Actual source code: ex17.c
petsc-3.4.5 2014-06-29
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*,MatStructure*,void*);
49: static PetscErrorCode FormFunction1(SNES,Vec,Vec,void*);
50: static PetscErrorCode FormJacobian2(SNES,Vec,Mat*,Mat*,MatStructure*,void*);
51: static PetscErrorCode FormFunction2(SNES,Vec,Vec,void*);
52: static PetscErrorCode FormJacobian1_block(SNES,Vec,Mat*,Mat*,MatStructure*,void*);
53: static PetscErrorCode FormFunction1_block(SNES,Vec,Vec,void*);
54: static PetscErrorCode FormJacobian2_block(SNES,Vec,Mat*,Mat*,MatStructure*,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,MatStructure *flag,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);
256: *flag = SAME_NONZERO_PATTERN;
258: /*
259: Restore vector
260: */
261: VecRestoreArray(x,&xx);
263: /*
264: Assemble matrix
265: */
266: MatAssemblyBegin(*jac,MAT_FINAL_ASSEMBLY);
267: MatAssemblyEnd(*jac,MAT_FINAL_ASSEMBLY);
268: return(0);
269: }
272: /* ------------------------------------------------------------------- */
275: static PetscErrorCode FormFunction2(SNES snes,Vec x,Vec f,void *dummy)
276: {
278: PetscScalar *xx,*ff;
281: /*
282: Get pointers to vector data.
283: - For default PETSc vectors, VecGetArray() returns a pointer to
284: the data array. Otherwise, the routine is implementation dependent.
285: - You MUST call VecRestoreArray() when you no longer need access to
286: the array.
287: */
288: VecGetArray(x,&xx);
289: VecGetArray(f,&ff);
291: /*
292: Compute function
293: */
294: ff[0] = PetscSinScalar(3.0*xx[0]) + xx[0];
295: ff[1] = xx[1];
297: /*
298: Restore vectors
299: */
300: VecRestoreArray(x,&xx);
301: VecRestoreArray(f,&ff);
302: return(0);
303: }
305: /* ------------------------------------------------------------------- */
308: static PetscErrorCode FormJacobian2(SNES snes,Vec x,Mat *jac,Mat *B,MatStructure *flag,void *dummy)
309: {
310: PetscScalar *xx,A[4];
312: PetscInt idx[2] = {0,1};
315: /*
316: Get pointer to vector data
317: */
318: VecGetArray(x,&xx);
320: /*
321: Compute Jacobian entries and insert into matrix.
322: - Since this is such a small problem, we set all entries for
323: the matrix at once.
324: */
325: A[0] = 3.0*PetscCosScalar(3.0*xx[0]) + 1.0; A[1] = 0.0;
326: A[2] = 0.0; A[3] = 1.0;
327: MatSetValues(*jac,2,idx,2,idx,A,INSERT_VALUES);
328: *flag = SAME_NONZERO_PATTERN;
330: /*
331: Restore vector
332: */
333: VecRestoreArray(x,&xx);
335: /*
336: Assemble matrix
337: */
338: MatAssemblyBegin(*jac,MAT_FINAL_ASSEMBLY);
339: MatAssemblyEnd(*jac,MAT_FINAL_ASSEMBLY);
340: return(0);
341: }
345: static int block_system(void)
346: {
347: SNES snes; /* nonlinear solver context */
348: KSP ksp; /* linear solver context */
349: PC pc; /* preconditioner context */
350: Vec x,r; /* solution, residual vectors */
351: Mat J; /* Jacobian matrix */
353: PetscInt its;
354: PetscScalar pfive = .5;
355: PetscBool flg;
357: Mat j11, j12, j21, j22;
358: Vec x1, x2, r1, r2;
359: Vec bv;
360: Vec bx[2];
361: Mat bA[2][2];
364: PetscPrintf(PETSC_COMM_WORLD, "\n\n========================= Block system =========================\n\n");
366: SNESCreate(PETSC_COMM_WORLD,&snes);
