Actual source code: eptorsion2.c
petsc-3.7.5 2017-01-01
1: /* Program usage: mpiexec -n <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: 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: PetscBool flg;
87: KSP ksp;
88: PC pc;
89: AppCtx user;
91: PetscInitialize(&argc, &argv, (char *)0, help);
93: /* Specify default dimension of the problem */
94: user.param = 5.0; user.mx = 10; user.my = 10;
95: Nx = Ny = PETSC_DECIDE;
97: /* Check for any command line arguments that override defaults */
98: PetscOptionsGetReal(NULL,NULL,"-par",&user.param,&flg);
99: PetscOptionsGetInt(NULL,NULL,"-my",&user.my,&flg);
100: PetscOptionsGetInt(NULL,NULL,"-mx",&user.mx,&flg);
102: PetscPrintf(PETSC_COMM_WORLD,"\n---- Elastic-Plastic Torsion Problem -----\n");
103: PetscPrintf(PETSC_COMM_WORLD,"mx: %D my: %D \n\n",user.mx,user.my);
105: /* Set up distributed array */
106: DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.mx,user.my,Nx,Ny,1,1,NULL,NULL,
107: &user.dm);
109: /* Create vectors */
110: DMCreateGlobalVector(user.dm,&x);
112: DMCreateLocalVector(user.dm,&user.localX);
114: /* Create Hessian */
115: DMCreateMatrix(user.dm,&H);
116: MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE);
118: /* The TAO code begins here */
120: /* Create TAO solver and set desired solution method */
121: TaoCreate(PETSC_COMM_WORLD,&tao);
122: TaoSetType(tao,TAOCG);
124: /* Set initial solution guess */
125: FormInitialGuess(&user,x);
126: TaoSetInitialVector(tao,x);
128: /* Set routine for function and gradient evaluation */
129: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
131: TaoSetHessianRoutine(tao,H,H,FormHessian,(void*)&user);
134: /* Check for any TAO command line options */
135: TaoSetFromOptions(tao);
137: TaoGetKSP(tao,&ksp);
138: if (ksp) {
139: KSPGetPC(ksp,&pc);
140: PCSetType(pc,PCNONE);
141: }
143: /* SOLVE THE APPLICATION */
144: TaoSolve(tao);
146: /* Free TAO data structures */
147: TaoDestroy(&tao);
149: /* Free PETSc data structures */
150: VecDestroy(&x);
151: MatDestroy(&H);
153: VecDestroy(&user.localX);
154: DMDestroy(&user.dm);
156: PetscFinalize();
157: return 0;
158: }
161: /* ------------------------------------------------------------------- */
164: /*
165: FormInitialGuess - Computes an initial approximation to the solution.
167: Input Parameters:
168: . user - user-defined application context
169: . X - vector
171: Output Parameters:
172: X - vector
173: */
174: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
175: {
177: PetscInt i, j, k, mx = user->mx, my = user->my;
178: PetscInt xs, ys, xm, ym, gxm, gym, gxs, gys, xe, ye;
179: PetscReal hx = 1.0/(mx+1), hy = 1.0/(my+1), temp, val;
182: /* Get local mesh boundaries */
183: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
184: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
186: /* Compute initial guess over locally owned part of mesh */
187: xe = xs+xm;
188: ye = ys+ym;
189: for (j=ys; j<ye; j++) { /* for (j=0; j<my; j++) */
190: temp = PetscMin(j+1,my-j)*hy;
191: for (i=xs; i<xe; i++) { /* for (i=0; i<mx; i++) */
192: k = (j-gys)*gxm + i-gxs;
193: val = PetscMin((PetscMin(i+1,mx-i))*hx,temp);
194: VecSetValuesLocal(X,1,&k,&val,ADD_VALUES);
195: }
196: }
197: VecAssemblyBegin(X);
198: VecAssemblyEnd(X);
199: return(0);
200: }
203: /* ------------------------------------------------------------------ */
206: /*
207: FormFunctionGradient - Evaluates the function and corresponding gradient.
209: Input Parameters:
210: tao - the Tao context
211: X - the input vector
212: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
214: Output Parameters:
215: f - the newly evaluated function
216: G - the newly evaluated gradient
217: */
218: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f,Vec G,void *ptr){
220: AppCtx *user = (AppCtx *)ptr;
222: PetscInt i,j,k,ind;
223: PetscInt xe,ye,xsm,ysm,xep,yep;
224: PetscInt xs, ys, xm, ym, gxm, gym, gxs, gys;
225: PetscInt mx = user->mx, my = user->my;
226: PetscReal three = 3.0, zero = 0.0, *x, floc, cdiv3 = user->param/three;
227: PetscReal p5 = 0.5, area, val, flin, fquad;
228: PetscReal v,vb,vl,vr,vt,dvdx,dvdy;
229: PetscReal hx = 1.0/(user->mx + 1);
230: PetscReal hy = 1.0/(user->my + 1);
231: Vec localX = user->localX;
234: /* Initialize */
235: flin = fquad = zero;
237: VecSet(G, zero);
238: /*
239: Scatter ghost points to local vector,using the 2-step process
240: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
241: By placing code between these two statements, computations can be
242: done while messages are in transition.
