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 mpiexec 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: */
50: /* ------------------------------------------------------------------------
52: Solid Fuel Ignition (SFI) problem. This problem is modeled by
53: the partial differential equation
55: -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
57: with boundary conditions
59: u = 0 for x = 0, x = 1, y = 0, y = 1.
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: petscsys.h - base PETSc routines petscvec.h - vectors
74: 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: */
94: extern int FormFunction(SNES,Vec,Vec,void*),FormInitialGuess(AppCtx*,Vec);
95: extern int FormFunctionFortran(SNES,Vec,Vec,void*);
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: PetscBool 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(NULL,"-mx",&user.mx,NULL);
129: PetscOptionsGetInt(NULL,"-my",&user.my,NULL);
130: PetscOptionsGetReal(NULL,"-par",&user.param,NULL);
131: if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) SETERRQ(PETSC_COMM_SELF,1,"Lambda is out of range");
132: N = user.mx*user.my;
134: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135: Create nonlinear solver context
136: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138: SNESCreate(PETSC_COMM_WORLD,&snes);
140: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141: Create vector data structures; set function evaluation routine
142: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144: /*
145: The routine VecCreateShared() creates a parallel vector with each processor
146: assigned its own segment, BUT, in addition, the first processor has access to the
147: entire array. This is to allow the users function to be based on loop level
148: parallelism rather than MPI.
149: */
150: VecCreateShared(PETSC_COMM_WORLD,PETSC_DECIDE,N,&x);
151: VecDuplicate(x,&r);
153: PetscOptionsHasName(NULL,"-use_fortran_function",&flg);
154: if (flg) fnc = FormFunctionFortran;
155: else fnc = FormFunction;
157: /*
158: Set function evaluation routine and vector
159: */
160: SNESSetFunction(snes,r,fnc,&user);
162: /*
163: Currently when using VecCreateShared() and using loop level parallelism
164: to automatically parallelise the user function it makes no sense for the
165: Jacobian to be computed via loop level parallelism, because all the threads
166: would be simultaneously calling MatSetValues() causing a bottle-neck.
168: Thus this example uses the PETSc Jacobian calculations via finite differencing
169: to approximate the Jacobian
170: */
172: /*
174: */
175: VecGetOwnershipRange(r,&rstart,&rend);
176: PetscMalloc((rend-rstart)*sizeof(PetscInt),&colors);
177: for (i=rstart; i<rend; i++) colors[i - rstart] = 3*((i/user.mx) % 3) + (i % 3);
179: ISColoringCreate(PETSC_COMM_WORLD,3*2+2,rend-rstart,colors,&iscoloring);
180: PetscFree(colors);
182: /*
183: Create and set the nonzero pattern for the Jacobian: This is not done
184: particularly efficiently. One should process the boundary nodes separately and
185: then use a simple loop for the interior nodes.
186: Note that for this code we use the "natural" number of the nodes on the
187: grid (since that is what is good for the user provided function). In the
188: DMDA examples we must use the DMDA numbering where each processor is assigned a
189: chunk of data.
190: */
191: MatCreateAIJ(PETSC_COMM_WORLD,rend-rstart,rend-rstart,N,N,5,0,0,0,&J);
192: for (i=rstart; i<rend; i++) {
193: rj = i % user.mx; /* column in grid */
194: ri = i / user.mx; /* row in grid */
195: if (ri != 0) { /* first row does not have neighbor below */
196: ii = i - user.mx;
197: MatSetValues(J,1,&i,1,&ii,&zero,INSERT_VALUES);
198: }
199: if (ri != user.my - 1) { /* last row does not have neighbors above */
200: ii = i + user.mx;
201: MatSetValues(J,1,&i,1,&ii,&zero,INSERT_VALUES);
202: }
203: if (rj != 0) { /* first column does not have neighbor to left */
204: ii = i - 1;
205: MatSetValues(J,1,&i,1,&ii,&zero,INSERT_VALUES);
206: }
207: if (rj != user.mx - 1) { /* last column does not have neighbor to right */
208: ii = i + 1;
209: MatSetValues(J,1,&i,1,&ii,&zero,INSERT_VALUES);
210: }
211: MatSetValues(J,1,&i,1,&i,&zero,INSERT_VALUES);
212: }
213: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
214: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
216: /*
217: Create the data structure that SNESComputeJacobianDefaultColor() uses
218: to compute the actual Jacobians via finite differences.