368: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
369: Create matrix and vector data structures; set corresponding routines
370: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
372: /*
373: Create sub vectors for solution and nonlinear function
374: */
375: VecCreateSeq(PETSC_COMM_SELF,1,&x1);
376: VecDuplicate(x1,&r1);
378: VecCreateSeq(PETSC_COMM_SELF,1,&x2);
379: VecDuplicate(x2,&r2);
381: /*
382: Create the block vectors
383: */
384: bx[0] = x1;
385: bx[1] = x2;
386: VecCreateNest(PETSC_COMM_WORLD,2,NULL,bx,&x);
387: VecAssemblyBegin(x);
388: VecAssemblyEnd(x);
389: VecDestroy(&x1);
390: VecDestroy(&x2);
392: bx[0] = r1;
393: bx[1] = r2;
394: VecCreateNest(PETSC_COMM_WORLD,2,NULL,bx,&r);
395: VecDestroy(&r1);
396: VecDestroy(&r2);
397: VecAssemblyBegin(r);
398: VecAssemblyEnd(r);
400: /*
401: Create sub Jacobian matrix data structure
402: */
403: MatCreate(PETSC_COMM_WORLD, &j11);
404: MatSetSizes(j11, 1, 1, 1, 1);
405: MatSetType(j11, MATSEQAIJ);
406: MatSetUp(j11);
408: MatCreate(PETSC_COMM_WORLD, &j12);
409: MatSetSizes(j12, 1, 1, 1, 1);
410: MatSetType(j12, MATSEQAIJ);
411: MatSetUp(j12);
413: MatCreate(PETSC_COMM_WORLD, &j21);
414: MatSetSizes(j21, 1, 1, 1, 1);
415: MatSetType(j21, MATSEQAIJ);
416: MatSetUp(j21);
418: MatCreate(PETSC_COMM_WORLD, &j22);
419: MatSetSizes(j22, PETSC_DECIDE, PETSC_DECIDE, 1, 1);
420: MatSetType(j22, MATSEQAIJ);
421: MatSetUp(j22);
422: /*
423: Create block Jacobian matrix data structure
424: */
425: bA[0][0] = j11;
426: bA[0][1] = j12;
427: bA[1][0] = j21;
428: bA[1][1] = j22;
430: MatCreateNest(PETSC_COMM_WORLD,2,NULL,2,NULL,&bA[0][0],&J);
431: MatSetUp(J);
432: MatNestSetVecType(J,VECNEST);
433: MatDestroy(&j11);
434: MatDestroy(&j12);
435: MatDestroy(&j21);
436: MatDestroy(&j22);
438: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
439: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
441: PetscOptionsHasName(NULL,"-hard",&flg);
442: if (!flg) {
443: /*
444: Set function evaluation routine and vector.
445: */
446: SNESSetFunction(snes,r,FormFunction1_block,NULL);
448: /*
449: Set Jacobian matrix data structure and Jacobian evaluation routine
450: */
451: SNESSetJacobian(snes,J,J,FormJacobian1_block,NULL);
452: } else {
453: SNESSetFunction(snes,r,FormFunction2_block,NULL);
454: SNESSetJacobian(snes,J,J,FormJacobian2_block,NULL);
455: }
457: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
458: Customize nonlinear solver; set runtime options
459: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
461: /*
462: Set linear solver defaults for this problem. By extracting the
463: KSP, KSP, and PC contexts from the SNES context, we can then
464: directly call any KSP, KSP, and PC routines to set various options.
465: */
466: SNESGetKSP(snes,&ksp);
467: KSPGetPC(ksp,&pc);
468: PCSetType(pc,PCNONE);
469: KSPSetTolerances(ksp,1.e-4,PETSC_DEFAULT,PETSC_DEFAULT,20);
471: /*
472: Set SNES/KSP/KSP/PC runtime options, e.g.,
473: -snes_view -snes_monitor -ksp_type <ksp> -pc_type <pc>
474: These options will override those specified above as long as
475: SNESSetFromOptions() is called _after_ any other customization
476: routines.
