Actual source code: plate2.c
petsc-3.7.5 2017-01-01
1: #include <petscdmda.h>
2: #include <petsctao.h>
4: static char help[] =
5: "This example demonstrates use of the TAO package to \n\
6: solve an unconstrained minimization problem. This example is based on a \n\
7: problem from the MINPACK-2 test suite. Given a rectangular 2-D domain, \n\
8: boundary values along the edges of the domain, and a plate represented by \n\
9: lower boundary conditions, the objective is to find the\n\
10: surface with the minimal area that satisfies the boundary conditions.\n\
11: The command line options are:\n\
12: -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
13: -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
14: -bmx <bxg>, where <bxg> = number of grid points under plate in 1st direction\n\
15: -bmy <byg>, where <byg> = number of grid points under plate in 2nd direction\n\
16: -bheight <ht>, where <ht> = height of the plate\n\
17: -start <st>, where <st> =0 for zero vector, <st> >0 for random start, and <st> <0 \n\
18: for an average of the boundary conditions\n\n";
20: /*T
21: Concepts: TAO^Solving a bound constrained minimization problem
22: Routines: TaoCreate();
23: Routines: TaoSetType(); TaoSetObjectiveAndGradientRoutine();
24: Routines: TaoSetHessianRoutine();
25: Routines: TaoSetInitialVector();
26: Routines: TaoSetVariableBounds();
27: Routines: TaoSetFromOptions();
28: Routines: TaoSolve(); TaoView();
29: Routines: TaoDestroy();
30: Processors: n
31: T*/
34: /*
35: User-defined application context - contains data needed by the
36: application-provided call-back routines, FormFunctionGradient(),
37: FormHessian().
38: */
39: typedef struct {
40: /* problem parameters */
41: PetscReal bheight; /* Height of plate under the surface */
42: PetscInt mx, my; /* discretization in x, y directions */
43: PetscInt bmx,bmy; /* Size of plate under the surface */
44: Vec Bottom, Top, Left, Right; /* boundary values */
46: /* Working space */
47: Vec localX, localV; /* ghosted local vector */
48: DM dm; /* distributed array data structure */
49: Mat H;
50: } AppCtx;
52: /* -------- User-defined Routines --------- */
54: static PetscErrorCode MSA_BoundaryConditions(AppCtx*);
55: static PetscErrorCode MSA_InitialPoint(AppCtx*,Vec);
56: static PetscErrorCode MSA_Plate(Vec,Vec,void*);
57: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
58: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*);
60: /* For testing matrix free submatrices */
61: PetscErrorCode MatrixFreeHessian(Tao,Vec,Mat, Mat,void*);
62: PetscErrorCode MyMatMult(Mat,Vec,Vec);
66: int main( int argc, char **argv )
67: {
68: PetscErrorCode ierr; /* used to check for functions returning nonzeros */
69: PetscInt Nx, Ny; /* number of processors in x- and y- directions */
70: PetscInt m, N; /* number of local and global elements in vectors */
71: Vec x,xl,xu; /* solution vector and bounds*/
72: PetscBool flg; /* A return variable when checking for user options */
73: Tao tao; /* Tao solver context */
74: ISLocalToGlobalMapping isltog; /* local-to-global mapping object */
75: Mat H_shell; /* to test matrix-free submatrices */
76: AppCtx user; /* user-defined work context */
78: /* Initialize PETSc, TAO */
79: PetscInitialize( &argc, &argv,(char *)0,help );
81: /* Specify default dimension of the problem */
82: user.mx = 10; user.my = 10; user.bheight=0.1;
84: /* Check for any command line arguments that override defaults */
85: PetscOptionsGetInt(NULL,NULL,"-mx",&user.mx,&flg);
86: PetscOptionsGetInt(NULL,NULL,"-my",&user.my,&flg);
87: PetscOptionsGetReal(NULL,NULL,"-bheight",&user.bheight,&flg);
89: user.bmx = user.mx/2; user.bmy = user.my/2;
90: PetscOptionsGetInt(NULL,NULL,"-bmx",&user.bmx,&flg);
91: PetscOptionsGetInt(NULL,NULL,"-bmy",&user.bmy,&flg);
93: PetscPrintf(PETSC_COMM_WORLD,"\n---- Minimum Surface Area With Plate Problem -----\n");
94: PetscPrintf(PETSC_COMM_WORLD,"mx:%D, my:%D, bmx:%D, bmy:%D, height:%g\n",user.mx,user.my,user.bmx,user.bmy,(double)user.bheight);
96: /* Calculate any derived values from parameters */
97: N = user.mx*user.my;
99: /* Let Petsc determine the dimensions of the local vectors */
100: Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;
102: /*
103: A two dimensional distributed array will help define this problem,
104: which derives from an elliptic PDE on two dimensional domain. From
105: the distributed array, Create the vectors.
