Actual source code: ex9.c
2: static char help[] = "This program demonstrates use of the SNES package. Solve systems of\n\
3: nonlinear equations in parallel. This example uses matrix-free Krylov\n\
4: Newton methods with no preconditioner to solve the Bratu (SFI - solid fuel\n\
5: ignition) test problem. The command line options are:\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: -mz <zg>, where <zg> = number of grid points in the z-direction\n\n";
12: /*
13: 1) Solid Fuel Ignition (SFI) problem. This problem is modeled by
14: the partial differential equation
15:
16: -Laplacian u - lambda*exp(u) = 0, 0 < x,y,z < 1,
17:
18: with boundary conditions
19:
20: u = 0 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.
21:
22: A finite difference approximation with the usual 7-point stencil
23: is used to discretize the boundary value problem to obtain a nonlinear
24: system of equations.
25: */
27: #include petscsnes.h
28: #include petscda.h
30: typedef struct {
31: PetscReal param; /* test problem nonlinearity parameter */
32: PetscInt mx,my,mz; /* discretization in x,y,z-directions */
33: Vec localX,localF; /* ghosted local vectors */
34: DA da; /* distributed array datastructure */
35: } AppCtx;
41: int main(int argc,char **argv)
42: {
43: SNES snes; /* nonlinear solver */
44: KSP ksp; /* linear solver */
45: PC pc; /* preconditioner */
46: Mat J; /* Jacobian matrix */
47: AppCtx user; /* user-defined application context */
48: Vec x,r; /* vectors */
49: DAStencilType stencil = DA_STENCIL_BOX;
51: PetscTruth flg;
52: PetscInt Nx = PETSC_DECIDE,Ny = PETSC_DECIDE,Nz = PETSC_DECIDE,its;
53: PetscReal bratu_lambda_max = 6.81,bratu_lambda_min = 0.;
55: PetscInitialize(&argc,&argv,(char *)0,help);
56: PetscOptionsHasName(PETSC_NULL,"-star",&flg);
57: if (flg) stencil = DA_STENCIL_STAR;
59: user.mx = 4;
60: user.my = 4;
61: user.mz = 4;
62: user.param = 6.0;
63: PetscOptionsGetInt(PETSC_NULL,"-mx",&user.mx,PETSC_NULL);
64: PetscOptionsGetInt(PETSC_NULL,"-my",&user.my,PETSC_NULL);
65: PetscOptionsGetInt(PETSC_NULL,"-mz",&user.mz,PETSC_NULL);
66: PetscOptionsGetInt(PETSC_NULL,"-Nx",&Nx,PETSC_NULL);
67: PetscOptionsGetInt(PETSC_NULL,"-Ny",&Ny,PETSC_NULL);
68: PetscOptionsGetInt(PETSC_NULL,"-Nz",&Nz,PETSC_NULL);
69: PetscOptionsGetReal(PETSC_NULL,"-par",&user.param,PETSC_NULL);
70: if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) {
71: SETERRQ(1,"Lambda is out of range");
72: }
73:
74: /* Set up distributed array */
75: DACreate3d(PETSC_COMM_WORLD,DA_NONPERIODIC,stencil,user.mx,user.my,user.mz,
76: Nx,Ny,Nz,1,1,PETSC_NULL,PETSC_NULL,PETSC_NULL,&user.da);
77: DACreateGlobalVector(user.da,&x);
78: VecDuplicate(x,&r);
79: DACreateLocalVector(user.da,&user.localX);
80: VecDuplicate(user.localX,&user.localF);
82: /* Create nonlinear solver */
83: SNESCreate(PETSC_COMM_WORLD,&snes);
84: /* Set various routines and options */
85: SNESSetFunction(snes,r,FormFunction1,(void*)&user);
86: MatCreateSNESMF(snes,x,&J);
87: SNESSetJacobian(snes,J,J,MatSNESMFComputeJacobian,&user);
88: SNESSetFromOptions(snes);
90: /* Force no preconditioning to be used. Note that this overrides whatever
91: choices may have been specified in the options database. */
92: SNESGetKSP(snes,&ksp);
93: KSPGetPC(ksp,&pc);
94: PCSetType(pc,PCNONE);
96: /* Solve nonlinear system */
97: FormInitialGuess1(&user,x);
98: SNESSolve(snes,PETSC_NULL,x);
