Actual source code: ex17.c
petsc-3.5.4 2015-05-23
1: static const char help[] = "Newton's method to solve a two-variable system, sequentially.\n"
2: "The same problem is solved twice - i) fully assembled system + ii) block system\n\n";
4: /*T
5: Concepts: SNES^basic uniprocessor example, block objects
6: Processors: 1
7: T*/
9: /*
10: Include "petscsnes.h" so that we can use SNES solvers. Note that this
11: file automatically includes:
12: petscsys.h - base PETSc routines petscvec.h - vectors
13: petscsys.h - system routines petscmat.h - matrices
14: petscis.h - index sets petscksp.h - Krylov subspace methods
15: petscviewer.h - viewers petscpc.h - preconditioners
16: petscksp.h - linear solvers
17: */
18: #include <petscsnes.h>
20: /*
21: This example is block version of the test found at
22: ${PETSC_DIR}/src/snes/examples/tutorials/ex1.c
23: In this test we replace the Jacobian systems
24: [J]{x} = {F}
25: where
27: [J] = (j_00, j_01), {x} = (x_0, x_1)^T, {F} = (f_0, f_1)^T
28: (j_10, j_11)
29: where [J] \in \mathbb^{2 \times 2}, {x},{F} \in \mathbb^{2 \times 1},
31: with a block system in which each block is of length 1.
32: i.e. The block system is thus
34: [J] = ([j00], [j01]), {x} = ({x0}, {x1})^T, {F} = ({f0}, {f1})^T
35: ([j10], [j11])
36: where
37: [j00], [j01], [j10], [j11] \in \mathbb^{1 \times 1}
38: {x0}, {x1}, {f0}, {f1} \in \mathbb^{1 \times 1}
40: In practice we would not bother defing blocks of size one, and would instead assemble the
41: full system. This is just a simple test to illustrate how to manipulate the blocks and
42: to confirm the implementation is correct.
43: */
45: /*
46: User-defined routines
47: */
48: static PetscErrorCode FormJacobian1(SNES,Vec,Mat,Mat,void*);
49: static PetscErrorCode FormFunction1(SNES,Vec,Vec,void*);
50: static PetscErrorCode FormJacobian2(SNES,Vec,Mat,Mat,void*);
51: static PetscErrorCode FormFunction2(SNES,Vec,Vec,void*);
52: static PetscErrorCode FormJacobian1_block(SNES,Vec,Mat,Mat,void*);
53: static PetscErrorCode FormFunction1_block(SNES,Vec,Vec,void*);
54: static PetscErrorCode FormJacobian2_block(SNES,Vec,Mat,Mat,void*);
55: static PetscErrorCode FormFunction2_block(SNES,Vec,Vec,void*);
60: static PetscErrorCode assembled_system(void)
61: {
62: SNES snes; /* nonlinear solver context */
63: KSP ksp; /* linear solver context */
64: PC pc; /* preconditioner context */
65: Vec x,r; /* solution, residual vectors */
66: Mat J; /* Jacobian matrix */
68: PetscInt its;
69: PetscScalar pfive = .5,*xx;
70: PetscBool flg;
73: PetscPrintf(PETSC_COMM_WORLD, "\n\n========================= Assembled system =========================\n\n");
75: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
76: Create nonlinear solver context
77: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
79: SNESCreate(PETSC_COMM_WORLD,&snes);
81: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
82: Create matrix and vector data structures; set corresponding routines
83: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
85: /*
86: Create vectors for solution and nonlinear function
87: */
88: VecCreateSeq(PETSC_COMM_SELF,2,&x);
89: VecDuplicate(x,&r);
91: /*
92: Create Jacobian matrix data structure
93: */
94: MatCreate(PETSC_COMM_SELF,&J);
95: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,2,2);
96: MatSetFromOptions(J);
97: MatSetUp(J);
99: PetscOptionsHasName(NULL,"-hard",&flg);
100: if (!flg) {
101: /*
102: Set function evaluation routine and vector.
103: */
104: SNESSetFunction(snes,r,FormFunction1,NULL);
106: /*
107: Set Jacobian matrix data structure and Jacobian evaluation routine
108: */
109: SNESSetJacobian(snes,J,J,FormJacobian1,NULL);
110: } else {
111: SNESSetFunction(snes,r,FormFunction2,NULL);
112: SNESSetJacobian(snes,J,J,FormJacobian2,NULL);
113: }
115: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116: Customize nonlinear solver; set runtime options
117: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
119: /*
120: Set linear solver defaults for this problem. By extracting the
121: KSP, KSP, and PC contexts from the SNES context, we can then
122: directly call any KSP, KSP, and PC routines to set various options.
