Actual source code: ex46.c
petsc-3.7.5 2017-01-01
1: static char help[] = "Surface processes in geophysics.\n\n";
3: /*T
4: Concepts: SNES^parallel Surface process example
5: Concepts: DMDA^using distributed arrays;
6: Concepts: IS coloirng types;
7: Processors: n
8: T*/
11: #include <petscsnes.h>
12: #include <petscdm.h>
13: #include <petscdmda.h>
15: /*
16: User-defined application context - contains data needed by the
17: application-provided call-back routines, FormJacobianLocal() and
18: FormFunctionLocal().
19: */
20: typedef struct {
21: PetscReal D; /* The diffusion coefficient */
22: PetscReal K; /* The advection coefficient */
23: PetscInt m; /* Exponent for A */
24: } AppCtx;
26: /*
27: User-defined routines
28: */
29: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*);
30: extern PetscErrorCode FormJacobianLocal(DMDALocalInfo*,PetscScalar**,Mat,AppCtx*);
34: int main(int argc,char **argv)
35: {
36: SNES snes; /* nonlinear solver */
37: AppCtx user; /* user-defined work context */
38: PetscInt its; /* iterations for convergence */
40: DM da;
42: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
43: Initialize program
44: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
46: PetscInitialize(&argc,&argv,(char*)0,help);
48: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
49: Initialize problem parameters
50: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
51: PetscOptionsBegin(PETSC_COMM_WORLD, "", "Surface Process Problem Options", "SNES");
52: user.D = 1.0;
53: PetscOptionsReal("-D", "The diffusion coefficient D", __FILE__, user.D, &user.D, NULL);
54: user.K = 1.0;
55: PetscOptionsReal("-K", "The advection coefficient K", __FILE__, user.K, &user.K, NULL);
56: user.m = 1;
57: PetscOptionsInt("-m", "The exponent for A", __FILE__, user.m, &user.m, NULL);
58: PetscOptionsEnd();
60: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
61: Create distributed array (DMDA) to manage parallel grid and vectors
62: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
63: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
64: DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
65: DMSetApplicationContext(da,&user);
66: SNESCreate(PETSC_COMM_WORLD, &snes);
67: SNESSetDM(snes, da);
69: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
70: Set local function evaluation routine
71: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
72: DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);
74: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
75: Customize solver; set runtime options
76: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
77: SNESSetFromOptions(snes);
80: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
81: Solve nonlinear system
82: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
83: SNESSolve(snes,0,0);
84: SNESGetIterationNumber(snes,&its);
86: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
87: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
88: PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its);
90: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
91: Free work space. All PETSc objects should be destroyed when they
92: are no longer needed.
93: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
95: SNESDestroy(&snes);
96: DMDestroy(&da);
98: PetscFinalize();
99: return(0);
100: }
104: PetscScalar funcU(DMDACoor2d *coords)
105: {
106: return coords->x + coords->y;
107: }
111: PetscScalar funcA(PetscScalar z, AppCtx *user)
112: {
113: PetscScalar v = 1.0;
114: PetscInt i;
116: for (i = 0; i < user->m; ++i) v *= z;
117: return v;
118: }
122: PetscScalar funcADer(PetscScalar z, AppCtx *user)
123: {
124: PetscScalar v = 1.0;
125: PetscInt i;
127: for (i = 0; i < user->m-1; ++i) v *= z;
128: return (PetscScalar)user->m*v;
129: }
133: /*
134: FormFunctionLocal - Evaluates nonlinear function, F(x).