99: SNESGetIterationNumber(snes,&its);
100: PetscPrintf(PETSC_COMM_WORLD,"Number of Newton iterations = %D\n",its);
102: /* Free data structures */
103: VecDestroy(user.localX);
104: VecDestroy(user.localF);
105: DADestroy(user.da);
106: VecDestroy(x); VecDestroy(r);
107: MatDestroy(J); SNESDestroy(snes);
109: PetscFinalize();
110: return 0;
111: }/* -------------------- Form initial approximation ----------------- */
114: PetscErrorCode FormInitialGuess1(AppCtx *user,Vec X)
115: {
116: PetscInt i,j,k,loc,mx,my,mz,xs,ys,zs,xm,ym,zm,Xm,Ym,Zm,Xs,Ys,Zs,base1;
118: PetscReal one = 1.0,lambda,temp1,temp,Hx,Hy;
119: PetscScalar *x;
120: Vec localX = user->localX;
122: mx = user->mx; my = user->my; mz = user->mz; lambda = user->param;
123: Hx = one / (PetscReal)(mx-1); Hy = one / (PetscReal)(my-1);
125: VecGetArray(localX,&x);
126: temp1 = lambda/(lambda + one);
127: DAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);
128: DAGetGhostCorners(user->da,&Xs,&Ys,&Zs,&Xm,&Ym,&Zm);
129:
130: for (k=zs; k<zs+zm; k++) {
131: base1 = (Xm*Ym)*(k-Zs);
132: for (j=ys; j<ys+ym; j++) {
133: temp = (PetscReal)(PetscMin(j,my-j-1))*Hy;
134: for (i=xs; i<xs+xm; i++) {
135: loc = base1 + i-Xs + (j-Ys)*Xm;
136: if (i == 0 || j == 0 || k == 0 || i==mx-1 || j==my-1 || k==mz-1) {
137: x[loc] = 0.0;
138: continue;
139: }
140: x[loc] = temp1*sqrt(PetscMin((PetscReal)(PetscMin(i,mx-i-1))*Hx,temp));
141: }
142: }
143: }
145: VecRestoreArray(localX,&x);
146: /* stick values into global vector */
147: DALocalToGlobal(user->da,localX,INSERT_VALUES,X);
148: return 0;
149: }/* -------------------- Evaluate Function F(x) --------------------- */
152: PetscErrorCode FormFunction1(SNES snes,Vec X,Vec F,void *ptr)
153: {
154: AppCtx *user = (AppCtx*)ptr;
156: PetscInt i,j,k,loc,mx,my,mz,xs,ys,zs,xm,ym,zm,Xs,Ys,Zs,Xm,Ym,Zm,base1,base2;
157: PetscReal two = 2.0,one = 1.0,lambda,Hx,Hy,Hz,HxHzdHy,HyHzdHx,HxHydHz;
158: PetscScalar u,uxx,uyy,sc,*x,*f,uzz;
159: Vec localX = user->localX,localF = user->localF;
161: mx = user->mx; my = user->my; mz = user->mz; lambda = user->param;
162: Hx = one / (PetscReal)(mx-1);
163: Hy = one / (PetscReal)(my-1);
164: Hz = one / (PetscReal)(mz-1);
165: sc = Hx*Hy*Hz*lambda; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
166: HxHydHz = Hx*Hy/Hz;
168: DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
169: DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
170: VecGetArray(localX,&x);
171: VecGetArray(localF,&f);
173: DAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);
174: DAGetGhostCorners(user->da,&Xs,&Ys,&Zs,&Xm,&Ym,&Zm);
176: for (k=zs; k<zs+zm; k++) {
177: base1 = (Xm*Ym)*(k-Zs);
178: for (j=ys; j<ys+ym; j++) {
179: base2 = base1 + (j-Ys)*Xm;
180: for (i=xs; i<xs+xm; i++) {
181: loc = base2 + (i-Xs);
182: if (i == 0 || j == 0 || k== 0 || i == mx-1 || j == my-1 || k == mz-1) {
183: f[loc] = x[loc];
184: }
185: else {
186: u = x[loc];
187: uxx = (two*u - x[loc-1] - x[loc+1])*HyHzdHx;
188: uyy = (two*u - x[loc-Xm] - x[loc+Xm])*HxHzdHy;
189: uzz = (two*u - x[loc-Xm*Ym] - x[loc+Xm*Ym])*HxHydHz;
190: f[loc] = uxx + uyy + uzz - sc*PetscExpScalar(u);
191: }
192: }
193: }
194: }
195: VecRestoreArray(localX,&x);
196: VecRestoreArray(localF,&f);
197: /* stick values into global vector */
198: DALocalToGlobal(user->da,localF,INSERT_VALUES,F);
199: PetscLogFlops(11*ym*xm*zm);
200: return 0;
201: }
202:
207: