda*exp(x[row]); col[2] = grow;
358: v[3] = -hydhx; col[3] = ltog[row + 1];
359: v[4] = -hxdhy; col[4] = ltog[row + Xm];
360: MatSetValues(jac,1,&grow,5,col,v,INSERT_VALUES);
361: } else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)){
362: value = .5*two*(hydhx + hxdhy);
363: MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
364: } else {
365: value = .25*two*(hydhx + hxdhy);
366: MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
367: }
368: }
369: }
370: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
371: VecRestoreArray(localX,&x);
372: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
374: return 0;
375: }
377: /*
378: Computes the ENTIRE Jacobian associated with the ENTIRE grid sequentially
379: This is for generating the coarse grid redundantly.
381: This is BAD code duplication, since the bulk of this routine is the
382: same as the routine above
384: Note the numbering of the rows/columns is the NATURAL numbering
385: */
388: PetscErrorCode FormJacobian_Coarse(AppCtx *user,GridCtx *grid,Vec X, Mat *J,Mat *B)
389: {
390: Mat jac = *J;
392: PetscInt i, j, row, mx, my, col[5];
393: PetscScalar two = 2.0, one = 1.0, lambda, v[5], hx, hy, hxdhy, hydhx, sc, *x, value;
395: mx = grid->mx; my = grid->my; lambda = user->param;
396: hx = one/(double)(mx-1); hy = one/(double)(my-1);
397: sc = hx*hy; hxdhy = hx/hy; hydhx = hy/hx;
399: VecGetArray(X,&x);
401: /* Evaluate Jacobian of function */
402: for (j=0; j<my; j++) {
403: row = j*mx - 1;
404: for (i=0; i<mx; i++) {
405: row++;
406: if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
407: v[0] = -hxdhy; col[0] = row - mx;
408: v[1] = -hydhx; col[1] = row - 1;
409: v[2] = two*(hydhx + hxdhy) - sc*lambda*exp(x[row]); col[2] = row;
410: v[3] = -hydhx; col[3] = row + 1;
411: v[4] = -hxdhy; col[4] = row + mx;
412: MatSetValues(jac,1,&row,5,col,v,INSERT_VALUES);
413: } else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)){
414: value = .5*two*(hydhx + hxdhy);
415: MatSetValues(jac,1,&row,1,&row,&value,INSERT_VALUES);
416: } else {
417: value = .25*two*(hydhx + hxdhy);
418: MatSetValues(jac,1,&row,1,&row,&value,INSERT_VALUES);
419: }
420: }
421: }
422: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
423: VecRestoreArray(X,&x);
424: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
426: return 0;
427: }
429: /* -------------------- Evaluate Jacobian F'(x) --------------------- */
432: PetscErrorCode FormJacobian(SNES snes,Vec X,Mat *J,Mat *B,MatStructure *flag,void *ptr)
433: {
434: AppCtx *user = (AppCtx *) ptr;
436: KSP ksp;
437: PC pc;
438: PetscTruth ismg;
440: *flag = SAME_NONZERO_PATTERN;
441: FormJacobian_Grid(user,&user->fine,X,J,B);
443: /* create coarse grid jacobian for preconditioner */
444: SNESGetKSP(snes,&ksp);
445: KSPGetPC(ksp,&pc);
446:
447: PetscTypeCompare((PetscObject)pc,PCMG,&ismg);
448: if (ismg) {
450: KSPSetOperators(user->ksp_fine,user->fine.J,user->fine.J,SAME_NONZERO_PATTERN);
452: /* restrict X to coarse grid */
453: MatMult(user->R,X,user->coarse.x);
454: VecPointwiseMult(user->coarse.x,user->coarse.x,user->Rscale);
456: /* form Jacobian on coarse grid */
457: if (user->redundant_build) {
458: /* get copy of coarse X onto each processor */
459: VecScatterBegin(user->coarse.x,user->localall,INSERT_VALUES,SCATTER_FORWARD,user->tolocalall);
460: VecScatterEnd(user->coarse.x,user->localall,INSERT_VALUES,SCATTER_FORWARD,user->tolocalall);
461: FormJacobian_Coarse(user,&user->coarse,user->localall,&user->coarse.J,&user->coarse.J);
463: } else {
464: /* coarse grid Jacobian computed in parallel */
465: FormJacobian_Grid(user,&user->coarse,user->coarse.x,&user->coarse.J,&user->coarse.J);
466: }
467: KSPSetOperators(user->ksp_coarse,user->coarse.J,user->coarse.J,SAME_NONZERO_PATTERN);
468: }
470: return 0;
471: }
476: /*
477: Forms the interpolation (and restriction) operator from
478: coarse grid to fine.