477: */
478: SNESSetFromOptions(snes);
480: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
481: Evaluate initial guess; then solve nonlinear system
482: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
483: if (!flg) {
484: VecSet(x,pfive);
485: } else {
486: Vec *vecs;
487: VecNestGetSubVecs(x, NULL, &vecs);
488: bv = vecs[0];
489: /* VecBlockGetSubVec(x, 0, &bv); */
490: VecSetValue(bv, 0, 2.0, INSERT_VALUES); /* xx[0] = 2.0; */
491: VecAssemblyBegin(bv);
492: VecAssemblyEnd(bv);
494: /* VecBlockGetSubVec(x, 1, &bv); */
495: bv = vecs[1];
496: VecSetValue(bv, 0, 3.0, INSERT_VALUES); /* xx[1] = 3.0; */
497: VecAssemblyBegin(bv);
498: VecAssemblyEnd(bv);
499: }
500: /*
501: Note: The user should initialize the vector, x, with the initial guess
502: for the nonlinear solver prior to calling SNESSolve(). In particular,
503: to employ an initial guess of zero, the user should explicitly set
504: this vector to zero by calling VecSet().
505: */
506: SNESSolve(snes,NULL,x);
507: SNESGetIterationNumber(snes,&its);
508: if (flg) {
509: Vec f;
510: VecView(x,PETSC_VIEWER_STDOUT_WORLD);
511: SNESGetFunction(snes,&f,0,0);
512: VecView(r,PETSC_VIEWER_STDOUT_WORLD);
513: }
515: PetscPrintf(PETSC_COMM_SELF,"number of SNES iterations = %D\n\n",its);
517: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
518: Free work space. All PETSc objects should be destroyed when they
519: are no longer needed.
520: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
521: VecDestroy(&x); VecDestroy(&r);
522: MatDestroy(&J); SNESDestroy(&snes);
523: return(0);
524: }
526: /* ------------------------------------------------------------------- */
529: static PetscErrorCode FormFunction1_block(SNES snes,Vec x,Vec f,void *dummy)
530: {
531: Vec *xx, *ff, x1,x2, f1,f2;
532: PetscScalar ff_0, ff_1;
533: PetscScalar xx_0, xx_1;
534: PetscInt index,nb;
538: /* get blocks for function */
539: VecNestGetSubVecs(f, &nb, &ff);
540: f1 = ff[0]; f2 = ff[1];
542: /* get blocks for solution */
543: VecNestGetSubVecs(x, &nb, &xx);
544: x1 = xx[0]; x2 = xx[1];
546: /* get solution values */
547: index = 0;
548: VecGetValues(x1,1, &index, &xx_0);
549: VecGetValues(x2,1, &index, &xx_1);
551: /* Compute function */
552: ff_0 = xx_0*xx_0 + xx_0*xx_1 - 3.0;
553: ff_1 = xx_0*xx_1 + xx_1*xx_1 - 6.0;
555: /* set function values */
556: VecSetValue(f1, index, ff_0, INSERT_VALUES);
558: VecSetValue(f2, index, ff_1, INSERT_VALUES);
560: VecAssemblyBegin(f);
561: VecAssemblyEnd(f);
562: return(0);
563: }
565: /* ------------------------------------------------------------------- */
568: static PetscErrorCode FormJacobian1_block(SNES snes,Vec x,Mat *jac,Mat *B,MatStructure *flag,void *dummy)
569: {
570: Vec *xx, x1,x2;
571: PetscScalar xx_0, xx_1;
572: PetscInt index,nb;
573: PetscScalar A_00, A_01, A_10, A_11;
574: Mat j11, j12, j21, j22;
575: Mat **mats;
579: /* get blocks for solution */
