Actual source code: eptorsion2.c
petsc-3.6.4 2016-04-12
1: /* Program usage: mpirun -np <proc> eptorsion2 [-help] [all TAO options] */
3: /* ----------------------------------------------------------------------
5: Elastic-plastic torsion problem.
7: The elastic plastic torsion problem arises from the determination
8: of the stress field on an infinitely long cylindrical bar, which is
9: equivalent to the solution of the following problem:
11: min{ .5 * integral(||gradient(v(x))||^2 dx) - C * integral(v(x) dx)}
13: where C is the torsion angle per unit length.
15: The uniprocessor version of this code is eptorsion1.c; the Fortran
16: version of this code is eptorsion2f.F.
18: This application solves the problem without calculating hessians
19: ---------------------------------------------------------------------- */
21: /*
22: Include "petsctao.h" so that we can use TAO solvers. Note that this
23: file automatically includes files for lower-level support, such as those
24: provided by the PETSc library:
25: petsc.h - base PETSc routines petscvec.h - vectors
26: petscsys.h - sysem routines petscmat.h - matrices
27: petscis.h - index sets petscksp.h - Krylov subspace methods
28: petscviewer.h - viewers petscpc.h - preconditioners
29: Include "petscdmda.h" so that we can use distributed arrays (DMs) for managing
30: the parallel mesh.
31: */
33: #include <petsctao.h>
34: #include <petscdmda.h>
36: static char help[] =
37: "Demonstrates use of the TAO package to solve \n\
38: unconstrained minimization problems in parallel. This example is based on \n\
39: the Elastic-Plastic Torsion (dept) problem from the MINPACK-2 test suite.\n\
40: The command line options are:\n\
41: -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
42: -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
43: -par <param>, where <param> = angle of twist per unit length\n\n";
45: /*T
46: Concepts: TAO^Solving an unconstrained minimization problem
47: Routines: TaoCreate(); TaoSetType();
48: Routines: TaoSetInitialVector();
49: Routines: TaoSetObjectiveAndGradientRoutine();
50: Routines: TaoSetHessianRoutine(); TaoSetFromOptions();
51: Routines: TaoSolve();
52: Routines: TaoGetConvergedReason(); TaoDestroy();
53: Processors: n
54: T*/
56: /*
57: User-defined application context - contains data needed by the
58: application-provided call-back routines, FormFunction() and
59: FormGradient().
60: */
61: typedef struct {
62: /* parameters */
63: PetscInt mx, my; /* global discretization in x- and y-directions */
64: PetscReal param; /* nonlinearity parameter */
66: /* work space */
67: Vec localX; /* local vectors */
68: DM dm; /* distributed array data structure */
69: } AppCtx;
72: PetscErrorCode FormInitialGuess(AppCtx*, Vec);
73: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
74: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*);
79: int main(int argc, char **argv)
80: {
81: PetscErrorCode ierr;
82: Vec x;
83: Mat H;
84: PetscInt Nx, Ny;
85: Tao tao;
86: TaoConvergedReason reason;
87: PetscBool flg;
88: KSP ksp;
89: PC pc;
90: AppCtx user;
92: PetscInitialize(&argc, &argv, (char *)0, help);
94: /* Specify default dimension of the problem */
95: user.param = 5.0; user.mx = 10; user.my = 10;
96: Nx = Ny = PETSC_DECIDE;
98: /* Check for any command line arguments that override defaults */
99: PetscOptionsGetReal(NULL,"-par",&user.param,&flg);
100: PetscOptionsGetInt(NULL,"-my",&user.my,&flg);
101: PetscOptionsGetInt(NULL,"-mx",&user.mx,&flg);
103: PetscPrintf(PETSC_COMM_WORLD,"\n---- Elastic-Plastic Torsion Problem -----\n");
104: PetscPrintf(PETSC_COMM_WORLD,"mx: %D my: %D \n\n",user.mx,user.my);
106: /* Set up distributed array */
107: DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.mx,user.my,Nx,Ny,1,1,NULL,NULL,
108: &user.dm);
110: /* Create vectors */
111: DMCreateGlobalVector(user.dm,&x);
113: DMCreateLocalVector(user.dm,&user.localX);
115: /* Create Hessian */
116: DMCreateMatrix(user.dm,&H);
117: MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE);
119: /* The TAO code begins here */
121: /* Create TAO solver and set desired solution method */
122: TaoCreate(PETSC_COMM_WORLD,&tao);
123: TaoSetType(tao,TAOCG);
125: /* Set initial solution guess */
126: FormInitialGuess(&user,x);
127: TaoSetInitialVector(tao,x);
129: /* Set routine for function and gradient evaluation */
130: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
132: TaoSetHessianRoutine(tao,H,H,FormHessian,(void*)&user);
135: /* Check for any TAO command line options */
136: TaoSetFromOptions(tao);
138: TaoGetKSP(tao,&ksp);
139: if (ksp) {
140: KSPGetPC(ksp,&pc);
141: PCSetType(pc,PCNONE);
142: }
144: /* SOLVE THE APPLICATION */
145: TaoSolve(tao);
147: /* Get information on termination */
148: TaoGetConvergedReason(tao,&reason);
149: if (reason <= 0){
150: ierr=PetscPrintf(MPI_COMM_WORLD, "Try another method! \n");
151: }
153: /* Free TAO data structures */
154: TaoDestroy(&tao);
156: /* Free PETSc data structures */
157: VecDestroy(&x);
158: MatDestroy(&H);
160: VecDestroy(&user.localX);
161: DMDestroy(&user.dm);
163: PetscFinalize();
164: return 0;
165: }
168: /* ------------------------------------------------------------------- */
171: /*
172: FormInitialGuess - Computes an initial approximation to the solution.
174: Input Parameters:
175: . user - user-defined application context
176: . X - vector
178: Output Parameters:
179: X - vector
180: */
181: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
182: {
184: PetscInt i, j, k, mx = user->mx, my = user->my;
185: PetscInt xs, ys, xm, ym, gxm, gym, gxs, gys, xe, ye;
186: PetscReal hx = 1.0/(mx+1), hy = 1.0/(my+1), temp, val;
189: /* Get local mesh boundaries */
190: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
191: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
193: /* Compute initial guess over locally owned part of mesh */
194: xe = xs+xm;
195: ye = ys+ym;
196: for (j=ys; j<ye; j++) { /* for (j=0; j<my; j++) */
197: temp = PetscMin(j+1,my-j)*hy;
198: for (i=xs; i<xe; i++) { /* for (i=0; i<mx; i++) */
199: k = (j-gys)*gxm + i-gxs;
200: val = PetscMin((PetscMin(i+1,mx-i))*hx,temp);
201: VecSetValuesLocal(X,1,&k,&val,ADD_VALUES);
202: }
203: }
204: VecAssemblyBegin(X);
205: VecAssemblyEnd(X);
206: return(0);
207: }
210: /* ------------------------------------------------------------------ */
213: /*
214: FormFunctionGradient - Evaluates the function and corresponding gradient.
216: Input Parameters:
217: tao - the Tao context
218: X - the input vector
219: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
221: Output Parameters:
222: f - the newly evaluated function
223: G - the newly evaluated gradient
224: */
225: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f,Vec G,void *ptr){
227: AppCtx *user = (AppCtx *)ptr;
229: PetscInt i,j,k,ind;
230: PetscInt xe,ye,xsm,ysm,xep,yep;
231: PetscInt xs, ys, xm, ym, gxm, gym, gxs, gys;
232: PetscInt mx = user->mx, my = user->my;
233: PetscReal three = 3.0, zero = 0.0, *x, floc, cdiv3 = user->param/three;
234: PetscReal p5 = 0.5, area, val, flin, fquad;
235: PetscReal v,vb,vl,vr,vt,dvdx,dvdy;
236: PetscReal hx = 1.0/(user->mx + 1);
237: PetscReal hy = 1.0/(user->my + 1);
238: Vec localX = user->localX;
241: /* Initialize */
242: flin = fquad = zero;
244: VecSet(G, zero);
245: /*
246: Scatter ghost points to local vector,using the 2-step process
247: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
248: By placing code between these two statements, computations can be
249: done while messages are in transition.
