Actual source code: ex13.c
2: static char help[] = "This program is a replica of ex6.c except that it does 2 solves to avoid paging.\n\
3: This program demonstrates use of the SNES package to solve systems of\n\
4: nonlinear equations in parallel, using 2-dimensional distributed arrays.\n\
5: The 2-dim Bratu (SFI - solid fuel ignition) test problem is used, where\n\
6: analytic formation of the Jacobian is the default. The command line\n\
7: options are:\n\
8: -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
9: problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)\n\
10: -mx <xg>, where <xg> = number of grid points in the x-direction\n\
11: -my <yg>, where <yg> = number of grid points in the y-direction\n\
12: -Nx <npx>, where <npx> = number of processors in the x-direction\n\
13: -Ny <npy>, where <npy> = number of processors in the y-direction\n\n";
15: /*
16: 1) Solid Fuel Ignition (SFI) problem. This problem is modeled by
17: the partial differential equation
18:
19: -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
20:
21: with boundary conditions
22:
23: u = 0 for x = 0, x = 1, y = 0, y = 1.
24:
25: A finite difference approximation with the usual 5-point stencil
26: is used to discretize the boundary value problem to obtain a nonlinear
27: system of equations.
28: */
30: #include petscsnes.h
31: #include petscda.h
33: /* User-defined application context */
34: typedef struct {
35: PetscReal param; /* test problem parameter */
36: PetscInt mx,my; /* discretization in x, y directions */
37: Vec localX,localF; /* ghosted local vector */
38: DA da; /* distributed array data structure */
39: } AppCtx;
46: int main(int argc,char **argv)
47: {
48: SNES snes; /* nonlinear solver */
49: const SNESType type = SNESLS; /* nonlinear solution method */
50: Vec x,r; /* solution, residual vectors */
51: Mat J; /* Jacobian matrix */
52: AppCtx user; /* user-defined work context */
53: PetscInt i,its,N,Nx = PETSC_DECIDE,Ny = PETSC_DECIDE;
55: PetscTruth matrix_free = PETSC_FALSE;
56: PetscMPIInt size;
57: PetscReal bratu_lambda_max = 6.81,bratu_lambda_min = 0.;
58: #if defined(PETSC_USE_LOG)
59: PetscLogStage stages[2];
60: #endif
62: PetscInitialize(&argc,&argv,(char *)0,help);
64: PetscLogStageRegister("stage 1",&stages[0]);
65: PetscLogStageRegister("stage 2",&stages[1]);
66: for (i=0; i<2; i++) {
67: PetscLogStagePush(stages[i]);
68: user.mx = 4; user.my = 4; user.param = 6.0;
69:
70: if (i!=0) {
71: PetscOptionsGetInt(PETSC_NULL,"-mx",&user.mx,PETSC_NULL);
72: PetscOptionsGetInt(PETSC_NULL,"-my",&user.my,PETSC_NULL);
73: PetscOptionsGetReal(PETSC_NULL,"-par",&user.param,PETSC_NULL);
74: if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) {
75: SETERRQ(1,"Lambda is out of range");
76: }
77: }
78: N = user.mx*user.my;
80: MPI_Comm_size(PETSC_COMM_WORLD,&size);
81: PetscOptionsGetInt(PETSC_NULL,"-Nx",&Nx,PETSC_NULL);
82: PetscOptionsGetInt(PETSC_NULL,"-Ny",&Ny,PETSC_NULL);
83: if (Nx*Ny != size && (Nx != PETSC_DECIDE || Ny != PETSC_DECIDE))
84: SETERRQ(1,"Incompatible number of processors: Nx * Ny != size");
85:
86: /* Set up distributed array */
87: DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,user.mx,user.my,Nx,Ny,1,1,
88: PETSC_NULL,PETSC_NULL,&user.da);
89: DACreateGlobalVector(user.da,&x);
90: VecDuplicate(x,&r);
91: DACreateLocalVector(user.da,&user.localX);
92: VecDuplicate(user.localX,&user.localF);
94: /* Create nonlinear solver and set function evaluation routine */
95: SNESCreate(PETSC_COMM_WORLD,&snes);
96: SNESSetType(snes,type);
97: SNESSetFunction(snes,r,FormFunction1,&user);
99: /* Set default Jacobian evaluation routine. User can override with:
100: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
101: (unless user explicitly sets preconditioner)
102: -snes_fd : default finite differencing approximation of Jacobian
103: */
104: PetscOptionsGetTruth(PETSC_NULL,"-snes_mf",&matrix_free,PETSC_NULL);
105: if (!matrix_free) {
106: PetscTruth matrix_free_operator = PETSC_FALSE;
107: PetscOptionsGetTruth(PETSC_NULL,"-snes_mf_operator",&matrix_free_operator,PETSC_NULL);
108: if (matrix_free_operator) matrix_free = PETSC_FALSE;
109: }
110: if (!matrix_free) {
111: MatCreate(PETSC_COMM_WORLD,&J);
112: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,N,N);
113: MatSetFromOptions(J);
114: SNESSetJacobian(snes,J,J,FormJacobian1,&user);
115: }
117: /* Set PetscOptions, then solve nonlinear system */
118: SNESSetFromOptions(snes);
119: FormInitialGuess1(&user,x);
120: SNESSolve(snes,PETSC_NULL,x);
121: SNESGetIterationNumber(snes,&its);
122: PetscPrintf(PETSC_COMM_WORLD,"Number of Newton iterations = %D\n",its);
124: /* Free data structures */
125: if (!matrix_free) {
126: MatDestroy(J);
127: }
128: VecDestroy(x);
129: VecDestroy(r);
130: VecDestroy(user.localX);
131: VecDestroy(user.localF);
132: SNESDestroy(snes);
133: DADestroy(user.da);
134: }
135: PetscFinalize();
137: return 0;
138: }/* -------------------- Form initial approximation ----------------- */
141: PetscErrorCode FormInitialGuess1(AppCtx *user,Vec X)
142: {
143: PetscInt i,j,row,mx,my,xs,ys,xm,ym,Xm,Ym,Xs,Ys;
145: PetscReal one = 1.0,lambda,temp1,temp,hx,hy;
146: PetscScalar *x;
147: Vec localX = user->localX;
149: mx = user->mx; my = user->my; lambda = user->param;
150: hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
152: /* Get ghost points */
153: VecGetArray(localX,&x);
154: temp1 = lambda/(lambda + one);
155: DAGetCorners(user->da,&xs,&ys,0,&xm,&ym,0);
156: DAGetGhostCorners(user->da,&Xs,&Ys,0,&Xm,&Ym,0);
158: /* Compute initial guess */
159: for (j=ys; j<ys+ym; j++) {
160: temp = (PetscReal)(PetscMin(j,my-j-1))*hy;
161: for (i=xs; i<xs+xm; i++) {
162: row = i - Xs + (j - Ys)*Xm;
163: if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
164: x[row] = 0.0;
165: continue;
166: }
167: x[row] = temp1*sqrt(PetscMin((PetscReal)(PetscMin(i,mx-i-1))*hx,temp));
168: }
169: }
170: VecRestoreArray(localX,&x);
172: /* Insert values into global vector */
173: DALocalToGlobal(user->da,localX,INSERT_VALUES,X);
174: return 0;
175: } /* -------------------- Evaluate Function F(x) --------------------- */
178: PetscErrorCode FormFunction1(SNES snes,Vec X,Vec F,void *ptr)
179: {
180: AppCtx *user = (AppCtx*)ptr;
182: PetscInt i,j,row,mx,my,xs,ys,xm,ym,Xs,Ys,Xm,Ym;
183: PetscReal two = 2.0,one = 1.0,lambda,hx,hy,hxdhy,hydhx,sc;
184: PetscScalar u,uxx,uyy,*x,*f;
185: Vec localX = user->localX,localF = user->localF;
187: mx = user->mx; my = user->my; lambda = user->param;
188: hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
189: sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
191: /* Get ghost points */
192: DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
193: DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
194: VecGetArray(localX,&x);
195: VecGetArray(localF,&f);
196: DAGetCorners(user->da,&xs,&ys,0,&xm,&ym,0);
197: DAGetGhostCorners(user->da,&Xs,&Ys,0,&Xm,&Ym,0);
199: /* Evaluate function */
200: for (j=ys; j<ys+ym; j++) {
201: row = (j - Ys)*Xm + xs - Xs - 1;
202: for (i=xs; i<xs+xm; i++) {
203: row++;
204: if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
205: f[row] = x[row];
206: continue;
207: }
208: u = x[row];
209: uxx = (two*u - x[row-1] - x[row+1])*hydhx;
210: uyy = (two*u - x[row-Xm] - x[row+Xm])*hxdhy;
211: f[row] = uxx + uyy - sc*PetscExpScalar(u);
212: }
213: }
214: VecRestoreArray(localX,&x);
215: VecRestoreArray(localF,&f);
217: /* Insert values into global vector */
218: DALocalToGlobal(user->da,localF,INSERT_VALUES,F);
219: PetscLogFlops(11.0*ym*xm);
220: return 0;
221: } /* -------------------- Evaluate Jacobian F'(x) --------------------- */
224: PetscErrorCode FormJacobian1(SNES snes,Vec X,Mat *J,Mat *B,MatStructure *flag,void *ptr)
225: {
226: AppCtx *user = (AppCtx*)ptr;
227: Mat jac = *J;
229: PetscInt i,j,row,mx,my,xs,ys,xm,ym,Xs,Ys,Xm,Ym,col[5];
230: PetscInt nloc,*ltog,grow;
231: PetscScalar two = 2.0,one = 1.0,lambda,v[5],hx,hy,hxdhy,hydhx,sc,*x;
232: Vec localX = user->localX;
234: mx = user->mx; my = user->my; lambda = user->param;
235: hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
236: sc = hx*hy; hxdhy = hx/hy; hydhx = hy/hx;
238: /* Get ghost points */
239: DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
240: DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
241: VecGetArray(localX,&x);
242: DAGetCorners(user->da,&xs,&ys,0,&xm,&ym,0);
243: DAGetGhostCorners(user->da,&Xs,&Ys,0,&Xm,&Ym,0);
244: DAGetGlobalIndices(user->da,&nloc,<og);
246: /* Evaluate function */
247: for (j=ys; j<ys+ym; j++) {
248: row = (j - Ys)*Xm + xs - Xs - 1;
249: for (i=xs; i<xs+xm; i++) {
250: row++;
251: grow = ltog[row];
252: if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
253: MatSetValues(jac,1,&grow,1,&grow,&one,INSERT_VALUES);
254: continue;
255: }
256: v[0] = -hxdhy; col[0] = ltog[row - Xm];
257: v[1] = -hydhx; col[1] = ltog[row - 1];
258: v[2] = two*(hydhx + hxdhy) - sc*lambda*PetscExpScalar(x[row]); col[2] = grow;
259: v[3] = -hydhx; col[3] = ltog[row + 1];
260: v[4] = -hxdhy; col[4] = ltog[row + Xm];
261: MatSetValues(jac,1,&grow,5,col,v,INSERT_VALUES);
262: }
263: }
264: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
265: VecRestoreArray(X,&x);
266: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
267: *flag = SAME_NONZERO_PATTERN;
268: return 0;
269: }