106: */
107: DMDACreate2d(MPI_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,
108: DMDA_STENCIL_BOX,user.mx,user.my,Nx,Ny,1,1,
109: NULL,NULL,&user.dm);
111: /*
112: Extract global and local vectors from DM; The local vectors are
113: used solely as work space for the evaluation of the function,
114: gradient, and Hessian. Duplicate for remaining vectors that are
115: the same types.
116: */
117: DMCreateGlobalVector(user.dm,&x); /* Solution */
118: DMCreateLocalVector(user.dm,&user.localX);
119: VecDuplicate(user.localX,&user.localV);
121: VecDuplicate(x,&xl);
122: VecDuplicate(x,&xu);
126: /* The TAO code begins here */
128: /*
129: Create TAO solver and set desired solution method
130: The method must either be TAOTRON or TAOBLMVM
131: If TAOBLMVM is used, then hessian function is not called.
132: */
133: TaoCreate(PETSC_COMM_WORLD,&tao);
134: TaoSetType(tao,TAOBLMVM);
136: /* Set initial solution guess; */
137: MSA_BoundaryConditions(&user);
138: MSA_InitialPoint(&user,x);
139: TaoSetInitialVector(tao,x);
141: /* Set routines for function, gradient and hessian evaluation */
142: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void*) &user);
144: VecGetLocalSize(x,&m);
145: MatCreateAIJ(MPI_COMM_WORLD,m,m,N,N,7,NULL,3,NULL,&(user.H));
146: MatSetOption(user.H,MAT_SYMMETRIC,PETSC_TRUE);
148: DMGetLocalToGlobalMapping(user.dm,&isltog);
149: MatSetLocalToGlobalMapping(user.H,isltog,isltog);
150: PetscOptionsHasName(NULL,NULL,"-matrixfree",&flg);
151: if (flg) {
152: MatCreateShell(PETSC_COMM_WORLD,m,m,N,N,(void*)&user,&H_shell);
153: MatShellSetOperation(H_shell,MATOP_MULT,(void(*)(void))MyMatMult);
154: MatSetOption(H_shell,MAT_SYMMETRIC,PETSC_TRUE);
155: TaoSetHessianRoutine(tao,H_shell,H_shell,MatrixFreeHessian,(void*)&user);
156: } else {
157: TaoSetHessianRoutine(tao,user.H,user.H,FormHessian,(void*)&user);
158: }
160: /* Set Variable bounds */
161: MSA_Plate(xl,xu,(void*)&user);
162: TaoSetVariableBounds(tao,xl,xu);
164: /* Check for any tao command line options */
165: TaoSetFromOptions(tao);
167: /* SOLVE THE APPLICATION */
168: TaoSolve(tao);
170: TaoView(tao,PETSC_VIEWER_STDOUT_WORLD);
172: /* Free TAO data structures */
173: TaoDestroy(&tao);
175: /* Free PETSc data structures */
176: VecDestroy(&x);
177: VecDestroy(&xl);
178: VecDestroy(&xu);
179: MatDestroy(&user.H);
180: VecDestroy(&user.localX);
181: VecDestroy(&user.localV);
182: VecDestroy(&user.Bottom);
183: VecDestroy(&user.Top);
184: VecDestroy(&user.Left);
185: VecDestroy(&user.Right);
186: DMDestroy(&user.dm);
187: if (flg) {
188: MatDestroy(&H_shell);
189: }
190: PetscFinalize();
191: return 0;
192: }
196: /* FormFunctionGradient - Evaluates f(x) and gradient g(x).
198: Input Parameters:
199: . tao - the Tao context
200: . X - input vector
201: . userCtx - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
203: Output Parameters:
204: . fcn - the function value
205: . G - vector containing the newly evaluated gradient
207: Notes:
208: In this case, we discretize the domain and Create triangles. The
209: surface of each triangle is planar, whose surface area can be easily
210: computed. The total surface area is found by sweeping through the grid
211: and computing the surface area of the two triangles that have their
212: right angle at the grid point. The diagonal line segments on the
213: grid that define the triangles run from top left to lower right.
214: The numbering of points starts at the lower left and runs left to
215: right, then bottom to top.
216: */
217: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *fcn, Vec G,void *userCtx)
218: {
219: AppCtx *user = (AppCtx *) userCtx;
221: PetscInt i,j,row;
222: PetscInt mx=user->mx, my=user->my;
223: PetscInt xs,xm,gxs,gxm,ys,ym,gys,gym;
224: PetscReal ft=0;
225: PetscReal zero=0.0;
226: PetscReal hx=1.0/(mx+1),hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy, area=0.5*hx*hy;
227: PetscReal rhx=mx+1, rhy=my+1;
228: PetscReal f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
229: PetscReal df1dxc,df2dxc,df3dxc,df4dxc,df5dxc,df6dxc;
230: PetscReal *g, *x,*left,*right,*bottom,*top;
231: Vec localX = user->localX, localG = user->localV;
233: /* Get local mesh boundaries */
234: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
235: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
237: /* Scatter ghost points to local vector */
238: DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
239: DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);
241: /* Initialize vector to zero */
242: VecSet(localG, zero);
244: /* Get pointers to vector data */
245: VecGetArray(localX,&x);
246: VecGetArray(localG,&g);
247: VecGetArray(user->Top,&top);
248: VecGetArray(user->Bottom,&bottom);
249: VecGetArray(user->Left,&left);
250: VecGetArray(user->Right,&right);
252: /* Compute function over the locally owned part of the mesh */
253: for (j=ys; j<ys+ym; j++){
254: for (i=xs; i< xs+xm; i++){
255: row=(j-gys)*gxm + (i-gxs);
257: xc = x[row];
258: xlt=xrb=xl=xr=xb=xt=xc;
260: if (i==0){ /* left side */
261: xl= left[j-ys+1];
262: xlt = left[j-ys+2];
263: } else {
264: xl = x[row-1];
265: }
267: if (j==0){ /* bottom side */
268: xb=bottom[i-xs+1];
269: xrb = bottom[i-xs+2];
270: } else {
271: xb = x[row-gxm];
272: }
274: if (i+1 == gxs+gxm){ /* right side */
275: xr=right[j-ys+1];
276: xrb = right[j-ys];
277: } else {
278: xr = x[row+1];
279: }
281: if (j+1==gys+gym){ /* top side */
282: xt=top[i-xs+1];
283: xlt = top[i-xs];
284: }else {
285: xt = x[row+gxm];
286: }
288: if (i>gxs && j+1<gys+gym){
289: xlt = x[row-1+gxm];
290: }
291: if (j>gys && i+1<gxs+gxm){
292: xrb = x[row+1-gxm];
293: }
295: d1 = (xc-xl);
296: d2 = (xc-xr);
297: d3 = (xc-xt);
298: d4 = (xc-xb);
299: d5 = (xr-xrb);
300: d6 = (xrb-xb);
301: d7 = (xlt-xl);
302: d8 = (xt-xlt);
304: df1dxc = d1*hydhx;
305: df2dxc = ( d1*hydhx + d4*hxdhy );
306: df3dxc = d3*hxdhy;
307: df4dxc = ( d2*hydhx + d3*hxdhy );