479: */
480: PetscErrorCode FormInterpolation(AppCtx *user)
481: {
483: PetscInt i,j,i_start,m_fine,j_start,m,n,*idx;
484: PetscInt m_ghost,n_ghost,*idx_c,m_ghost_c,n_ghost_c,m_coarse;
485: PetscInt row,i_start_ghost,j_start_ghost,cols[4], m_c;
486: PetscInt nc,ratio = user->ratio,m_c_local,m_fine_locaol;
487: PetscInt i_c,j_c,i_start_c,j_start_c,n_c,i_start_ghost_c,j_start_ghost_c,col;
488: PetscScalar v[4],x,y, one = 1.0;
489: Mat mat;
490: Vec Rscale;
491:
492: DAGetCorners(user->fine.da,&i_start,&j_start,0,&m,&n,0);
493: DAGetGhostCorners(user->fine.da,&i_start_ghost,&j_start_ghost,0,&m_ghost,&n_ghost,0);
494: DAGetGlobalIndices(user->fine.da,PETSC_NULL,&idx);
496: DAGetCorners(user->coarse.da,&i_start_c,&j_start_c,0,&m_c,&n_c,0);
497: DAGetGhostCorners(user->coarse.da,&i_start_ghost_c,&j_start_ghost_c,0,&m_ghost_c,&n_ghost_c,0);
498: DAGetGlobalIndices(user->coarse.da,PETSC_NULL,&idx_c);
500: /* create interpolation matrix */
501: VecGetLocalSize(user->fine.x,&m_fine_local);
502: VecGetLocalSize(user->coarse.x,&m_c_local);
503: VecGetSize(user->fine.x,&m_fine);
504: VecGetSize(user->coarse.x,&m_coarse);
505: MatCreateMPIAIJ(PETSC_COMM_WORLD,m_fine_local,m_c_local,m_fine,m_coarse,
506: 5,0,3,0,&mat);
508: /* loop over local fine grid nodes setting interpolation for those*/
509: for ( j=j_start; j<j_start+n; j++ ) {
510: for ( i=i_start; i<i_start+m; i++ ) {
511: /* convert to local "natural" numbering and then to PETSc global numbering */
512: row = idx[m_ghost*(j-j_start_ghost) + (i-i_start_ghost)];
514: i_c = (i/ratio); /* coarse grid node to left of fine grid node */
515: j_c = (j/ratio); /* coarse grid node below fine grid node */
517: /*
518: Only include those interpolation points that are truly
519: nonzero. Note this is very important for final grid lines
520: in x and y directions; since they have no right/top neighbors
521: */
522: x = ((double)(i - i_c*ratio))/((double)ratio);
523: y = ((double)(j - j_c*ratio))/((double)ratio);
524: nc = 0;
525: /* one left and below; or we are right on it */
526: if (j_c < j_start_ghost_c || j_c > j_start_ghost_c+n_ghost_c) {
527: SETERRQ3(1,"Sorry j %D %D %D",j_c,j_start_ghost_c,j_start_ghost_c+n_ghost_c);
528: }
529: if (i_c < i_start_ghost_c || i_c > i_start_ghost_c+m_ghost_c) {
530: SETERRQ3(1,"Sorry i %D %D %D",i_c,i_start_ghost_c,i_start_ghost_c+m_ghost_c);
531: }
532: col = m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c);
533: cols[nc] = idx_c[col];
534: v[nc++] = x*y - x - y + 1.0;
535: /* one right and below */
536: if (i_c*ratio != i) {
537: cols[nc] = idx_c[col+1];
538: v[nc++] = -x*y + x;
539: }
540: /* one left and above */
541: if (j_c*ratio != j) {
542: cols[nc] = idx_c[col+m_ghost_c];
543: v[nc++] = -x*y + y;
544: }
545: /* one right and above */
546: if (j_c*ratio != j && i_c*ratio != i) {
547: cols[nc] = idx_c[col+m_ghost_c+1];
548: v[nc++] = x*y;
549: }
550: MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);
551: }
552: }
553: MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);
554: MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);
556: VecDuplicate(user->coarse.x,&Rscale);
557: VecSet(user->fine.x,one);
558: MatMultTranspose(mat,user->fine.x,Rscale);
559: VecReciprocal(Rscale);
560: user->Rscale = Rscale;
561: user->R = mat;
562: return 0;
563: }