123: */
124: SNESGetKSP(snes,&ksp);
125: KSPGetPC(ksp,&pc);
126: PCSetType(pc,PCNONE);
127: KSPSetTolerances(ksp,1.e-4,PETSC_DEFAULT,PETSC_DEFAULT,20);
129: /*
130: Set SNES/KSP/KSP/PC runtime options, e.g.,
131: -snes_view -snes_monitor -ksp_type <ksp> -pc_type <pc>
132: These options will override those specified above as long as
133: SNESSetFromOptions() is called _after_ any other customization
134: routines.
135: */
136: SNESSetFromOptions(snes);
138: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139: Evaluate initial guess; then solve nonlinear system
140: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
141: if (!flg) {
142: VecSet(x,pfive);
143: } else {
144: VecGetArray(x,&xx);
145: xx[0] = 2.0; xx[1] = 3.0;
146: VecRestoreArray(x,&xx);
147: }
148: /*
149: Note: The user should initialize the vector, x, with the initial guess
150: for the nonlinear solver prior to calling SNESSolve(). In particular,
151: to employ an initial guess of zero, the user should explicitly set
152: this vector to zero by calling VecSet().
153: */
155: SNESSolve(snes,NULL,x);
156: SNESGetIterationNumber(snes,&its);
157: if (flg) {
158: Vec f;
159: VecView(x,PETSC_VIEWER_STDOUT_WORLD);
160: SNESGetFunction(snes,&f,0,0);
161: VecView(r,PETSC_VIEWER_STDOUT_WORLD);
162: }
164: PetscPrintf(PETSC_COMM_SELF,"number of SNES iterations = %D\n\n",its);
166: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: Free work space. All PETSc objects should be destroyed when they
168: are no longer needed.
169: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
171: VecDestroy(&x); VecDestroy(&r);
172: MatDestroy(&J); SNESDestroy(&snes);
173: return(0);
174: }
176: /* ------------------------------------------------------------------- */
179: /*
180: FormFunction1 - Evaluates nonlinear function, F(x).
182: Input Parameters:
183: . snes - the SNES context
184: . x - input vector
185: . dummy - optional user-defined context (not used here)
187: Output Parameter:
188: . f - function vector
189: */
190: static PetscErrorCode FormFunction1(SNES snes,Vec x,Vec f,void *dummy)
191: {
193: PetscScalar *xx,*ff;
196: /*
197: Get pointers to vector data.
198: - For default PETSc vectors, VecGetArray() returns a pointer to
199: the data array. Otherwise, the routine is implementation dependent.
200: - You MUST call VecRestoreArray() when you no longer need access to
201: the array.
202: */
203: VecGetArray(x,&xx);
204: VecGetArray(f,&ff);
206: /*
207: Compute function
208: */
209: ff[0] = xx[0]*xx[0] + xx[0]*xx[1] - 3.0;
210: ff[1] = xx[0]*xx[1] + xx[1]*xx[1] - 6.0;
213: /*
214: Restore vectors
215: */
216: VecRestoreArray(x,&xx);
217: VecRestoreArray(f,&ff);
218: return(0);
219: }
220: /* ------------------------------------------------------------------- */
223: /*
224: FormJacobian1 - Evaluates Jacobian matrix.
226: Input Parameters:
227: . snes - the SNES context
228: . x - input vector
229: . dummy - optional user-defined context (not used here)
231: Output Parameters:
232: . jac - Jacobian matrix
233: . B - optionally different preconditioning matrix
234: . flag - flag indicating matrix structure
235: */
236: static PetscErrorCode FormJacobian1(SNES snes,Vec x,Mat jac,Mat B,void *dummy)
237: {
238: PetscScalar *xx,A[4];
240: PetscInt idx[2] = {0,1};
243: /*
244: Get pointer to vector data
245: */
246: VecGetArray(x,&xx);
248: /*
249: Compute Jacobian entries and insert into matrix.
250: - Since this is such a small problem, we set all entries for
251: the matrix at once.
252: */
253: A[0] = 2.0*xx[0] + xx[1]; A[1] = xx[0];
254: A[2] = xx[1]; A[3] = xx[0] + 2.0*xx[1];
255: MatSetValues(jac,2,idx,2,idx,A,INSERT_VALUES);
257: /*
258: Restore vector
259: */
260: VecRestoreArray(x,&xx);
262: /*
263: Assemble matrix
264: */
265: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
266: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
267: return(0);
268: }
271: /* ------------------------------------------------------------------- */
274: static PetscErrorCode FormFunction2(SNES snes,Vec x,Vec f,void *dummy)
275: {
277: PetscScalar *xx,*ff;
280: /*
281: Get pointers to vector data.
