Actual source code: ex5s.c
2: static char help[] = "2d Bratu problem in shared memory parallel with SNES.\n\
3: We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular\n\
4: domain, uses SHARED MEMORY to evaluate the user function.\n\
5: The command line options include:\n\
6: -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
7: problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)\n\
8: -mx <xg>, where <xg> = number of grid points in the x-direction\n\
9: -my <yg>, where <yg> = number of grid points in the y-direction\n\
10: -use_fortran_function: use Fortran coded function, rather than C\n";
12: /*
13: This code compiles ONLY on SGI systems
14: ========================================
15: */
16: /*T
17: Concepts: SNES^parallel Bratu example
18: Concepts: shared memory
19: Processors: n
20: T*/
22: /*
24: Programming model: Combination of
25: 1) MPI message passing for PETSc routines
26: 2) automatic loop parallism (using shared memory) for user
27: provided function.
29: While the user function is being evaluated all MPI processes except process
30: 0 blocks. Process zero spawns nt threads to evaluate the user function. Once
31: the user function is complete, the worker threads are suspended and all the MPI processes
32: continue.
34: Other useful options:
36: -snes_mf : use matrix free operator and no preconditioner
37: -snes_mf_operator : use matrix free operator but compute Jacobian via
38: finite differences to form preconditioner
40: Environmental variable:
42: setenv MPC_NUM_THREADS nt <- set number of threads processor 0 should
43: use to evaluate user provided function
45: Note: The number of MPI processes (set with the mpirun option -np) can
46: be set completely independently from the number of threads process 0
47: uses to evaluate the function (though usually one would make them the same).
48: */
49:
50: /* ------------------------------------------------------------------------
52: Solid Fuel Ignition (SFI) problem. This problem is modeled by
53: the partial differential equation
54:
55: -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
56:
57: with boundary conditions
58:
59: u = 0 for x = 0, x = 1, y = 0, y = 1.
60:
61: A finite difference approximation with the usual 5-point stencil
62: is used to discretize the boundary value problem to obtain a nonlinear
63: system of equations.
65: The uniprocessor version of this code is snes/examples/tutorials/ex4.c
66: A parallel distributed memory version is snes/examples/tutorials/ex5.c and ex5f.F
68: ------------------------------------------------------------------------- */
70: /*
71: Include "petscsnes.h" so that we can use SNES solvers. Note that this
72: file automatically includes:
73: petsc.h - base PETSc routines petscvec.h - vectors
74: petscsys.h - system routines petscmat.h - matrices
75: petscis.h - index sets petscksp.h - Krylov subspace methods
76: petscviewer.h - viewers petscpc.h - preconditioners
77: petscksp.h - linear solvers
78: */
79: #include petscsnes.h
81: /*
82: User-defined application context - contains data needed by the
83: application-provided call-back routines FormFunction().
84: */
85: typedef struct {
86: PetscReal param; /* test problem parameter */
87: int mx,my; /* discretization in x, y directions */
88: int rank; /* processor rank */
89: } AppCtx;
91: /*
92: User-defined routines
93: */
99: /*
100: The main program is written in C while the user provided function
101: is given in both Fortran and C. The main program could also be written
102: in Fortran; the ONE PROBLEM is that VecGetArray() cannot be called from
103: Fortran on the SGI machines; thus the routine FormFunctionFortran() must
104: be written in C.
105: */
106: int main(int argc,char **argv)
107: {
108: SNES snes; /* nonlinear solver */
109: Vec x,r; /* solution, residual vectors */
110: AppCtx user; /* user-defined work context */
111: int its; /* iterations for convergence */
112: int N,ierr,rstart,rend,*colors,i,ii,ri,rj;
113: PetscErrorCode (*fnc)(SNES,Vec,Vec,void*);
114: PetscReal bratu_lambda_max = 6.81,bratu_lambda_min = 0.;
115: MatFDColoring fdcoloring;
116: ISColoring iscoloring;
117: Mat J;
118: PetscScalar zero = 0.0;
119: PetscTruth flg;
121: PetscInitialize(&argc,&argv,(char *)0,help);
122: MPI_Comm_rank(PETSC_COMM_WORLD,&user.rank);
124: /*
125: Initialize problem parameters
126: */
127: user.mx = 4; user.my = 4; user.param = 6.0;
128: PetscOptionsGetInt(PETSC_NULL,"-mx",&user.mx,PETSC_NULL);
129: PetscOptionsGetInt(PETSC_NULL,"-my",&user.my,PETSC_NULL);
130: PetscOptionsGetReal(PETSC_NULL,"-par",&user.param,PETSC_NULL);
131: if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) {
132: SETERRQ(1,"Lambda is out of range");
133: }
134: N = user.mx*user.my;
136: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137: Create nonlinear solver context
138: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
140: SNESCreate(PETSC_COMM_WORLD,&snes);
142: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143: Create vector data structures; set function evaluation routine
144: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
146: /*
147: The routine VecCreateShared() creates a parallel vector with each processor
148: assigned its own segment, BUT, in addition, the first processor has access to the
149: entire array. This is to allow the users function to be based on loop level
150: parallelism rather than MPI.
151: */
152: VecCreateShared(PETSC_COMM_WORLD,PETSC_DECIDE,N,&x);
153: VecDuplicate(x,&r);
155: PetscOptionsHasName(PETSC_NULL,"-use_fortran_function",&flg);
156: if (flg) {
157: fnc = FormFunctionFortran;
158: } else {
159: fnc = FormFunction;
160: }
162: /*
163: Set function evaluation routine and vector
164: */
165: SNESSetFunction(snes,r,fnc,&user);
167: /*
168: Currently when using VecCreateShared() and using loop level parallelism
169: to automatically parallelise the user function it makes no sense for the
170: Jacobian to be computed via loop level parallelism, because all the threads
171: would be simultaneously calling MatSetValues() causing a bottle-neck.
173: Thus this example uses the PETSc Jacobian calculations via finite differencing
174: to approximate the Jacobian
175: */
177: /*
179: */
180: VecGetOwnershipRange(r,&rstart,&rend);
181: PetscMalloc((rend-rstart)*sizeof(PetscInt),&colors);
182: for (i=rstart; i<rend; i++) {
183: colors[i - rstart] = 3*((i/user.mx) % 3) + (i % 3);
184: }
185: ISColoringCreate(PETSC_COMM_WORLD,3*2+2,rend-rstart,colors,&iscoloring);
186: PetscFree(colors);
188: /*
189: Create and set the nonzero pattern for the Jacobian: This is not done
190: particularly efficiently. One should process the boundary nodes separately and
191: then use a simple loop for the interior nodes.
192: Note that for this code we use the "natural" number of the nodes on the
193: grid (since that is what is good for the user provided function). In the
194: DA examples we must use the DA numbering where each processor is assigned a
195: chunk of data.
196: */
197: MatCreateMPIAIJ(PETSC_COMM_WORLD,rend-rstart,rend-rstart,N,
198: N,5,0,0,0,&J);
199: for (i=rstart; i<rend; i++) {
200: rj = i % user.mx; /* column in grid */
201: ri = i / user.mx; /* row in grid */
202: if (ri != 0) { /* first row does not have neighbor below */
203: ii = i - user.mx;
204: MatSetValues(J,1,&i,1,&ii,&zero,INSERT_VALUES);
205: }
206: if (ri != user.my - 1) { /* last row does not have neighbors above */
207: ii = i + user.mx;
208: MatSetValues(J,1,&i,1,&ii,&zero,INSERT_VALUES);
209: }
210: if (rj != 0) { /* first column does not have neighbor to left */
211: ii = i - 1;
212: MatSetValues(J,1,&i,1,&ii,&zero,INSERT_VALUES);
213: }
214: if (rj != user.mx - 1) { /* last column does not have neighbor to right */
215: ii = i + 1;
216: MatSetValues(J,1,&i,1,&ii,&zero,INSERT_VALUES);
217: }
218: MatSetValues(J,1,&i,1,&i,&zero,INSERT_VALUES);
219: }
220: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
221: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
223: /*
224: Create the data structure that SNESDefaultComputeJacobianColor() uses
225: to compute the actual Jacobians via finite differences.
226: */
227: MatFDColoringCreate(J,iscoloring,&fdcoloring);
228: MatFDColoringSetFunction(fdcoloring,(PetscErrorCode (*)(void))fnc,&user);
229: MatFDColoringSetFromOptions(fdcoloring);
230: /*
231: Tell SNES to use the routine SNESDefaultComputeJacobianColor()
232: to compute Jacobians.
233: */
234: SNESSetJacobian(snes,J,J,SNESDefaultComputeJacobianColor,fdcoloring);
235: ISColoringDestroy(iscoloring);
238: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
239: Customize nonlinear solver; set runtime options
240: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
242: /*
243: Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
244: */
245: SNESSetFromOptions(snes);
247: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
248: Evaluate initial guess; then solve nonlinear system
249: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
250: /*
251: Note: The user should initialize the vector, x, with the initial guess
252: for the nonlinear solver prior to calling SNESSolve(). In particular,
253: to employ an initial guess of zero, the user should explicitly set
254: this vector to zero by calling VecSet().
255: */
256: FormInitialGuess(&user,x);
257: SNESSolve(snes,PETSC_NULL,x);
258: SNESGetIterationNumber(snes,&its);
259: PetscPrintf(PETSC_COMM_WORLD,"Number of Newton iterations = %D\n",its);
261: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
262: Free work space. All PETSc objects should be destroyed when they
263: are no longer needed.
264: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
265: VecDestroy(x);
266: VecDestroy(r);
267: SNESDestroy(snes);
268: PetscFinalize();
270: return 0;
271: }
272: /* ------------------------------------------------------------------- */
276: /*
277: FormInitialGuess - Forms initial approximation.
279: Input Parameters:
280: user - user-defined application context
281: X - vector
283: Output Parameter:
284: X - vector
285: */
286: int FormInitialGuess(AppCtx *user,Vec X)
287: {
288: int i,j,row,mx,my,ierr;
289: PetscReal one = 1.0,lambda,temp1,temp,hx,hy,hxdhy,hydhx,sc;
290: PetscScalar *x;
292: /*
293: Process 0 has to wait for all other processes to get here
294: before proceeding to write in the shared vector
295: */
296: PetscBarrier((PetscObject)X);
297: if (user->rank) {
298: /*
299: All the non-busy processors have to wait here for process 0 to finish
300: evaluating the function; otherwise they will start using the vector values
301: before they have been computed
302: */
303: PetscBarrier((PetscObject)X);
304: return 0;
305: }
307: mx = user->mx; my = user->my; lambda = user->param;
308: hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
309: sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
310: temp1 = lambda/(lambda + one);
312: /*
313: Get a pointer to vector data.
314: - For default PETSc vectors, VecGetArray() returns a pointer to
315: the data array. Otherwise, the routine is implementation dependent.
316: - You MUST call VecRestoreArray() when you no longer need access to
317: the array.
318: */
319: VecGetArray(X,&x);
321: /*
322: Compute initial guess over the locally owned part of the grid
323: */
324: #pragma arl(4)
325: #pragma distinct (*x,*f)
326: #pragma no side effects (sqrt)
327: for (j=0; j<my; j++) {
328: temp = (PetscReal)(PetscMin(j,my-j-1))*hy;
329: for (i=0; i<mx; i++) {
330: row = i + j*mx;
331: if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
332: x[row] = 0.0;
333: continue;
334: }
335: x[row] = temp1*sqrt(PetscMin((PetscReal)(PetscMin(i,mx-i-1))*hx,temp));
336: }
337: }
339: /*
340: Restore vector
341: */
342: VecRestoreArray(X,&x);
344: PetscBarrier((PetscObject)X);
345: return 0;
346: }
347: /* ------------------------------------------------------------------- */
350: /*
351: FormFunction - Evaluates nonlinear function, F(x).
