Actual source code: eptorsion2.c
petsc-3.14.6 2021-03-30
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*);
77: int main(int argc, char **argv)
78: {
79: PetscErrorCode ierr;
80: Vec x;
81: Mat H;
82: PetscInt Nx, Ny;
83: Tao tao;
84: PetscBool flg;
85: KSP ksp;
86: PC pc;
87: AppCtx user;
89: PetscInitialize(&argc, &argv, (char *)0, help);
91: /* Specify default dimension of the problem */
92: user.param = 5.0; user.mx = 10; user.my = 10;
93: Nx = Ny = PETSC_DECIDE;
95: /* Check for any command line arguments that override defaults */
96: PetscOptionsGetReal(NULL,NULL,"-par",&user.param,&flg);
97: PetscOptionsGetInt(NULL,NULL,"-my",&user.my,&flg);
98: PetscOptionsGetInt(NULL,NULL,"-mx",&user.mx,&flg);
100: PetscPrintf(PETSC_COMM_WORLD,"\n---- Elastic-Plastic Torsion Problem -----\n");
101: PetscPrintf(PETSC_COMM_WORLD,"mx: %D my: %D \n\n",user.mx,user.my);
103: /* Set up distributed array */
104: DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.mx,user.my,Nx,Ny,1,1,NULL,NULL,&user.dm);
105: DMSetFromOptions(user.dm);
106: DMSetUp(user.dm);
108: /* Create vectors */
109: DMCreateGlobalVector(user.dm,&x);
111: DMCreateLocalVector(user.dm,&user.localX);
113: /* Create Hessian */
114: DMCreateMatrix(user.dm,&H);
115: MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE);
117: /* The TAO code begins here */
119: /* Create TAO solver and set desired solution method */
120: TaoCreate(PETSC_COMM_WORLD,&tao);
121: TaoSetType(tao,TAOCG);
123: /* Set initial solution guess */
124: FormInitialGuess(&user,x);
125: TaoSetInitialVector(tao,x);
127: /* Set routine for function and gradient evaluation */
128: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
130: TaoSetHessianRoutine(tao,H,H,FormHessian,(void*)&user);
133: /* Check for any TAO command line options */
134: TaoSetFromOptions(tao);
136: TaoGetKSP(tao,&ksp);
137: if (ksp) {
138: KSPGetPC(ksp,&pc);
139: PCSetType(pc,PCNONE);
140: }
142: /* SOLVE THE APPLICATION */
143: TaoSolve(tao);
145: /* Free TAO data structures */
146: TaoDestroy(&tao);
148: /* Free PETSc data structures */
149: VecDestroy(&x);
150: MatDestroy(&H);
152: VecDestroy(&user.localX);
153: DMDestroy(&user.dm);
155: PetscFinalize();
156: return 0;
157: }
160: /* ------------------------------------------------------------------- */
161: /*
162: FormInitialGuess - Computes an initial approximation to the solution.
164: Input Parameters:
165: . user - user-defined application context
166: . X - vector
168: Output Parameters:
169: X - vector
170: */
171: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
172: {
174: PetscInt i, j, k, mx = user->mx, my = user->my;
175: PetscInt xs, ys, xm, ym, gxm, gym, gxs, gys, xe, ye;
176: PetscReal hx = 1.0/(mx+1), hy = 1.0/(my+1), temp, val;
179: /* Get local mesh boundaries */
180: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
181: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
183: /* Compute initial guess over locally owned part of mesh */
184: xe = xs+xm;
185: ye = ys+ym;
186: for (j=ys; j<ye; j++) { /* for (j=0; j<my; j++) */
187: temp = PetscMin(j+1,my-j)*hy;
188: for (i=xs; i<xe; i++) { /* for (i=0; i<mx; i++) */
189: k = (j-gys)*gxm + i-gxs;
190: val = PetscMin((PetscMin(i+1,mx-i))*hx,temp);
191: VecSetValuesLocal(X,1,&k,&val,ADD_VALUES);
192: }
193: }
194: VecAssemblyBegin(X);
195: VecAssemblyEnd(X);
196: return(0);
197: }
200: /* ------------------------------------------------------------------ */
201: /*
202: FormFunctionGradient - Evaluates the function and corresponding gradient.
204: Input Parameters:
205: tao - the Tao context
206: X - the input vector
207: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
209: Output Parameters:
210: f - the newly evaluated function
211: G - the newly evaluated gradient
212: */
213: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f,Vec G,void *ptr){
215: AppCtx *user = (AppCtx *)ptr;
217: PetscInt i,j,k,ind;
218: PetscInt xe,ye,xsm,ysm,xep,yep;
219: PetscInt xs, ys, xm, ym, gxm, gym, gxs, gys;
220: PetscInt mx = user->mx, my = user->my;
221: PetscReal three = 3.0, zero = 0.0, *x, floc, cdiv3 = user->param/three;
222: PetscReal p5 = 0.5, area, val, flin, fquad;
223: PetscReal v,vb,vl,vr,vt,dvdx,dvdy;
224: PetscReal hx = 1.0/(user->mx + 1);
225: PetscReal hy = 1.0/(user->my + 1);
226: Vec localX = user->localX;
229: /* Initialize */
230: flin = fquad = zero;
232: VecSet(G, zero);
233: /*
234: Scatter ghost points to local vector,using the 2-step process
235: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
236: By placing code between these two statements, computations can be
237: done while messages are in transition.