580: VecNestGetSubVecs(x, &nb, &xx);
581: x1 = xx[0]; x2 = xx[1];
583: /* get solution values */
584: index = 0;
585: VecGetValues(x1,1, &index, &xx_0);
586: VecGetValues(x2,1, &index, &xx_1);
588: /* get block matrices */
589: MatNestGetSubMats(*jac,NULL,NULL,&mats);
590: j11 = mats[0][0];
591: j12 = mats[0][1];
592: j21 = mats[1][0];
593: j22 = mats[1][1];
595: /* compute jacobian entries */
596: A_00 = 2.0*xx_0 + xx_1;
597: A_01 = xx_0;
598: A_10 = xx_1;
599: A_11 = xx_0 + 2.0*xx_1;
601: /* set jacobian values */
602: MatSetValue(j11, 0,0, A_00, INSERT_VALUES);
603: MatSetValue(j12, 0,0, A_01, INSERT_VALUES);
604: MatSetValue(j21, 0,0, A_10, INSERT_VALUES);
605: MatSetValue(j22, 0,0, A_11, INSERT_VALUES);
607: *flag = SAME_NONZERO_PATTERN;
609: /* Assemble sub matrix */
610: MatAssemblyBegin(*jac,MAT_FINAL_ASSEMBLY);
611: MatAssemblyEnd(*jac,MAT_FINAL_ASSEMBLY);
612: return(0);
613: }
615: /* ------------------------------------------------------------------- */
618: static PetscErrorCode FormFunction2_block(SNES snes,Vec x,Vec f,void *dummy)
619: {
621: PetscScalar *xx,*ff;
624: /*
625: Get pointers to vector data.
626: - For default PETSc vectors, VecGetArray() returns a pointer to
627: the data array. Otherwise, the routine is implementation dependent.
628: - You MUST call VecRestoreArray() when you no longer need access to
629: the array.
630: */
631: VecGetArray(x,&xx);
632: VecGetArray(f,&ff);
634: /*
635: Compute function
636: */
637: ff[0] = PetscSinScalar(3.0*xx[0]) + xx[0];
638: ff[1] = xx[1];
640: /*
641: Restore vectors
642: */
643: VecRestoreArray(x,&xx);
644: VecRestoreArray(f,&ff);
645: return(0);
646: }
648: /* ------------------------------------------------------------------- */
651: static PetscErrorCode FormJacobian2_block(SNES snes,Vec x,Mat *jac,Mat *B,MatStructure *flag,void *dummy)
652: {
653: PetscScalar *xx,A[4];
655: PetscInt idx[2] = {0,1};
658: /*
659: Get pointer to vector data
660: */
661: VecGetArray(x,&xx);
663: /*
664: Compute Jacobian entries and insert into matrix.
665: - Since this is such a small problem, we set all entries for
666: the matrix at once.
667: */
668: A[0] = 3.0*PetscCosScalar(3.0*xx[0]) + 1.0; A[1] = 0.0;
669: A[2] = 0.0; A[3] = 1.0;
670: MatSetValues(*jac,2,idx,2,idx,A,INSERT_VALUES);
671: *flag = SAME_NONZERO_PATTERN;
673: /*
674: Restore vector
675: */
676: VecRestoreArray(x,&xx);
678: /*
679: Assemble matrix
680: */
681: MatAssemblyBegin(*jac,MAT_FINAL_ASSEMBLY);
682: MatAssemblyEnd(*jac,MAT_FINAL_ASSEMBLY);
683: return(0);
684: }
688: int main(int argc,char **argv)
689: {
690: PetscMPIInt size;
693: PetscInitialize(&argc,&argv,(char*)0,help);
695: MPI_Comm_size(PETSC_COMM_WORLD,&size);
696: if (size != 1) SETERRQ(PETSC_COMM_WORLD, 1,"This is a uniprocessor example only!");
698: assembled_system();
700: block_system();
702: PetscFinalize();
703: return 0;
704: }