219: */
220: MatFDColoringCreate(J,iscoloring,&fdcoloring);
221: MatFDColoringSetFunction(fdcoloring,(PetscErrorCode (*)(void))fnc,&user);
222: MatFDColoringSetFromOptions(fdcoloring);
223: /*
224: Tell SNES to use the routine SNESComputeJacobianDefaultColor()
225: to compute Jacobians.
226: */
227: SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,fdcoloring);
228: ISColoringDestroy(&iscoloring);
231: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
232: Customize nonlinear solver; set runtime options
233: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
235: /*
236: Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
237: */
238: SNESSetFromOptions(snes);
240: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
241: Evaluate initial guess; then solve nonlinear system
242: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
243: /*
244: Note: The user should initialize the vector, x, with the initial guess
245: for the nonlinear solver prior to calling SNESSolve(). In particular,
246: to employ an initial guess of zero, the user should explicitly set
247: this vector to zero by calling VecSet().
248: */
249: FormInitialGuess(&user,x);
250: SNESSolve(snes,NULL,x);
251: SNESGetIterationNumber(snes,&its);
252: PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its);
254: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
255: Free work space. All PETSc objects should be destroyed when they
256: are no longer needed.
257: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
258: VecDestroy(&x);
259: VecDestroy(&r);
260: SNESDestroy(&snes);
261: PetscFinalize();
263: return 0;
264: }
265: /* ------------------------------------------------------------------- */
269: /*
270: FormInitialGuess - Forms initial approximation.
272: Input Parameters:
273: user - user-defined application context
274: X - vector
276: Output Parameter:
277: X - vector
278: */
279: int FormInitialGuess(AppCtx *user,Vec X)280: {
281: int i,j,row,mx,my,ierr;
282: PetscReal one = 1.0,lambda,temp1,temp,hx,hy,hxdhy,hydhx,sc;
283: PetscScalar *x;
285: /*
286: Process 0 has to wait for all other processes to get here
287: before proceeding to write in the shared vector
288: */
289: PetscBarrier((PetscObject)X);
290: if (user->rank) {
291: /*
292: All the non-busy processors have to wait here for process 0 to finish
293: evaluating the function; otherwise they will start using the vector values
294: before they have been computed
295: */
296: PetscBarrier((PetscObject)X);
297: return 0;
298: }
300: mx = user->mx; my = user->my; lambda = user->param;
301: hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
302: sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
304: temp1 = lambda/(lambda + one);
306: /*
307: Get a pointer to vector data.
308: - For default PETSc vectors, VecGetArray() returns a pointer to
309: the data array. Otherwise, the routine is implementation dependent.
310: - You MUST call VecRestoreArray() when you no longer need access to
311: the array.
312: */
313: VecGetArray(X,&x);
315: /*
316: Compute initial guess over the locally owned part of the grid
317: */
318: #pragma arl(4)
319: #pragma distinct (*x,*f)
320: #pragma no side effects (sqrt)
321: for (j=0; j<my; j++) {
322: temp = (PetscReal)(PetscMin(j,my-j-1))*hy;
323: for (i=0; i<mx; i++) {
324: row = i + j*mx;
325: if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
326: x[row] = 0.0;
327: continue;
328: }
329: x[row] = temp1*sqrt(PetscMin((PetscReal)(PetscMin(i,mx-i-1))*hx,temp));
330: }
331: }
333: /*
334: Restore vector
335: */
336: VecRestoreArray(X,&x);
338: PetscBarrier((PetscObject)X);
339: return 0;
340: }
341: /* ------------------------------------------------------------------- */
344: /*
345: FormFunction - Evaluates nonlinear function, F(x).