238: */
239: DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
240: DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);
242: /* Get pointer to vector data */
243: VecGetArray(localX,&x);
245: /* Get local mesh boundaries */
246: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
247: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
249: /* Set local loop dimensions */
250: xe = xs+xm;
251: ye = ys+ym;
252: if (xs == 0) xsm = xs-1;
253: else xsm = xs;
254: if (ys == 0) ysm = ys-1;
255: else ysm = ys;
256: if (xe == mx) xep = xe+1;
257: else xep = xe;
258: if (ye == my) yep = ye+1;
259: else yep = ye;
261: /* Compute local gradient contributions over the lower triangular elements */
262: for (j=ysm; j<ye; j++) { /* for (j=-1; j<my; j++) */
263: for (i=xsm; i<xe; i++) { /* for (i=-1; i<mx; i++) */
264: k = (j-gys)*gxm + i-gxs;
265: v = zero;
266: vr = zero;
267: vt = zero;
268: if (i >= 0 && j >= 0) v = x[k];
269: if (i < mx-1 && j > -1) vr = x[k+1];
270: if (i > -1 && j < my-1) vt = x[k+gxm];
271: dvdx = (vr-v)/hx;
272: dvdy = (vt-v)/hy;
273: if (i != -1 && j != -1) {
274: ind = k; val = - dvdx/hx - dvdy/hy - cdiv3;
275: VecSetValuesLocal(G,1,&k,&val,ADD_VALUES);
276: }
277: if (i != mx-1 && j != -1) {
278: ind = k+1; val = dvdx/hx - cdiv3;
279: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
280: }
281: if (i != -1 && j != my-1) {
282: ind = k+gxm; val = dvdy/hy - cdiv3;
283: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
284: }
285: fquad += dvdx*dvdx + dvdy*dvdy;
286: flin -= cdiv3 * (v + vr + vt);
287: }
288: }
290: /* Compute local gradient contributions over the upper triangular elements */
291: for (j=ys; j<yep; j++) { /* for (j=0; j<=my; j++) */
292: for (i=xs; i<xep; i++) { /* for (i=0; i<=mx; i++) */
293: k = (j-gys)*gxm + i-gxs;
294: vb = zero;
295: vl = zero;
296: v = zero;
297: if (i < mx && j > 0) vb = x[k-gxm];
298: if (i > 0 && j < my) vl = x[k-1];
299: if (i < mx && j < my) v = x[k];
300: dvdx = (v-vl)/hx;
301: dvdy = (v-vb)/hy;
302: if (i != mx && j != 0) {
303: ind = k-gxm; val = - dvdy/hy - cdiv3;
304: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
305: }
306: if (i != 0 && j != my) {
307: ind = k-1; val = - dvdx/hx - cdiv3;
308: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
309: }
310: if (i != mx && j != my) {
311: ind = k; val = dvdx/hx + dvdy/hy - cdiv3;
312: VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
313: }
314: fquad += dvdx*dvdx + dvdy*dvdy;
315: flin -= cdiv3 * (vb + vl + v);
316: }
317: }
320: /* Restore vector */
321: VecRestoreArray(localX,&x);
323: /* Assemble gradient vector */
324: VecAssemblyBegin(G);
325: VecAssemblyEnd(G);
327: /* Scale the gradient */
328: area = p5*hx*hy;
329: floc = area * (p5 * fquad + flin);
330: VecScale(G, area);
332: /* Sum function contributions from all processes */
333: (PetscErrorCode)MPI_Allreduce((void*)&floc,(void*)f,1,MPIU_REAL,MPIU_SUM,MPI_COMM_WORLD);
335: ierr=PetscLogFlops((ye-ysm)*(xe-xsm)*20+(xep-xs)*(yep-ys)*16);
337: return(0);
338: }
342: PetscErrorCode FormHessian(Tao tao, Vec X, Mat A, Mat Hpre, void*ctx)
343: {
344: AppCtx *user= (AppCtx*) ctx;
346: PetscInt i,j,k;
347: PetscInt col[5],row;
348: PetscInt xs,xm,gxs,gxm,ys,ym,gys,gym;
349: PetscReal v[5];
350: 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;
352: /* Compute the quadratic term in the objective function */
354: /*
355: Get local grid boundaries
356: */
359: DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
360: DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
362: for (j=ys; j<ys+ym; j++){
364: for (i=xs; i< xs+xm; i++){
366: row=(j-gys)*gxm + (i-gxs);
368: k=0;
369: if (j>gys){
370: v[k]=-2*hyhy; col[k]=row - gxm; k++;
371: }
373: if (i>gxs){
374: v[k]= -2*hxhx; col[k]=row - 1; k++;
375: }
377: v[k]= 4.0*(hxhx+hyhy); col[k]=row; k++;
379: if (i+1 < gxs+gxm){
380: v[k]= -2.0*hxhx; col[k]=row+1; k++;
381: }
383: if (j+1 <gys+gym){
384: v[k]= -2*hyhy; col[k] = row+gxm; k++;
385: }
387: MatSetValuesLocal(A,1,&row,k,col,v,INSERT_VALUES);
389: }
390: }
391: /*
392: Assemble matrix, using the 2-step process:
393: MatAssemblyBegin(), MatAssemblyEnd().
394: By placing code between these two statements, computations can be
395: done while messages are in transition.
396: */
397: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
398: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
399: /*
400: Tell the matrix we will never add a new nonzero location to the
401: matrix. If we do it will generate an error.
402: */
403: MatScale(A,area);
404: MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
405: MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);
406: PetscLogFlops(9*xm*ym+49*xm);
407: return(0);
408: }
411: /*TEST
413: build:
414: requires: !complex
416: test:
417: suffix: 1
418: nsize: 2
419: args: -tao_smonitor -tao_type nls -mx 16 -my 16 -tao_gatol 1.e-4
421: TEST*/