353: Input Parameters:
354: . snes - the SNES context
355: . X - input vector
356: . ptr - optional user-defined context, as set by SNESSetFunction()
358: Output Parameter:
359: . F - function vector
360: */
361: int FormFunction(SNES snes,Vec X,Vec F,void *ptr)
362: {
363: AppCtx *user = (AppCtx*)ptr;
364: int ierr,i,j,row,mx,my;
365: PetscReal two = 2.0,one = 1.0,lambda,hx,hy,hxdhy,hydhx,sc;
366: PetscScalar u,uxx,uyy,*x,*f;
368: /*
369: Process 0 has to wait for all other processes to get here
370: before proceeding to write in the shared vector
371: */
372: PetscBarrier((PetscObject)X);
374: if (user->rank) {
375: /*
376: All the non-busy processors have to wait here for process 0 to finish
377: evaluating the function; otherwise they will start using the vector values
378: before they have been computed
379: */
380: PetscBarrier((PetscObject)X);
381: return 0;
382: }
384: mx = user->mx; my = user->my; lambda = user->param;
385: hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
386: sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
388: /*
389: Get pointers to vector data
390: */
391: VecGetArray(X,&x);
392: VecGetArray(F,&f);
394: /*
395: The next line tells the SGI compiler that x and f contain no overlapping
396: regions and thus it can use addition optimizations.
397: */
398: #pragma arl(4)
399: #pragma distinct (*x,*f)
400: #pragma no side effects (exp)
402: /*
403: Compute function over the entire grid
404: */
405: for (j=0; j<my; j++) {
406: for (i=0; i<mx; i++) {
407: row = i + j*mx;
408: if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
409: f[row] = x[row];
410: continue;
411: }
412: u = x[row];
413: uxx = (two*u - x[row-1] - x[row+1])*hydhx;
414: uyy = (two*u - x[row-mx] - x[row+mx])*hxdhy;
415: f[row] = uxx + uyy - sc*exp(u);
416: }
417: }
419: /*
420: Restore vectors
421: */
422: VecRestoreArray(X,&x);
423: VecRestoreArray(F,&f);
425: PetscLogFlops(11*(mx-2)*(my-2))
426: PetscBarrier((PetscObject)X);
427: return 0;
428: }
430: #if defined(PETSC_HAVE_FORTRAN_CAPS)
431: #define applicationfunctionfortran_ APPLICATIONFUNCTIONFORTRAN
432: #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
433: #define applicationfunctionfortran_ applicationfunctionfortran
434: #endif
436: /* ------------------------------------------------------------------- */
439: /*
440: FormFunctionFortran - Evaluates nonlinear function, F(x) in Fortran.
442: */
443: int FormFunctionFortran(SNES snes,Vec X,Vec F,void *ptr)
444: {
445: AppCtx *user = (AppCtx*)ptr;
446: int ierr;
447: PetscScalar *x,*f;
449: /*
450: Process 0 has to wait for all other processes to get here
451: before proceeding to write in the shared vector
452: */
453: PetscBarrier((PetscObject)snes);
454: if (!user->rank) {
455: VecGetArray(X,&x);
456: VecGetArray(F,&f);
457: applicationfunctionfortran_(&user->param,&user->mx,&user->my,x,f,&ierr);
458: VecRestoreArray(X,&x);
459: VecRestoreArray(F,&f);
460: PetscLogFlops(11*(user->mx-2)*(user->my-2))
461: }
462: /*
463: All the non-busy processors have to wait here for process 0 to finish
464: evaluating the function; otherwise they will start using the vector values
465: before they have been computed
466: */
467: PetscBarrier((PetscObject)snes);
468: return 0;
469: }