250: */
251: DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
252: DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);
254: /* Get pointer to vector data */
255: VecGetArray(localX,&x);
257: /* Get local mesh boundaries */
258: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
259: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
261: /* Set local loop dimensions */
262: xe = xs+xm;
263: ye = ys+ym;
264: if (xs == 0) xsm = xs-1;
265: else xsm = xs;
266: if (ys == 0) ysm = ys-1;
267: else ysm = ys;
268: if (xe == mx) xep = xe+1;
269: else xep = xe;
270: if (ye == my) yep = ye+1;
271: else yep = ye;
273: /* Compute local gradient contributions over the lower triangular elements */
274: for (j=ysm; j<ye; j++) { /* for (j=-1; j<my; j++) */
275: for (i=xsm; i<xe; i++) { /* for (i=-1; i<mx; i++) */
276: k = (j-gys)*gxm + i-gxs;
277: v = zero;
278: vr = zero;
279: vt = zero;
280: if (i >= 0 && j >= 0) v = x[k];
281: if (i < mx-1 && j > -1) vr = x[k+1];
282: if (i > -1 && j < my-1) vt = x[k+gxm];
283: dvdx = (vr-v)/hx;
284: dvdy = (vt-v)/hy;
285: if (i != -1 && j != -1) {
286: ind = k; val = - dvdx/hx - dvdy/hy - cdiv3;
287: VecSetValuesLocal(G,1,&k,&val,ADD_VALUES);
288: }
289: if (i != mx-1 && j != -1) {
290: ind = k+1; val = dvdx/hx - cdiv3;
291: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
292: }
293: if (i != -1 && j != my-1) {
294: ind = k+gxm; val = dvdy/hy - cdiv3;
295: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
296: }
297: fquad += dvdx*dvdx + dvdy*dvdy;
298: flin -= cdiv3 * (v + vr + vt);
299: }
300: }
302: /* Compute local gradient contributions over the upper triangular elements */
303: for (j=ys; j<yep; j++) { /* for (j=0; j<=my; j++) */
304: for (i=xs; i<xep; i++) { /* for (i=0; i<=mx; i++) */
305: k = (j-gys)*gxm + i-gxs;
306: vb = zero;
307: vl = zero;
308: v = zero;
309: if (i < mx && j > 0) vb = x[k-gxm];
310: if (i > 0 && j < my) vl = x[k-1];
311: if (i < mx && j < my) v = x[k];
312: dvdx = (v-vl)/hx;
313: dvdy = (v-vb)/hy;
314: if (i != mx && j != 0) {
315: ind = k-gxm; val = - dvdy/hy - cdiv3;
316: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
317: }
318: if (i != 0 && j != my) {
319: ind = k-1; val = - dvdx/hx - cdiv3;
320: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
321: }
322: if (i != mx && j != my) {
323: ind = k; val = dvdx/hx + dvdy/hy - cdiv3;
324: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
325: }
326: fquad += dvdx*dvdx + dvdy*dvdy;
327: flin -= cdiv3 * (vb + vl + v);
328: }
329: }
332: /* Restore vector */
333: VecRestoreArray(localX,&x);
335: /* Assemble gradient vector */
336: VecAssemblyBegin(G);
337: VecAssemblyEnd(G);
339: /* Scale the gradient */
340: area = p5*hx*hy;
341: floc = area * (p5 * fquad + flin);
342: VecScale(G, area);
344: /* Sum function contributions from all processes */
345: (PetscErrorCode)MPI_Allreduce((void*)&floc,(void*)f,1,MPIU_REAL,MPIU_SUM,MPI_COMM_WORLD);
347: ierr=PetscLogFlops((ye-ysm)*(xe-xsm)*20+(xep-xs)*(yep-ys)*16);
349: return(0);
350: }
356: PetscErrorCode FormHessian(Tao tao, Vec X, Mat A, Mat Hpre, void*ctx)
357: {
358: AppCtx *user= (AppCtx*) ctx;
360: PetscInt i,j,k;
361: PetscInt col[5],row;
362: PetscInt xs,xm,gxs,gxm,ys,ym,gys,gym;
363: PetscReal v[5];
364: PetscReal hx=1.0/(user->mx+1), hy=1.0/(user->my+1), hxhx=1.0/(hx*hx), hyhy=1.0/(hy*hy), area=0.5*hx*hy;
366: /* Compute the quadratic term in the objective function */
368: /*
369: Get local grid boundaries
370: */
373: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
374: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
376: for (j=ys; j<ys+ym; j++){
378: for (i=xs; i< xs+xm; i++){
380: row=(j-gys)*gxm + (i-gxs);
382: k=0;
383: if (j>gys){
384: v[k]=-2*hyhy; col[k]=row - gxm; k++;
385: }
387: if (i>gxs){
388: v[k]= -2*hxhx; col[k]=row - 1; k++;
389: }
391: v[k]= 4.0*(hxhx+hyhy); col[k]=row; k++;
393: if (i+1 < gxs+gxm){
394: v[k]= -2.0*hxhx; col[k]=row+1; k++;
395: }
397: if (j+1 <gys+gym){
398: v[k]= -2*hyhy; col[k] = row+gxm; k++;
399: }
401: MatSetValuesLocal(A,1,&row,k,col,v,INSERT_VALUES);
403: }
404: }
405: /*
406: Assemble matrix, using the 2-step process:
407: MatAssemblyBegin(), MatAssemblyEnd().
408: By placing code between these two statements, computations can be
409: done while messages are in transition.
410: */
411: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
412: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
413: /*
414: Tell the matrix we will never add a new nonzero location to the
415: matrix. If we do it will generate an error.
416: */
417: MatScale(A,area);
418: MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
419: MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);
420: PetscLogFlops(9*xm*ym+49*xm);
421: return(0);
422: }