282: - For default PETSc vectors, VecGetArray() returns a pointer to
283: the data array. Otherwise, the routine is implementation dependent.
284: - You MUST call VecRestoreArray() when you no longer need access to
285: the array.
286: */
287: VecGetArray(x,&xx);
288: VecGetArray(f,&ff);
290: /*
291: Compute function
292: */
293: ff[0] = PetscSinScalar(3.0*xx[0]) + xx[0];
294: ff[1] = xx[1];
296: /*
297: Restore vectors
298: */
299: VecRestoreArray(x,&xx);
300: VecRestoreArray(f,&ff);
301: return(0);
302: }
304: /* ------------------------------------------------------------------- */
307: static PetscErrorCode FormJacobian2(SNES snes,Vec x,Mat jac,Mat B,void *dummy)
308: {
309: PetscScalar *xx,A[4];
311: PetscInt idx[2] = {0,1};
314: /*
315: Get pointer to vector data
316: */
317: VecGetArray(x,&xx);
319: /*
320: Compute Jacobian entries and insert into matrix.
321: - Since this is such a small problem, we set all entries for
322: the matrix at once.
323: */
324: A[0] = 3.0*PetscCosScalar(3.0*xx[0]) + 1.0; A[1] = 0.0;
325: A[2] = 0.0; A[3] = 1.0;
326: MatSetValues(jac,2,idx,2,idx,A,INSERT_VALUES);
328: /*
329: Restore vector
330: */
331: VecRestoreArray(x,&xx);
333: /*
334: Assemble matrix
335: */
336: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
337: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
338: return(0);
339: }
343: static int block_system(void)
344: {
345: SNES snes; /* nonlinear solver context */
346: KSP ksp; /* linear solver context */
347: PC pc; /* preconditioner context */
348: Vec x,r; /* solution, residual vectors */
349: Mat J; /* Jacobian matrix */
351: PetscInt its;
352: PetscScalar pfive = .5;
353: PetscBool flg;
355: Mat j11, j12, j21, j22;
356: Vec x1, x2, r1, r2;
357: Vec bv;
358: Vec bx[2];
359: Mat bA[2][2];
362: PetscPrintf(PETSC_COMM_WORLD, "\n\n========================= Block system =========================\n\n");
364: SNESCreate(PETSC_COMM_WORLD,&snes);
366: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
367: Create matrix and vector data structures; set corresponding routines
368: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
370: /*
371: Create sub vectors for solution and nonlinear function
372: */
373: VecCreateSeq(PETSC_COMM_SELF,1,&x1);
374: VecDuplicate(x1,&r1);
376: VecCreateSeq(PETSC_COMM_SELF,1,&x2);
377: VecDuplicate(x2,&r2);
379: /*
380: Create the block vectors
381: */
382: bx[0] = x1;
383: bx[1] = x2;
384: VecCreateNest(PETSC_COMM_WORLD,2,NULL,bx,&x);
385: VecAssemblyBegin(x);
386: VecAssemblyEnd(x);
387: VecDestroy(&x1);
388: VecDestroy(&x2);
390: bx[0] = r1;
391: bx[1] = r2;
392: VecCreateNest(PETSC_COMM_WORLD,2,NULL,bx,&r);
393: VecDestroy(&r1);
394: VecDestroy(&r2);
395: VecAssemblyBegin(r);
396: VecAssemblyEnd(r);
398: /*
399: Create sub Jacobian matrix data structure
400: */
401: MatCreate(PETSC_COMM_WORLD, &j11);
402: MatSetSizes(j11, 1, 1, 1, 1);
403: MatSetType(j11, MATSEQAIJ);
404: MatSetUp(j11);
406: MatCreate(PETSC_COMM_WORLD, &j12);
407: MatSetSizes(j12, 1, 1, 1, 1);
408: MatSetType(j12, MATSEQAIJ);
409: MatSetUp(j12);
411: MatCreate(PETSC_COMM_WORLD, &j21);
412: MatSetSizes(j21, 1, 1, 1, 1);
413: MatSetType(j21, MATSEQAIJ);
414: MatSetUp(j21);
416: MatCreate(PETSC_COMM_WORLD, &j22);
417: MatSetSizes(j22, PETSC_DECIDE, PETSC_DECIDE, 1, 1);
418: MatSetType(j22, MATSEQAIJ);
419: MatSetUp(j22);
420: /*
421: Create block Jacobian matrix data structure
422: */
423: bA[0][0] = j11;
424: bA[0][1] = j12;
425: bA[1][0] = j21;
426: bA[1][1] = j22;
428: MatCreateNest(PETSC_COMM_WORLD,2,NULL,2,NULL,&bA[0][0],&J);
429: MatSetUp(J);
430: MatNestSetVecType(J,VECNEST);
431: MatDestroy(&j11);
432: MatDestroy(&j12);
433: MatDestroy(&j21);
434: MatDestroy(&j22);
436: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
437: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
439: PetscOptionsHasName(NULL,"-hard",&flg);
440: if (!flg) {
441: /*
442: Set function evaluation routine and vector.
