Actual source code: ex11.c
1: /*$Id: ex11.c,v 1.38 1999/11/05 14:47:16 bsmith Exp bsmith $*/
3: static char help[] =
4: "This program demonstrates use of the SNES package to solve systems of\n\
5: nonlinear equations in parallel, using 2-dimensional distributed arrays.\n\
6: The 2-dim Bratu (SFI - solid fuel ignition) test problem is used, where\n\
7: analytic formation of the Jacobian is the default. \n\
8: \n\
9: Solves the linear systems via 2 level additive Schwarz \n\
10: \n\
11: The command line\n\
12: options are:\n\
13: -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
14: problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)\n\
15: -Mx <xg>, where <xg> = number of grid points in the x-direction on coarse grid\n\
16: -My <yg>, where <yg> = number of grid points in the y-direction on coarse grid\n\n";
18: /*
19: 1) Solid Fuel Ignition (SFI) problem. This problem is modeled by
20: the partial differential equation
21:
22: -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1 ,
23:
24: with boundary conditions
25:
26: u = 0 for x = 0, x = 1, y = 0, y = 1.
27:
28: A finite difference approximation with the usual 5-point stencil
29: is used to discretize the boundary value problem to obtain a nonlinear
30: system of equations.
32: The code has two cases for multilevel solver
33: I. the coarse grid Jacobian is computed in parallel
34: II. the coarse grid Jacobian is computed sequentially on each processor
35: in both cases the coarse problem is SOLVED redundantly.
37: */
39: #include petscsnes.h
40: #include petscda.h
41: #include petscmg.h
43: /* User-defined application contexts */
45: typedef struct {
46: int mx,my; /* number grid points in x and y direction */
47: Vec localX,localF; /* local vectors with ghost region */
48: DA da;
49: Vec x,b,r; /* global vectors */
50: Mat J; /* Jacobian on grid */
51: } GridCtx;
53: typedef struct {
54: double param; /* test problem parameter */
55: GridCtx fine;
56: GridCtx coarse;
57: SLES sles_coarse;
58: SLES sles_fine;
59: int ratio;
60: Mat R; /* restriction fine to coarse */
61: Vec Rscale;
62: PetscTruth redundant_build; /* build coarse matrix redundantly */
63: Vec localall; /* contains entire coarse vector on each processor in NATURAL order*/
64: VecScatter tolocalall; /* maps from parallel "global" coarse vector to localall */
65: VecScatter fromlocalall; /* maps from localall vector back to global coarse vector */
66: } AppCtx;
68: #define COARSE_LEVEL 0
69: #define FINE_LEVEL 1
71: extern int FormFunction(SNES,Vec,Vec,void*), FormInitialGuess1(AppCtx*,Vec);
72: extern int FormJacobian(SNES,Vec,Mat*,Mat*,MatStructure*,void*);
73: extern int FormInterpolation(AppCtx *);
75: /*
76: Mm_ratio - ration of grid lines between fine and coarse grids.
77: */
80: int main( int argc, char **argv )
81: {
82: SNES snes;
83: AppCtx user;
84: int ierr, its, N, n, Nx = PETSC_DECIDE, Ny = PETSC_DECIDE;
85: int size, nlocal,Nlocal;
86: double bratu_lambda_max = 6.81, bratu_lambda_min = 0.;
87: SLES sles;
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: SNESGetSLES(snes,&sles);
161: SLESGetPC(sles,&pc);
162: PCSetType(pc,PCMG);
163: MGSetLevels(pc,2,PETSC_NULL);
164: MGSetType(pc,MGADDITIVE);
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: MGGetCoarseSolve(pc,&user.sles_coarse);
172: SLESSetOptionsPrefix(user.sles_coarse,"coarse_");
173: SLESSetFromOptions(user.sles_coarse);