308: df5dxc = d2*hydhx;
309: df6dxc = d4*hxdhy;
311: d1 *= rhx;
312: d2 *= rhx;
313: d3 *= rhy;
314: d4 *= rhy;
315: d5 *= rhy;
316: d6 *= rhx;
317: d7 *= rhy;
318: d8 *= rhx;
320: f1 = PetscSqrtScalar( 1.0 + d1*d1 + d7*d7);
321: f2 = PetscSqrtScalar( 1.0 + d1*d1 + d4*d4);
322: f3 = PetscSqrtScalar( 1.0 + d3*d3 + d8*d8);
323: f4 = PetscSqrtScalar( 1.0 + d3*d3 + d2*d2);
324: f5 = PetscSqrtScalar( 1.0 + d2*d2 + d5*d5);
325: f6 = PetscSqrtScalar( 1.0 + d4*d4 + d6*d6);
327: ft = ft + (f2 + f4);
329: df1dxc /= f1;
330: df2dxc /= f2;
331: df3dxc /= f3;
332: df4dxc /= f4;
333: df5dxc /= f5;
334: df6dxc /= f6;
336: g[row] = (df1dxc+df2dxc+df3dxc+df4dxc+df5dxc+df6dxc ) * 0.5;
338: }
339: }
342: /* Compute triangular areas along the border of the domain. */
343: if (xs==0){ /* left side */
344: for (j=ys; j<ys+ym; j++){
345: d3=(left[j-ys+1] - left[j-ys+2])*rhy;
346: d2=(left[j-ys+1] - x[(j-gys)*gxm])*rhx;
347: ft = ft+PetscSqrtScalar( 1.0 + d3*d3 + d2*d2);
348: }
349: }
350: if (ys==0){ /* bottom side */
351: for (i=xs; i<xs+xm; i++){
352: d2=(bottom[i+1-xs]-bottom[i-xs+2])*rhx;
353: d3=(bottom[i-xs+1]-x[i-gxs])*rhy;
354: ft = ft+PetscSqrtScalar( 1.0 + d3*d3 + d2*d2);
355: }
356: }
358: if (xs+xm==mx){ /* right side */
359: for (j=ys; j< ys+ym; j++){
360: d1=(x[(j+1-gys)*gxm-1]-right[j-ys+1])*rhx;
361: d4=(right[j-ys]-right[j-ys+1])*rhy;
362: ft = ft+PetscSqrtScalar( 1.0 + d1*d1 + d4*d4);
363: }
364: }
365: if (ys+ym==my){ /* top side */
366: for (i=xs; i<xs+xm; i++){
367: d1=(x[(gym-1)*gxm + i-gxs] - top[i-xs+1])*rhy;
368: d4=(top[i-xs+1] - top[i-xs])*rhx;
369: ft = ft+PetscSqrtScalar( 1.0 + d1*d1 + d4*d4);
370: }
371: }
373: if (ys==0 && xs==0){
374: d1=(left[0]-left[1])*rhy;
375: d2=(bottom[0]-bottom[1])*rhx;
376: ft +=PetscSqrtScalar( 1.0 + d1*d1 + d2*d2);
377: }
378: if (ys+ym == my && xs+xm == mx){
379: d1=(right[ym+1] - right[ym])*rhy;
380: d2=(top[xm+1] - top[xm])*rhx;
381: ft +=PetscSqrtScalar( 1.0 + d1*d1 + d2*d2);
382: }
384: ft=ft*area;
385: MPI_Allreduce(&ft,fcn,1,MPIU_REAL,MPIU_SUM,MPI_COMM_WORLD);
388: /* Restore vectors */
389: VecRestoreArray(localX,&x);
390: VecRestoreArray(localG,&g);
391: VecRestoreArray(user->Left,&left);
392: VecRestoreArray(user->Top,&top);
393: VecRestoreArray(user->Bottom,&bottom);
394: VecRestoreArray(user->Right,&right);
396: /* Scatter values to global vector */
397: DMLocalToGlobalBegin(user->dm,localG,INSERT_VALUES,G);
398: DMLocalToGlobalEnd(user->dm,localG,INSERT_VALUES,G);
400: PetscLogFlops(70*xm*ym);
402: return 0;
403: }
405: /* ------------------------------------------------------------------- */
408: /*
409: FormHessian - Evaluates Hessian matrix.
411: Input Parameters:
412: . tao - the Tao context
413: . x - input vector
414: . ptr - optional user-defined context, as set by TaoSetHessianRoutine()
416: Output Parameters:
417: . A - Hessian matrix
418: . B - optionally different preconditioning matrix
420: Notes:
421: Due to mesh point reordering with DMs, we must always work
422: with the local mesh points, and then transform them to the new
423: global numbering with the local-to-global mapping. We cannot work
424: directly with the global numbers for the original uniprocessor mesh!