135: */
136: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
137: {
138: DM coordDA;
139: Vec coordinates;
140: DMDACoor2d **coords;
141: PetscScalar u, ux, uy, uxx, uyy;
142: PetscReal D, K, hx, hy, hxdhy, hydhx;
143: PetscInt i,j;
147: D = user->D;
148: K = user->K;
149: hx = 1.0/(PetscReal)(info->mx-1);
150: hy = 1.0/(PetscReal)(info->my-1);
151: hxdhy = hx/hy;
152: hydhx = hy/hx;
153: /*
154: Compute function over the locally owned part of the grid
155: */
156: DMGetCoordinateDM(info->da, &coordDA);
157: DMGetCoordinates(info->da, &coordinates);
158: DMDAVecGetArray(coordDA, coordinates, &coords);
159: for (j=info->ys; j<info->ys+info->ym; j++) {
160: for (i=info->xs; i<info->xs+info->xm; i++) {
161: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) f[j][i] = x[j][i];
162: else {
163: u = x[j][i];
164: ux = (x[j][i+1] - x[j][i])/hx;
165: uy = (x[j+1][i] - x[j][i])/hy;
166: uxx = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx;
167: uyy = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy;
168: f[j][i] = D*(uxx + uyy) - (K*funcA(x[j][i], user)*PetscSqrtScalar(ux*ux + uy*uy) + funcU(&coords[j][i]))*hx*hy;
169: if (PetscIsInfOrNanScalar(f[j][i])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", PetscRealPart(f[j][i]));
170: }
171: }
172: }
173: DMDAVecRestoreArray(coordDA, coordinates, &coords);
174: PetscLogFlops(11*info->ym*info->xm);
175: return(0);
176: }
180: /*
181: FormJacobianLocal - Evaluates Jacobian matrix.
182: */
183: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,AppCtx *user)
184: {
185: MatStencil col[5], row;
186: PetscScalar D, K, A, v[5], hx, hy, hxdhy, hydhx, ux, uy;
187: PetscReal normGradZ;
188: PetscInt i, j,k;
192: D = user->D;
193: K = user->K;
194: hx = 1.0/(PetscReal)(info->mx-1);
195: hy = 1.0/(PetscReal)(info->my-1);
196: hxdhy = hx/hy;
197: hydhx = hy/hx;
199: /*
200: Compute entries for the locally owned part of the Jacobian.
201: - Currently, all PETSc parallel matrix formats are partitioned by
202: contiguous chunks of rows across the processors.
203: - Each processor needs to insert only elements that it owns
204: locally (but any non-local elements will be sent to the
205: appropriate processor during matrix assembly).
206: - Here, we set all entries for a particular row at once.
207: - We can set matrix entries either using either
208: MatSetValuesLocal() or MatSetValues(), as discussed above.
209: */
210: for (j=info->ys; j<info->ys+info->ym; j++) {
211: for (i=info->xs; i<info->xs+info->xm; i++) {
212: row.j = j; row.i = i;
213: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
214: /* boundary points */
215: v[0] = 1.0;
216: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
217: } else {
218: /* interior grid points */
219: ux = (x[j][i+1] - x[j][i])/hx;
220: uy = (x[j+1][i] - x[j][i])/hy;
221: normGradZ = PetscRealPart(PetscSqrtScalar(ux*ux + uy*uy));
222: /* PetscPrintf(PETSC_COMM_SELF, "i: %d j: %d normGradZ: %g\n", i, j, normGradZ); */
223: if (normGradZ < 1.0e-8) normGradZ = 1.0e-8;
224: A = funcA(x[j][i], user);
226: v[0] = -D*hxdhy; col[0].j = j - 1; col[0].i = i;
227: v[1] = -D*hydhx; col[1].j = j; col[1].i = i-1;
228: v[2] = D*2.0*(hydhx + hxdhy) + K*(funcADer(x[j][i], user)*normGradZ - A/normGradZ)*hx*hy; col[2].j = row.j; col[2].i = row.i;
229: v[3] = -D*hydhx + K*A*hx*hy/(2.0*normGradZ); col[3].j = j; col[3].i = i+1;
230: v[4] = -D*hxdhy + K*A*hx*hy/(2.0*normGradZ); col[4].j = j + 1; col[4].i = i;
231: for (k = 0; k < 5; ++k) {
232: if (PetscIsInfOrNanScalar(v[k])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", PetscRealPart(v[k]));
233: }
234: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
235: }
236: }
237: }
239: /*
240: Assemble matrix, using the 2-step process:
241: MatAssemblyBegin(), MatAssemblyEnd().
242: */
243: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
244: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
245: /*
246: Tell the matrix we will never add a new nonzero location to the
247: matrix. If we do, it will generate an error.
248: */
249: MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
250: return(0);
251: }