174: SLESSetOperators(user.sles_coarse,user.coarse.J,user.coarse.J,DIFFERENT_NONZERO_PATTERN);
175: MGSetX(pc,COARSE_LEVEL,user.coarse.x);
176: MGSetRhs(pc,COARSE_LEVEL,user.coarse.b);
177: if (user.redundant_build) {
178: PC rpc;
179: SLESGetPC(user.sles_coarse,&rpc);
180: PCRedundantSetScatter(rpc,user.tolocalall,user.fromlocalall);
181: }
183: /* Create fine level */
184: MGGetSmoother(pc,FINE_LEVEL,&user.sles_fine);
185: SLESSetOptionsPrefix(user.sles_fine,"fine_");
186: SLESSetFromOptions(user.sles_fine);
187: SLESSetOperators(user.sles_fine,user.fine.J,user.fine.J,DIFFERENT_NONZERO_PATTERN);
188: MGSetR(pc,FINE_LEVEL,user.fine.r);
189: MGSetResidual(pc,FINE_LEVEL,MGDefaultResidual,user.fine.J);
191: /* Create interpolation between the levels */
192: FormInterpolation(&user);
193: MGSetInterpolate(pc,FINE_LEVEL,user.R);
194: MGSetRestriction(pc,FINE_LEVEL,user.R);
196: /* Set options, then solve nonlinear system */
197: SNESSetFromOptions(snes);
198: FormInitialGuess1(&user,user.fine.x);
199: SNESSolve(snes,user.fine.x,&its);
200: PetscPrintf(PETSC_COMM_WORLD,"Number of Newton iterations = %d\n", its );
202: /* Free data structures */
203: if (user.redundant_build) {
204: VecScatterDestroy(user.tolocalall);
205: VecScatterDestroy(user.fromlocalall);
206: VecDestroy(user.localall);
207: } else {
208: VecDestroy(user.coarse.localX);
209: VecDestroy(user.coarse.localF);
210: }
212: MatDestroy(user.fine.J);
213: VecDestroy(user.fine.x);
214: VecDestroy(user.fine.r);
215: VecDestroy(user.fine.b);
216: DADestroy(user.fine.da);
217: VecDestroy(user.fine.localX);
218: VecDestroy(user.fine.localF);
220: MatDestroy(user.coarse.J);
221: VecDestroy(user.coarse.x);
222: VecDestroy(user.coarse.b);
223: DADestroy(user.coarse.da);
225: SNESDestroy(snes);
226: MatDestroy(user.R);
227: VecDestroy(user.Rscale);
228: PetscFinalize();
230: return 0;
231: }/* -------------------- Form initial approximation ----------------- */
234: int FormInitialGuess1(AppCtx *user,Vec X)
235: {
236: int i, j, row, mx, my, ierr, xs, ys, xm, ym, Xm, Ym, Xs, Ys;
237: double one = 1.0, lambda, temp1, temp, hx, hy, hxdhy, hydhx,sc;
238: PetscScalar *x;
239: Vec localX = user->fine.localX;
241: mx = user->fine.mx; my = user->fine.my; lambda = user->param;
242: hx = one/(double)(mx-1); hy = one/(double)(my-1);
243: sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
245: temp1 = lambda/(lambda + one);
247: /* Get ghost points */
248: DAGetCorners(user->fine.da,&xs,&ys,0,&xm,&ym,0);
249: DAGetGhostCorners(user->fine.da,&Xs,&Ys,0,&Xm,&Ym,0);
250: VecGetArray(localX,&x);
252: /* Compute initial guess */
253: for (j=ys; j<ys+ym; j++) {
254: temp = (double)(PetscMin(j,my-j-1))*hy;
255: for (i=xs; i<xs+xm; i++) {
256: row = i - Xs + (j - Ys)*Xm;
257: if (i == 0 || j == 0 || i == mx-1 || j == my-1 ) {
258: x[row] = 0.0;
259: continue;
260: }
261: x[row] = temp1*sqrt( PetscMin( (double)(PetscMin(i,mx-i-1))*hx,temp) );
262: }
263: }
264: VecRestoreArray(localX,&x);
266: /* Insert values into global vector */
267: DALocalToGlobal(user->fine.da,localX,INSERT_VALUES,X);
268: return 0;
269: }
271: /* -------------------- Evaluate Function F(x) --------------------- */
274: int FormFunction(SNES snes,Vec X,Vec F,void *ptr)
275: {
276: AppCtx *user = (AppCtx *) ptr;
277: int ierr, i, j, row, mx, my, xs, ys, xm, ym, Xs, Ys, Xm, Ym;
278: double two = 2.0, one = 1.0, lambda,hx, hy, hxdhy, hydhx,sc;
279: PetscScalar u, uxx, uyy, *x,*f;