243: */
244: DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
245: DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);
247: /* Get pointer to vector data */
248: VecGetArray(localX,&x);
250: /* Get local mesh boundaries */
251: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
252: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
254: /* Set local loop dimensions */
255: xe = xs+xm;
256: ye = ys+ym;
257: if (xs == 0) xsm = xs-1;
258: else xsm = xs;
259: if (ys == 0) ysm = ys-1;
260: else ysm = ys;
261: if (xe == mx) xep = xe+1;
262: else xep = xe;
263: if (ye == my) yep = ye+1;
264: else yep = ye;
266: /* Compute local gradient contributions over the lower triangular elements */
267: for (j=ysm; j<ye; j++) { /* for (j=-1; j<my; j++) */
268: for (i=xsm; i<xe; i++) { /* for (i=-1; i<mx; i++) */
269: k = (j-gys)*gxm + i-gxs;
270: v = zero;
271: vr = zero;
272: vt = zero;
273: if (i >= 0 && j >= 0) v = x[k];
274: if (i < mx-1 && j > -1) vr = x[k+1];
275: if (i > -1 && j < my-1) vt = x[k+gxm];
276: dvdx = (vr-v)/hx;
277: dvdy = (vt-v)/hy;
278: if (i != -1 && j != -1) {
279: ind = k; val = - dvdx/hx - dvdy/hy - cdiv3;
280: VecSetValuesLocal(G,1,&k,&val,ADD_VALUES);
281: }
282: if (i != mx-1 && j != -1) {
283: ind = k+1; val = dvdx/hx - cdiv3;
284: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
285: }
286: if (i != -1 && j != my-1) {
287: ind = k+gxm; val = dvdy/hy - cdiv3;
288: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
289: }
290: fquad += dvdx*dvdx + dvdy*dvdy;
291: flin -= cdiv3 * (v + vr + vt);
292: }
293: }
295: /* Compute local gradient contributions over the upper triangular elements */
296: for (j=ys; j<yep; j++) { /* for (j=0; j<=my; j++) */
297: for (i=xs; i<xep; i++) { /* for (i=0; i<=mx; i++) */
298: k = (j-gys)*gxm + i-gxs;
299: vb = zero;
300: vl = zero;
301: v = zero;
302: if (i < mx && j > 0) vb = x[k-gxm];
303: if (i > 0 && j < my) vl = x[k-1];
304: if (i < mx && j < my) v = x[k];
305: dvdx = (v-vl)/hx;
306: dvdy = (v-vb)/hy;
307: if (i != mx && j != 0) {
308: ind = k-gxm; val = - dvdy/hy - cdiv3;
309: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
310: }
311: if (i != 0 && j != my) {
312: ind = k-1; val = - dvdx/hx - cdiv3;
313: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
314: }
315: if (i != mx && j != my) {
316: ind = k; val = dvdx/hx + dvdy/hy - cdiv3;
317: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
318: }
319: fquad += dvdx*dvdx + dvdy*dvdy;
320: flin -= cdiv3 * (vb + vl + v);
321: }
322: }
325: /* Restore vector */
326: VecRestoreArray(localX,&x);
328: /* Assemble gradient vector */
329: VecAssemblyBegin(G);
330: VecAssemblyEnd(G);
332: /* Scale the gradient */
333: area = p5*hx*hy;
334: floc = area * (p5 * fquad + flin);
335: VecScale(G, area);
337: /* Sum function contributions from all processes */
338: (PetscErrorCode)MPI_Allreduce((void*)&floc,(void*)f,1,MPIU_REAL,MPIU_SUM,MPI_COMM_WORLD);
340: ierr=PetscLogFlops((ye-ysm)*(xe-xsm)*20+(xep-xs)*(yep-ys)*16);
342: return(0);
343: }
349: PetscErrorCode FormHessian(Tao tao, Vec X, Mat A, Mat Hpre, void*ctx)
350: {
351: AppCtx *user= (AppCtx*) ctx;
353: PetscInt i,j,k;
354: PetscInt col[5],row;
355: PetscInt xs,xm,gxs,gxm,ys,ym,gys,gym;
356: PetscReal v[5];
357: 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;
359: /* Compute the quadratic term in the objective function */
361: /*
362: Get local grid boundaries
363: */
366: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
367: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
369: for (j=ys; j<ys+ym; j++){
371: for (i=xs; i< xs+xm; i++){
373: row=(j-gys)*gxm + (i-gxs);
375: k=0;
376: if (j>gys){
377: v[k]=-2*hyhy; col[k]=row - gxm; k++;
378: }
380: if (i>gxs){
381: v[k]= -2*hxhx; col[k]=row - 1; k++;
382: }
384: v[k]= 4.0*(hxhx+hyhy); col[k]=row; k++;
386: if (i+1 < gxs+gxm){
387: v[k]= -2.0*hxhx; col[k]=row+1; k++;
388: }
390: if (j+1 <gys+gym){
391: v[k]= -2*hyhy; col[k] = row+gxm; k++;
392: }
394: MatSetValuesLocal(A,1,&row,k,col,v,INSERT_VALUES);
396: }
397: }
398: /*
399: Assemble matrix, using the 2-step process:
400: MatAssemblyBegin(), MatAssemblyEnd().
401: By placing code between these two statements, computations can be
402: done while messages are in transition.
403: */
404: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
405: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
406: /*
407: Tell the matrix we will never add a new nonzero location to the
408: matrix. If we do it will generate an error.
409: */
410: MatScale(A,area);
411: MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
412: MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);
413: PetscLogFlops(9*xm*ym+49*xm);
414: return(0);
415: }