443: */
444: SNESSetFunction(snes,r,FormFunction1_block,NULL);
446: /*
447: Set Jacobian matrix data structure and Jacobian evaluation routine
448: */
449: SNESSetJacobian(snes,J,J,FormJacobian1_block,NULL);
450: } else {
451: SNESSetFunction(snes,r,FormFunction2_block,NULL);
452: SNESSetJacobian(snes,J,J,FormJacobian2_block,NULL);
453: }
455: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
456: Customize nonlinear solver; set runtime options
457: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
459: /*
460: Set linear solver defaults for this problem. By extracting the
461: KSP, KSP, and PC contexts from the SNES context, we can then
462: directly call any KSP, KSP, and PC routines to set various options.
463: */
464: SNESGetKSP(snes,&ksp);
465: KSPGetPC(ksp,&pc);
466: PCSetType(pc,PCNONE);
467: KSPSetTolerances(ksp,1.e-4,PETSC_DEFAULT,PETSC_DEFAULT,20);
469: /*
470: Set SNES/KSP/KSP/PC runtime options, e.g.,
471: -snes_view -snes_monitor -ksp_type <ksp> -pc_type <pc>
472: These options will override those specified above as long as
473: SNESSetFromOptions() is called _after_ any other customization
474: routines.
475: */
476: SNESSetFromOptions(snes);
478: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
479: Evaluate initial guess; then solve nonlinear system
480: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
481: if (!flg) {
482: VecSet(x,pfive);
483: } else {
484: Vec *vecs;
485: VecNestGetSubVecs(x, NULL, &vecs);
486: bv = vecs[0];
487: /* VecBlockGetSubVec(x, 0, &bv); */
488: VecSetValue(bv, 0, 2.0, INSERT_VALUES); /* xx[0] = 2.0; */
489: VecAssemblyBegin(bv);
490: VecAssemblyEnd(bv);
492: /* VecBlockGetSubVec(x, 1, &bv); */
493: bv = vecs[1];
494: VecSetValue(bv, 0, 3.0, INSERT_VALUES); /* xx[1] = 3.0; */
495: VecAssemblyBegin(bv);
496: VecAssemblyEnd(bv);
497: }
498: /*
499: Note: The user should initialize the vector, x, with the initial guess
500: for the nonlinear solver prior to calling SNESSolve(). In particular,
501: to employ an initial guess of zero, the user should explicitly set
502: this vector to zero by calling VecSet().
503: */
504: SNESSolve(snes,NULL,x);
505: SNESGetIterationNumber(snes,&its);
506: if (flg) {
507: Vec f;
508: VecView(x,PETSC_VIEWER_STDOUT_WORLD);
509: SNESGetFunction(snes,&f,0,0);
510: VecView(r,PETSC_VIEWER_STDOUT_WORLD);
511: }
513: PetscPrintf(PETSC_COMM_SELF,"number of SNES iterations = %D\n\n",its);
515: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
516: Free work space. All PETSc objects should be destroyed when they
517: are no longer needed.