426: Two methods are available for imposing this transformation
427: when setting matrix entries:
428: (A) MatSetValuesLocal(), using the local ordering (including
429: ghost points!)
430: - Do the following two steps once, before calling TaoSolve()
431: - Use DMGetISLocalToGlobalMapping() to extract the
432: local-to-global map from the DM
433: - Associate this map with the matrix by calling
434: MatSetLocalToGlobalMapping()
435: - Then set matrix entries using the local ordering
436: by calling MatSetValuesLocal()
437: (B) MatSetValues(), using the global ordering
438: - Use DMGetGlobalIndices() to extract the local-to-global map
439: - Then apply this map explicitly yourself
440: - Set matrix entries using the global ordering by calling
441: MatSetValues()
442: Option (A) seems cleaner/easier in many cases, and is the procedure
443: used in this example.
444: */
445: PetscErrorCode FormHessian(Tao tao,Vec X,Mat Hptr, Mat Hessian, void *ptr)
446: {
448: AppCtx *user = (AppCtx *) ptr;
449: PetscInt i,j,k,row;
450: PetscInt mx=user->mx, my=user->my;
451: PetscInt xs,xm,gxs,gxm,ys,ym,gys,gym,col[7];
452: PetscReal hx=1.0/(mx+1), hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy;
453: PetscReal rhx=mx+1, rhy=my+1;
454: PetscReal f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
455: PetscReal hl,hr,ht,hb,hc,htl,hbr;
456: PetscReal *x,*left,*right,*bottom,*top;
457: PetscReal v[7];
458: Vec localX = user->localX;
459: PetscBool assembled;
462: /* Set various matrix options */
463: MatSetOption(Hessian,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE);
465: /* Initialize matrix entries to zero */
466: MatAssembled(Hessian,&assembled);
467: if (assembled){MatZeroEntries(Hessian);}
469: /* Get local mesh boundaries */
470: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
471: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
473: /* Scatter ghost points to local vector */
474: DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
475: DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);
477: /* Get pointers to vector data */
478: VecGetArray(localX,&x);
479: VecGetArray(user->Top,&top);
480: VecGetArray(user->Bottom,&bottom);
481: VecGetArray(user->Left,&left);
482: VecGetArray(user->Right,&right);
484: /* Compute Hessian over the locally owned part of the mesh */
486: for (i=xs; i< xs+xm; i++){
488: for (j=ys; j<ys+ym; j++){
490: row=(j-gys)*gxm + (i-gxs);
492: xc = x[row];
493: xlt=xrb=xl=xr=xb=xt=xc;
495: /* Left side */
496: if (i==gxs){
497: xl= left[j-ys+1];
498: xlt = left[j-ys+2];
499: } else {
500: xl = x[row-1];
501: }
503: if (j==gys){
504: xb=bottom[i-xs+1];
505: xrb = bottom[i-xs+2];
506: } else {
507: xb = x[row-gxm];
508: }
510: if (i+1 == gxs+gxm){
511: xr=right[j-ys+1];
512: xrb = right[j-ys];
513: } else {
514: xr = x[row+1];
515: }
517: if (j+1==gys+gym){
518: xt=top[i-xs+1];
519: xlt = top[i-xs];
520: }else {
521: xt = x[row+gxm];
522: }
524: if (i>gxs && j+1<gys+gym){
525: xlt = x[row-1+gxm];
526: }
527: if (j>gys && i+1<gxs+gxm){
528: xrb = x[row+1-gxm];
529: }
532: d1 = (xc-xl)*rhx;
533: d2 = (xc-xr)*rhx;
534: d3 = (xc-xt)*rhy;
535: d4 = (xc-xb)*rhy;
536: d5 = (xrb-xr)*rhy;
537: d6 = (xrb-xb)*rhx;
538: d7 = (xlt-xl)*rhy;
539: d8 = (xlt-xt)*rhx;
541: f1 = PetscSqrtScalar( 1.0 + d1*d1 + d7*d7);
542: f2 = PetscSqrtScalar( 1.0 + d1*d1 + d4*d4);
543: f3 = PetscSqrtScalar( 1.0 + d3*d3 + d8*d8);
544: f4 = PetscSqrtScalar( 1.0 + d3*d3 + d2*d2);
545: f5 = PetscSqrtScalar( 1.0 + d2*d2 + d5*d5);
546: f6 = PetscSqrtScalar( 1.0 + d4*d4 + d6*d6);