280: Vec localX = user->fine.localX, localF = user->fine.localF;
282: mx = user->fine.mx; my = user->fine.my; lambda = user->param;
283: hx = one/(double)(mx-1); hy = one/(double)(my-1);
284: sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
286: /* Get ghost points */
287: DAGlobalToLocalBegin(user->fine.da,X,INSERT_VALUES,localX);
288: DAGlobalToLocalEnd(user->fine.da,X,INSERT_VALUES,localX);
289: DAGetCorners(user->fine.da,&xs,&ys,0,&xm,&ym,0);
290: DAGetGhostCorners(user->fine.da,&Xs,&Ys,0,&Xm,&Ym,0);
291: VecGetArray(localX,&x);
292: VecGetArray(localF,&f);
294: /* Evaluate function */
295: for (j=ys; j<ys+ym; j++) {
296: row = (j - Ys)*Xm + xs - Xs - 1;
297: for (i=xs; i<xs+xm; i++) {
298: row++;
299: if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
300: u = x[row];
301: uxx = (two*u - x[row-1] - x[row+1])*hydhx;
302: uyy = (two*u - x[row-Xm] - x[row+Xm])*hxdhy;
303: f[row] = uxx + uyy - sc*exp(u);
304: } else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)){
305: f[row] = .5*two*(hydhx + hxdhy)*x[row];
306: } else {
307: f[row] = .25*two*(hydhx + hxdhy)*x[row];
308: }
309: }
310: }
311: VecRestoreArray(localX,&x);
312: VecRestoreArray(localF,&f);
314: /* Insert values into global vector */
315: DALocalToGlobal(user->fine.da,localF,INSERT_VALUES,F);
316: PetscLogFlops(11*ym*xm);
317: return 0;
318: }
320: /*
321: Computes the part of the Jacobian associated with this processor
322: */
325: int FormJacobian_Grid(AppCtx *user,GridCtx *grid,Vec X, Mat *J,Mat *B)
326: {
327: Mat jac = *J;
328: int ierr, i, j, row, mx, my, xs, ys, xm, ym, Xs, Ys, Xm, Ym, col[5];
329: int nloc, *ltog, grow;
330: PetscScalar two = 2.0, one = 1.0, lambda, v[5], hx, hy, hxdhy, hydhx, sc, *x, value;
331: Vec localX = grid->localX;
333: mx = grid->mx; my = grid->my; lambda = user->param;
334: hx = one/(double)(mx-1); hy = one/(double)(my-1);
335: sc = hx*hy; hxdhy = hx/hy; hydhx = hy/hx;
337: /* Get ghost points */
338: DAGlobalToLocalBegin(grid->da,X,INSERT_VALUES,localX);
339: DAGlobalToLocalEnd(grid->da,X,INSERT_VALUES,localX);
340: DAGetCorners(grid->da,&xs,&ys,0,&xm,&ym,0);
341: DAGetGhostCorners(grid->da,&Xs,&Ys,0,&Xm,&Ym,0);
342: DAGetGlobalIndices(grid->da,&nloc,<og);
343: VecGetArray(localX,&x);
345: /* Evaluate Jacobian of function */
346: for (j=ys; j<ys+ym; j++) {
347: row = (j - Ys)*Xm + xs - Xs - 1;
348: for (i=xs; i<xs+xm; i++) {
349: row++;
350: grow = ltog[row];
351: if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
352: v[0] = -hxdhy; col[0] = ltog[row - Xm];
353: v[1] = -hydhx; col[1] = ltog[row - 1];
354: v[2] = two*(hydhx + hxdhy) - sc*lambda*exp(x[row]); col[2] = grow;
355: v[3] = -hydhx; col[3] = ltog[row + 1];
356: v[4] = -hxdhy; col[4] = ltog[row + Xm];
357: MatSetValues(jac,1,&grow,5,col,v,INSERT_VALUES);
358: } else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)){
359: value = .5*two*(hydhx + hxdhy);
360: MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
361: } else {
362: value = .25*two*(hydhx + hxdhy);
363: MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
364: }
365: }
366: }
367: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
368: VecRestoreArray(localX,&x);
369: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
371: return 0;
372: }
374: /*
375: Computes the ENTIRE Jacobian associated with the ENTIRE grid sequentially
376: This is for generating the coarse grid redundantly.