347: Input Parameters:
348: . snes - the SNES context
349: . X - input vector
350: . ptr - optional user-defined context, as set by SNESSetFunction()
352: Output Parameter:
353: . F - function vector
354: */
355: int FormFunction(SNES snes,Vec X,Vec F,void *ptr)356: {
357: AppCtx *user = (AppCtx*)ptr;
358: int ierr,i,j,row,mx,my;
359: PetscReal two = 2.0,one = 1.0,lambda,hx,hy,hxdhy,hydhx,sc;
360: PetscScalar u,uxx,uyy,*x,*f;
362: /*
363: Process 0 has to wait for all other processes to get here
364: before proceeding to write in the shared vector
365: */
366: PetscBarrier((PetscObject)X);
368: if (user->rank) {
369: /*
370: All the non-busy processors have to wait here for process 0 to finish
371: evaluating the function; otherwise they will start using the vector values
372: before they have been computed
373: */
374: PetscBarrier((PetscObject)X);
375: return 0;
376: }
378: mx = user->mx; my = user->my; lambda = user->param;
379: hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
380: sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
382: /*
383: Get pointers to vector data
384: */
385: VecGetArray(X,&x);
386: VecGetArray(F,&f);
388: /*
389: The next line tells the SGI compiler that x and f contain no overlapping
390: regions and thus it can use addition optimizations.
391: */
392: #pragma arl(4)
393: #pragma distinct (*x,*f)
394: #pragma no side effects (exp)
396: /*
397: Compute function over the entire grid
398: */
399: for (j=0; j<my; j++) {
400: for (i=0; i<mx; i++) {
401: row = i + j*mx;
402: if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
403: f[row] = x[row];
404: continue;
405: }
406: u = x[row];
407: uxx = (two*u - x[row-1] - x[row+1])*hydhx;
408: uyy = (two*u - x[row-mx] - x[row+mx])*hxdhy;
409: f[row] = uxx + uyy - sc*exp(u);
410: }
411: }
413: /*
414: Restore vectors
415: */
416: VecRestoreArray(X,&x);
417: VecRestoreArray(F,&f);
419: PetscLogFlops(11.0*(mx-2)*(my-2))
420: PetscBarrier((PetscObject)X);
421: return 0;
422: }
424: #if defined(PETSC_HAVE_FORTRAN_CAPS)
425: #define applicationfunctionfortran_ APPLICATIONFUNCTIONFORTRAN426: #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
427: #define applicationfunctionfortran_ applicationfunctionfortran428: #endif
430: /* ------------------------------------------------------------------- */
433: /*
434: FormFunctionFortran - Evaluates nonlinear function, F(x) in Fortran.
436: */
437: int FormFunctionFortran(SNES snes,Vec X,Vec F,void *ptr)438: {
439: AppCtx *user = (AppCtx*)ptr;
440: int ierr;
441: PetscScalar *x,*f;
443: /*
444: Process 0 has to wait for all other processes to get here
445: before proceeding to write in the shared vector
446: */
447: PetscBarrier((PetscObject)snes);
448: if (!user->rank) {
449: VecGetArray(X,&x);
450: VecGetArray(F,&f);
451: applicationfunctionfortran_(&user->param,&user->mx,&user->my,x,f,&ierr);
452: VecRestoreArray(X,&x);
453: VecRestoreArray(F,&f);
454: PetscLogFlops(11.0*(user->mx-2)*(user->my-2))
455: }
456: /*
457: All the non-busy processors have to wait here for process 0 to finish
458: evaluating the function; otherwise they will start using the vector values
459: before they have been computed
460: */
461: PetscBarrier((PetscObject)snes);
462: return 0;
463: }