549: hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+
550: (-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2);
551: hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+
552: (-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4);
553: ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+
554: (-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4);
555: hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+
556: (-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2);
558: hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6);
559: htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3);
561: hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) +
562: hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) +
563: (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2*d1*d4)/(f2*f2*f2) +
564: (hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4);
566: hl*=0.5; hr*=0.5; ht*=0.5; hb*=0.5; hbr*=0.5; htl*=0.5; hc*=0.5;
568: k=0;
569: if (j>0){
570: v[k]=hb; col[k]=row - gxm; k++;
571: }
573: if (j>0 && i < mx -1){
574: v[k]=hbr; col[k]=row - gxm+1; k++;
575: }
577: if (i>0){
578: v[k]= hl; col[k]=row - 1; k++;
579: }
581: v[k]= hc; col[k]=row; k++;
583: if (i < mx-1 ){
584: v[k]= hr; col[k]=row+1; k++;
585: }
587: if (i>0 && j < my-1 ){
588: v[k]= htl; col[k] = row+gxm-1; k++;
589: }
591: if (j < my-1 ){
592: v[k]= ht; col[k] = row+gxm; k++;
593: }
595: /*
596: Set matrix values using local numbering, which was defined
597: earlier, in the main routine.
598: */
599: MatSetValuesLocal(Hessian,1,&row,k,col,v,INSERT_VALUES);
601: }
602: }
604: /* Restore vectors */
605: VecRestoreArray(localX,&x);
606: VecRestoreArray(user->Left,&left);
607: VecRestoreArray(user->Top,&top);
608: VecRestoreArray(user->Bottom,&bottom);
609: VecRestoreArray(user->Right,&right);
611: /* Assemble the matrix */
612: MatAssemblyBegin(Hessian,MAT_FINAL_ASSEMBLY);
613: MatAssemblyEnd(Hessian,MAT_FINAL_ASSEMBLY);
615: PetscLogFlops(199*xm*ym);
616: return 0;
617: }
619: /* ------------------------------------------------------------------- */
622: /*
623: MSA_BoundaryConditions - Calculates the boundary conditions for
624: the region.
626: Input Parameter:
627: . user - user-defined application context
629: Output Parameter:
630: . user - user-defined application context
631: */
632: static PetscErrorCode MSA_BoundaryConditions(AppCtx * user)
633: {
634: int ierr;
635: PetscInt i,j,k,maxits=5,limit=0;
636: PetscInt xs,ys,xm,ym,gxs,gys,gxm,gym;
637: PetscInt mx=user->mx,my=user->my;
638: PetscInt bsize=0, lsize=0, tsize=0, rsize=0;
639: PetscReal one=1.0, two=2.0, three=3.0, scl=1.0, tol=1e-10;
640: PetscReal fnorm,det,hx,hy,xt=0,yt=0;
641: PetscReal u1,u2,nf1,nf2,njac11,njac12,njac21,njac22;
642: PetscReal b=-0.5, t=0.5, l=-0.5, r=0.5;
643: PetscReal *boundary;
644: PetscBool flg;
645: Vec Bottom,Top,Right,Left;
647: /* Get local mesh boundaries */
648: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
649: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
652: bsize=xm+2;
653: lsize=ym+2;
654: rsize=ym+2;
655: tsize=xm+2;
657: VecCreateMPI(MPI_COMM_WORLD,bsize,PETSC_DECIDE,&Bottom);
658: VecCreateMPI(MPI_COMM_WORLD,tsize,PETSC_DECIDE,&Top);
659: VecCreateMPI(MPI_COMM_WORLD,lsize,PETSC_DECIDE,&Left);
660: VecCreateMPI(MPI_COMM_WORLD,rsize,PETSC_DECIDE,&Right);
662: user->Top=Top;
663: user->Left=Left;
664: user->Bottom=Bottom;
665: user->Right=Right;
667: hx= (r-l)/(mx+1); hy=(t-b)/(my+1);
669: for (j=0; j<4; j++){
670: if (j==0){
671: yt=b;