378: This is BAD code duplication, since the bulk of this routine is the
379: same as the routine above
381: Note the numbering of the rows/columns is the NATURAL numbering
382: */
385: int FormJacobian_Coarse(AppCtx *user,GridCtx *grid,Vec X, Mat *J,Mat *B)
386: {
387: Mat jac = *J;
388: int ierr, i, j, row, mx, my, col[5];
389: PetscScalar two = 2.0, one = 1.0, lambda, v[5], hx, hy, hxdhy, hydhx, sc, *x, value;
391: mx = grid->mx; my = grid->my; lambda = user->param;
392: hx = one/(double)(mx-1); hy = one/(double)(my-1);
393: sc = hx*hy; hxdhy = hx/hy; hydhx = hy/hx;
395: VecGetArray(X,&x);
397: /* Evaluate Jacobian of function */
398: for (j=0; j<my; j++) {
399: row = j*mx - 1;
400: for (i=0; i<mx; i++) {
401: row++;
402: if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
403: v[0] = -hxdhy; col[0] = row - mx;
404: v[1] = -hydhx; col[1] = row - 1;
405: v[2] = two*(hydhx + hxdhy) - sc*lambda*exp(x[row]); col[2] = row;
406: v[3] = -hydhx; col[3] = row + 1;
407: v[4] = -hxdhy; col[4] = row + mx;
408: MatSetValues(jac,1,&row,5,col,v,INSERT_VALUES);
409: } else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)){
410: value = .5*two*(hydhx + hxdhy);
411: MatSetValues(jac,1,&row,1,&row,&value,INSERT_VALUES);
412: } else {
413: value = .25*two*(hydhx + hxdhy);
414: MatSetValues(jac,1,&row,1,&row,&value,INSERT_VALUES);
415: }
416: }
417: }
418: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
419: VecRestoreArray(X,&x);
420: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
422: return 0;
423: }
425: /* -------------------- Evaluate Jacobian F'(x) --------------------- */
428: int FormJacobian(SNES snes,Vec X,Mat *J,Mat *B,MatStructure *flag,void *ptr)
429: {
430: AppCtx *user = (AppCtx *) ptr;
431: int ierr;
432: SLES sles;
433: PC pc;
434: PetscTruth ismg;
436: *flag = SAME_NONZERO_PATTERN;
437: FormJacobian_Grid(user,&user->fine,X,J,B);
439: /* create coarse grid jacobian for preconditioner */
440: SNESGetSLES(snes,&sles);
441: SLESGetPC(sles,&pc);
442:
443: PetscTypeCompare((PetscObject)pc,PCMG,&ismg);
444: if (ismg) {
446: SLESSetOperators(user->sles_fine,user->fine.J,user->fine.J,SAME_NONZERO_PATTERN);
448: /* restrict X to coarse grid */
449: MatMult(user->R,X,user->coarse.x);
450: VecPointwiseMult(user->Rscale,user->coarse.x,user->coarse.x);
452: /* form Jacobian on coarse grid */
453: if (user->redundant_build) {
454: /* get copy of coarse X onto each processor */
455: VecScatterBegin(user->coarse.x,user->localall,INSERT_VALUES,SCATTER_FORWARD,user->tolocalall);
456: VecScatterEnd(user->coarse.x,user->localall,INSERT_VALUES,SCATTER_FORWARD,user->tolocalall);
457: FormJacobian_Coarse(user,&user->coarse,user->localall,&user->coarse.J,&user->coarse.J);
459: } else {
460: /* coarse grid Jacobian computed in parallel */
461: FormJacobian_Grid(user,&user->coarse,user->coarse.x,&user->coarse.J,&user->coarse.J);
462: }
463: SLESSetOperators(user->sles_coarse,user->coarse.J,user->coarse.J,SAME_NONZERO_PATTERN);
464: }
466: return 0;
467: }
472: /*
473: Forms the interpolation (and restriction) operator from
474: coarse grid to fine.