518: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
519: VecDestroy(&x); VecDestroy(&r);
520: MatDestroy(&J); SNESDestroy(&snes);
521: return(0);
522: }
524: /* ------------------------------------------------------------------- */
527: static PetscErrorCode FormFunction1_block(SNES snes,Vec x,Vec f,void *dummy)
528: {
529: Vec *xx, *ff, x1,x2, f1,f2;
530: PetscScalar ff_0, ff_1;
531: PetscScalar xx_0, xx_1;
532: PetscInt index,nb;
536: /* get blocks for function */
537: VecNestGetSubVecs(f, &nb, &ff);
538: f1 = ff[0]; f2 = ff[1];
540: /* get blocks for solution */
541: VecNestGetSubVecs(x, &nb, &xx);
542: x1 = xx[0]; x2 = xx[1];
544: /* get solution values */
545: index = 0;
546: VecGetValues(x1,1, &index, &xx_0);
547: VecGetValues(x2,1, &index, &xx_1);
549: /* Compute function */
550: ff_0 = xx_0*xx_0 + xx_0*xx_1 - 3.0;
551: ff_1 = xx_0*xx_1 + xx_1*xx_1 - 6.0;
553: /* set function values */
554: VecSetValue(f1, index, ff_0, INSERT_VALUES);
556: VecSetValue(f2, index, ff_1, INSERT_VALUES);
558: VecAssemblyBegin(f);
559: VecAssemblyEnd(f);
560: return(0);
561: }
563: /* ------------------------------------------------------------------- */
566: static PetscErrorCode FormJacobian1_block(SNES snes,Vec x,Mat jac,Mat B,void *dummy)
567: {
568: Vec *xx, x1,x2;
569: PetscScalar xx_0, xx_1;
570: PetscInt index,nb;
571: PetscScalar A_00, A_01, A_10, A_11;
572: Mat j11, j12, j21, j22;
573: Mat **mats;
577: /* get blocks for solution */
578: VecNestGetSubVecs(x, &nb, &xx);
579: x1 = xx[0]; x2 = xx[1];
581: /* get solution values */
582: index = 0;
583: VecGetValues(x1,1, &index, &xx_0);
584: VecGetValues(x2,1, &index, &xx_1);
586: /* get block matrices */
587: MatNestGetSubMats(jac,NULL,NULL,&mats);
588: j11 = mats[0][0];
589: j12 = mats[0][1];
590: j21 = mats[1][0];
591: j22 = mats[1][1];
593: /* compute jacobian entries */
594: A_00 = 2.0*xx_0 + xx_1;
595: A_01 = xx_0;
596: A_10 = xx_1;
597: A_11 = xx_0 + 2.0*xx_1;
599: /* set jacobian values */
600: MatSetValue(j11, 0,0, A_00, INSERT_VALUES);
601: MatSetValue(j12, 0,0, A_01, INSERT_VALUES);
602: MatSetValue(j21, 0,0, A_10, INSERT_VALUES);
603: MatSetValue(j22, 0,0, A_11, INSERT_VALUES);
605: /* Assemble sub matrix */
606: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
607: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
608: return(0);
609: }
611: /* ------------------------------------------------------------------- */
614: static PetscErrorCode FormFunction2_block(SNES snes,Vec x,Vec f,void *dummy)
615: {
617: PetscScalar *xx,*ff;
620: /*
621: Get pointers to vector data.
622: - For default PETSc vectors, VecGetArray() returns a pointer to
623: the data array. Otherwise, the routine is implementation dependent.
624: - You MUST call VecRestoreArray() when you no longer need access to
625: the array.
626: */
627: VecGetArray(x,&xx);
628: VecGetArray(f,&ff);
630: /*
631: Compute function
632: */
633: ff[0] = PetscSinScalar(3.0*xx[0]) + xx[0];
634: ff[1] = xx[1];
636: /*
637: Restore vectors
638: */
639: VecRestoreArray(x,&xx);
640: VecRestoreArray(f,&ff);
641: return(0);
642: }
644: /* ------------------------------------------------------------------- */
647: static PetscErrorCode FormJacobian2_block(SNES snes,Vec x,Mat jac,Mat B,void *dummy)
648: {
649: PetscScalar *xx,A[4];
651: PetscInt idx[2] = {0,1};
654: /*
655: Get pointer to vector data
656: */
657: VecGetArray(x,&xx);
659: /*
660: Compute Jacobian entries and insert into matrix.
661: - Since this is such a small problem, we set all entries for
662: the matrix at once.
663: */
664: A[0] = 3.0*PetscCosScalar(3.0*xx[0]) + 1.0; A[1] = 0.0;
665: A[2] = 0.0; A[3] = 1.0;
666: MatSetValues(jac,2,idx,2,idx,A,INSERT_VALUES);
668: /*
669: Restore vector
670: */
671: VecRestoreArray(x,&xx);
673: /*
674: Assemble matrix
675: */
676: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
677: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
678: return(0);
679: }
683: int main(int argc,char **argv)
684: {
685: PetscMPIInt size;
688: PetscInitialize(&argc,&argv,(char*)0,help);
690: MPI_Comm_size(PETSC_COMM_WORLD,&size);
691: if (size != 1) SETERRQ(PETSC_COMM_WORLD, 1,"This is a uniprocessor example only!");
693: assembled_system();
695: block_system();
697: PetscFinalize();
698: return 0;
699: }