672: xt=l+hx*xs;
673: limit=bsize;
674: VecGetArray(Bottom,&boundary);
675: } else if (j==1){
676: yt=t;
677: xt=l+hx*xs;
678: limit=tsize;
679: VecGetArray(Top,&boundary);
680: } else if (j==2){
681: yt=b+hy*ys;
682: xt=l;
683: limit=lsize;
684: VecGetArray(Left,&boundary);
685: } else if (j==3){
686: yt=b+hy*ys;
687: xt=r;
688: limit=rsize;
689: VecGetArray(Right,&boundary);
690: }
692: for (i=0; i<limit; i++){
693: u1=xt;
694: u2=-yt;
695: for (k=0; k<maxits; k++){
696: nf1=u1 + u1*u2*u2 - u1*u1*u1/three-xt;
697: nf2=-u2 - u1*u1*u2 + u2*u2*u2/three-yt;
698: fnorm=PetscSqrtScalar(nf1*nf1+nf2*nf2);
699: if (fnorm <= tol) break;
700: njac11=one+u2*u2-u1*u1;
701: njac12=two*u1*u2;
702: njac21=-two*u1*u2;
703: njac22=-one - u1*u1 + u2*u2;
704: det = njac11*njac22-njac21*njac12;
705: u1 = u1-(njac22*nf1-njac12*nf2)/det;
706: u2 = u2-(njac11*nf2-njac21*nf1)/det;
707: }
709: boundary[i]=u1*u1-u2*u2;
710: if (j==0 || j==1) {
711: xt=xt+hx;
712: } else if (j==2 || j==3){
713: yt=yt+hy;
714: }
715: }
716: if (j==0){
717: VecRestoreArray(Bottom,&boundary);
718: } else if (j==1){
719: VecRestoreArray(Top,&boundary);
720: } else if (j==2){
721: VecRestoreArray(Left,&boundary);
722: } else if (j==3){
723: VecRestoreArray(Right,&boundary);
724: }
725: }
727: /* Scale the boundary if desired */
729: PetscOptionsGetReal(NULL,NULL,"-bottom",&scl,&flg);
730: if (flg){
731: VecScale(Bottom, scl);
732: }
733: PetscOptionsGetReal(NULL,NULL,"-top",&scl,&flg);
734: if (flg){
735: VecScale(Top, scl);
736: }
737: PetscOptionsGetReal(NULL,NULL,"-right",&scl,&flg);
738: if (flg){
739: VecScale(Right, scl);
740: }
742: PetscOptionsGetReal(NULL,NULL,"-left",&scl,&flg);
743: if (flg){
744: VecScale(Left, scl);
745: }
746: return 0;
747: }
750: /* ------------------------------------------------------------------- */
753: /*
754: MSA_Plate - Calculates an obstacle for surface to stretch over.
756: Input Parameter:
757: . user - user-defined application context
759: Output Parameter:
760: . user - user-defined application context
761: */
762: static PetscErrorCode MSA_Plate(Vec XL,Vec XU,void *ctx){
764: AppCtx *user=(AppCtx *)ctx;
766: PetscInt i,j,row;
767: PetscInt xs,ys,xm,ym;
768: PetscInt mx=user->mx, my=user->my, bmy, bmx;
769: PetscReal t1,t2,t3;
770: PetscReal *xl, lb=PETSC_NINFINITY, ub=PETSC_INFINITY;
771: PetscBool cylinder;
773: user->bmy = PetscMax(0,user->bmy);user->bmy = PetscMin(my,user->bmy);
774: user->bmx = PetscMax(0,user->bmx);user->bmx = PetscMin(mx,user->bmx);
775: bmy=user->bmy, bmx=user->bmx;
777: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
779: VecSet(XL, lb);
780: VecSet(XU, ub);
782: VecGetArray(XL,&xl);
784: PetscOptionsHasName(NULL,NULL,"-cylinder",&cylinder);
785: /* Compute the optional lower box */
786: if (cylinder){
787: for (i=xs; i< xs+xm; i++){
788: for (j=ys; j<ys+ym; j++){
789: row=(j-ys)*xm + (i-xs);
790: t1=(2.0*i-mx)*bmy;
791: t2=(2.0*j-my)*bmx;
792: t3=bmx*bmx*bmy*bmy;
793: if ( t1*t1 + t2*t2 <= t3 ){
794: xl[row] = user->bheight;
795: }
796: }
797: }
798: } else {
799: /* Compute the optional lower box */
800: for (i=xs; i< xs+xm; i++){
801: for (j=ys; j<ys+ym; j++){
802: row=(j-ys)*xm + (i-xs);
803: if (i>=(mx-bmx)/2 && i<mx-(mx-bmx)/2 &&
804: j>=(my-bmy)/2 && j<my-(my-bmy)/2 ){
805: xl[row] = user->bheight;
806: }
807: }
808: }
809: }
810: VecRestoreArray(XL,&xl);
812: return 0;
813: }
816: /* ------------------------------------------------------------------- */
819: /*
820: MSA_InitialPoint - Calculates the initial guess in one of three ways.