475: */
476: int FormInterpolation(AppCtx *user)
477: {
478: int ierr,i,j,i_start,m_fine,j_start,m,n,M,Mx = user->coarse.mx,My = user->coarse.my,*idx;
479: int m_ghost,n_ghost,*idx_c,m_ghost_c,n_ghost_c,m_coarse;
480: int row,i_start_ghost,j_start_ghost,cols[4],mx = user->fine.mx, m_c,my = user->fine.my;
481: int c0,c1,c2,c3,nc,ratio = user->ratio,i_end,i_end_ghost,m_c_local,m_fine_local;
482: int i_c,j_c,i_start_c,j_start_c,n_c,i_start_ghost_c,j_start_ghost_c,col;
483: PetscScalar v[4],x,y, one = 1.0;
484: Mat mat;
485: Vec Rscale;
486:
487: DAGetCorners(user->fine.da,&i_start,&j_start,0,&m,&n,0);
488: DAGetGhostCorners(user->fine.da,&i_start_ghost,&j_start_ghost,0,&m_ghost,&n_ghost,0);
489: DAGetGlobalIndices(user->fine.da,PETSC_NULL,&idx);
491: DAGetCorners(user->coarse.da,&i_start_c,&j_start_c,0,&m_c,&n_c,0);
492: DAGetGhostCorners(user->coarse.da,&i_start_ghost_c,&j_start_ghost_c,0,&m_ghost_c,&n_ghost_c,0);
493: DAGetGlobalIndices(user->coarse.da,PETSC_NULL,&idx_c);
495: /* create interpolation matrix */
496: VecGetLocalSize(user->fine.x,&m_fine_local);
497: VecGetLocalSize(user->coarse.x,&m_c_local);
498: VecGetSize(user->fine.x,&m_fine);
499: VecGetSize(user->coarse.x,&m_coarse);
500: MatCreateMPIAIJ(PETSC_COMM_WORLD,m_fine_local,m_c_local,m_fine,m_coarse,
501: 5,0,3,0,&mat);
503: /* loop over local fine grid nodes setting interpolation for those*/
504: for ( j=j_start; j<j_start+n; j++ ) {
505: for ( i=i_start; i<i_start+m; i++ ) {
506: /* convert to local "natural" numbering and then to PETSc global numbering */
507: row = idx[m_ghost*(j-j_start_ghost) + (i-i_start_ghost)];
509: i_c = (i/ratio); /* coarse grid node to left of fine grid node */
510: j_c = (j/ratio); /* coarse grid node below fine grid node */
512: /*
513: Only include those interpolation points that are truly
514: nonzero. Note this is very important for final grid lines
515: in x and y directions; since they have no right/top neighbors
516: */
517: x = ((double)(i - i_c*ratio))/((double)ratio);
518: y = ((double)(j - j_c*ratio))/((double)ratio);
519: /* printf("i j %d %d %g %g\n",i,j,x,y); */
520: nc = 0;
521: /* one left and below; or we are right on it */
522: if (j_c < j_start_ghost_c || j_c > j_start_ghost_c+n_ghost_c) {
523: SETERRQ3(1,"Sorry j %d %d %d",j_c,j_start_ghost_c,j_start_ghost_c+n_ghost_c);
524: }
525: if (i_c < i_start_ghost_c || i_c > i_start_ghost_c+m_ghost_c) {
526: SETERRQ3(1,"Sorry i %d %d %d",i_c,i_start_ghost_c,i_start_ghost_c+m_ghost_c);
527: }
528: col = m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c);
529: cols[nc] = idx_c[col];
530: v[nc++] = x*y - x - y + 1.0;
531: /* one right and below */
532: if (i_c*ratio != i) {
533: cols[nc] = idx_c[col+1];
534: v[nc++] = -x*y + x;
535: }
536: /* one left and above */
537: if (j_c*ratio != j) {
538: cols[nc] = idx_c[col+m_ghost_c];
539: v[nc++] = -x*y + y;
540: }
541: /* one right and above */
542: if (j_c*ratio != j && i_c*ratio != i) {
543: cols[nc] = idx_c[col+m_ghost_c+1];
544: v[nc++] = x*y;
545: }
546: MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);
547: }
548: }
549: MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);
550: MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);
552: VecDuplicate(user->coarse.x,&Rscale);
553: VecSet(&one,user->fine.x);
554: MatMultTranspose(mat,user->fine.x,Rscale);
555: VecReciprocal(Rscale);
556: user->Rscale = Rscale;
557: user->R = mat;
558: return 0;
559: }