822: Input Parameters:
823: . user - user-defined application context
824: . X - vector for initial guess
826: Output Parameters:
827: . X - newly computed initial guess
828: */
829: static PetscErrorCode MSA_InitialPoint(AppCtx * user, Vec X)
830: {
832: PetscInt start=-1,i,j;
833: PetscReal zero=0.0;
834: PetscBool flg;
836: PetscOptionsGetInt(NULL,NULL,"-start",&start,&flg);
837: if (flg && start==0){ /* The zero vector is reasonable */
838: VecSet(X, zero);
839: } else if (flg && start>0){ /* Try a random start between -0.5 and 0.5 */
840: PetscRandom rctx; PetscReal np5=-0.5;
842: PetscRandomCreate(MPI_COMM_WORLD,&rctx);
843: for (i=0; i<start; i++){
844: VecSetRandom(X, rctx);
845: }
846: PetscRandomDestroy(&rctx);
847: VecShift(X, np5);
849: } else { /* Take an average of the boundary conditions */
851: PetscInt row,xs,xm,gxs,gxm,ys,ym,gys,gym;
852: PetscInt mx=user->mx,my=user->my;
853: PetscReal *x,*left,*right,*bottom,*top;
854: Vec localX = user->localX;
856: /* Get local mesh boundaries */
857: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
858: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
860: /* Get pointers to vector data */
861: VecGetArray(user->Top,&top);
862: VecGetArray(user->Bottom,&bottom);
863: VecGetArray(user->Left,&left);
864: VecGetArray(user->Right,&right);
866: VecGetArray(localX,&x);
867: /* Perform local computations */
868: for (j=ys; j<ys+ym; j++){
869: for (i=xs; i< xs+xm; i++){
870: row=(j-gys)*gxm + (i-gxs);
871: x[row] = ( (j+1)*bottom[i-xs+1]/my + (my-j+1)*top[i-xs+1]/(my+2)+
872: (i+1)*left[j-ys+1]/mx + (mx-i+1)*right[j-ys+1]/(mx+2))/2.0;
873: }
874: }
876: /* Restore vectors */
877: VecRestoreArray(localX,&x);
879: VecRestoreArray(user->Left,&left);
880: VecRestoreArray(user->Top,&top);
881: VecRestoreArray(user->Bottom,&bottom);
882: VecRestoreArray(user->Right,&right);
884: /* Scatter values into global vector */
885: DMLocalToGlobalBegin(user->dm,localX,INSERT_VALUES,X);
886: DMLocalToGlobalEnd(user->dm,localX,INSERT_VALUES,X);
888: }
889: return 0;
890: }
892: /* For testing matrix free submatrices */
895: PetscErrorCode MatrixFreeHessian(Tao tao, Vec x, Mat H, Mat Hpre, void *ptr)
896: {
898: AppCtx *user = (AppCtx*)ptr;
900: FormHessian(tao,x,user->H,user->H,ptr);
901: return(0);
902: }
905: PetscErrorCode MyMatMult(Mat H_shell, Vec X, Vec Y)
906: {
908: void *ptr;
909: AppCtx *user;
911: MatShellGetContext(H_shell,&ptr);
912: user = (AppCtx*)ptr;
913: MatMult(user->H,X,Y);
914: return(0);
915: }