Actual source code: ex46.c
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*/
10: #include <petscsnes.h>
11: #include <petscdm.h>
12: #include <petscdmda.h>
14: /*
15: User-defined application context - contains data needed by the
16: application-provided call-back routines, FormJacobianLocal() and
17: FormFunctionLocal().
18: */
19: typedef struct {
20: PetscReal D; /* The diffusion coefficient */
21: PetscReal K; /* The advection coefficient */
22: PetscInt m; /* Exponent for A */
23: } AppCtx;
25: /*
26: User-defined routines
27: */
28: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*);
29: extern PetscErrorCode FormJacobianLocal(DMDALocalInfo*,PetscScalar**,Mat,AppCtx*);
31: int main(int argc,char **argv)
32: {
33: SNES snes; /* nonlinear solver */
34: AppCtx user; /* user-defined work context */
35: PetscInt its; /* iterations for convergence */
37: DM da;
39: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
40: Initialize program
41: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
43: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
45: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
46: Initialize problem parameters
47: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
48: PetscOptionsBegin(PETSC_COMM_WORLD, "", "Surface Process Problem Options", "SNES");
49: user.D = 1.0;
50: PetscOptionsReal("-D", "The diffusion coefficient D", __FILE__, user.D, &user.D, NULL);
51: user.K = 1.0;
52: PetscOptionsReal("-K", "The advection coefficient K", __FILE__, user.K, &user.K, NULL);
53: user.m = 1;
54: PetscOptionsInt("-m", "The exponent for A", __FILE__, user.m, &user.m, NULL);
55: PetscOptionsEnd();
57: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
58: Create distributed array (DMDA) to manage parallel grid and vectors
59: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
61: DMSetFromOptions(da);
62: DMSetUp(da);
63: DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
64: DMSetApplicationContext(da,&user);
65: SNESCreate(PETSC_COMM_WORLD, &snes);
66: SNESSetDM(snes, da);
68: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
69: Set local function evaluation routine
70: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
71: DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);
73: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
74: Customize solver; set runtime options
75: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
76: SNESSetFromOptions(snes);
78: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
79: Solve nonlinear system
80: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
81: SNESSolve(snes,0,0);
82: SNESGetIterationNumber(snes,&its);
84: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
85: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its);
88: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
89: Free work space. All PETSc objects should be destroyed when they
90: are no longer needed.
91: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
93: SNESDestroy(&snes);
94: DMDestroy(&da);
96: PetscFinalize();
97: return ierr;
98: }
100: PetscScalar funcU(DMDACoor2d *coords)
101: {
102: return coords->x + coords->y;
103: }
105: PetscScalar funcA(PetscScalar z, AppCtx *user)
106: {
107: PetscScalar v = 1.0;
108: PetscInt i;
110: for (i = 0; i < user->m; ++i) v *= z;
111: return v;
112: }
114: PetscScalar funcADer(PetscScalar z, AppCtx *user)
115: {
116: PetscScalar v = 1.0;
117: PetscInt i;
119: for (i = 0; i < user->m-1; ++i) v *= z;
120: return (PetscScalar)user->m*v;
121: }
123: /*
124: FormFunctionLocal - Evaluates nonlinear function, F(x).
125: */
126: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
127: {
128: DM coordDA;
129: Vec coordinates;
130: DMDACoor2d **coords;
131: PetscScalar u, ux, uy, uxx, uyy;
132: PetscReal D, K, hx, hy, hxdhy, hydhx;
133: PetscInt i,j;
137: D = user->D;
138: K = user->K;
139: hx = 1.0/(PetscReal)(info->mx-1);
140: hy = 1.0/(PetscReal)(info->my-1);
141: hxdhy = hx/hy;
142: hydhx = hy/hx;
143: /*
144: Compute function over the locally owned part of the grid
145: */
146: DMGetCoordinateDM(info->da, &coordDA);
147: DMGetCoordinates(info->da, &coordinates);
148: DMDAVecGetArray(coordDA, coordinates, &coords);
149: for (j=info->ys; j<info->ys+info->ym; j++) {
150: for (i=info->xs; i<info->xs+info->xm; i++) {
151: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) f[j][i] = x[j][i];
152: else {
153: u = x[j][i];
154: ux = (x[j][i+1] - x[j][i])/hx;
155: uy = (x[j+1][i] - x[j][i])/hy;
156: uxx = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx;
157: uyy = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy;
158: f[j][i] = D*(uxx + uyy) - (K*funcA(x[j][i], user)*PetscSqrtScalar(ux*ux + uy*uy) + funcU(&coords[j][i]))*hx*hy;
159: if (PetscIsInfOrNanScalar(f[j][i])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", (double)PetscRealPart(f[j][i]));
160: }
161: }
162: }
163: DMDAVecRestoreArray(coordDA, coordinates, &coords);
164: PetscLogFlops(11.0*info->ym*info->xm);
165: return(0);
166: }
168: /*
169: FormJacobianLocal - Evaluates Jacobian matrix.
170: */
171: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,AppCtx *user)
172: {
173: MatStencil col[5], row;
174: PetscScalar D, K, A, v[5], hx, hy, hxdhy, hydhx, ux, uy;
175: PetscReal normGradZ;
176: PetscInt i, j,k;
180: D = user->D;
181: K = user->K;
182: hx = 1.0/(PetscReal)(info->mx-1);
183: hy = 1.0/(PetscReal)(info->my-1);
184: hxdhy = hx/hy;
185: hydhx = hy/hx;
187: /*
188: Compute entries for the locally owned part of the Jacobian.
189: - Currently, all PETSc parallel matrix formats are partitioned by
190: contiguous chunks of rows across the processors.
191: - Each processor needs to insert only elements that it owns
192: locally (but any non-local elements will be sent to the
193: appropriate processor during matrix assembly).
194: - Here, we set all entries for a particular row at once.
195: - We can set matrix entries either using either
196: MatSetValuesLocal() or MatSetValues(), as discussed above.
197: */
198: for (j=info->ys; j<info->ys+info->ym; j++) {
199: for (i=info->xs; i<info->xs+info->xm; i++) {
200: row.j = j; row.i = i;
201: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
202: /* boundary points */
203: v[0] = 1.0;
204: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
205: } else {
206: /* interior grid points */
207: ux = (x[j][i+1] - x[j][i])/hx;
208: uy = (x[j+1][i] - x[j][i])/hy;
209: normGradZ = PetscRealPart(PetscSqrtScalar(ux*ux + uy*uy));
210: if (normGradZ < 1.0e-8) normGradZ = 1.0e-8;
211: A = funcA(x[j][i], user);
213: v[0] = -D*hxdhy; col[0].j = j - 1; col[0].i = i;
214: v[1] = -D*hydhx; col[1].j = j; col[1].i = i-1;
215: 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;
216: v[3] = -D*hydhx + K*A*hx*hy/(2.0*normGradZ); col[3].j = j; col[3].i = i+1;
217: v[4] = -D*hxdhy + K*A*hx*hy/(2.0*normGradZ); col[4].j = j + 1; col[4].i = i;
218: for (k = 0; k < 5; ++k) {
219: if (PetscIsInfOrNanScalar(v[k])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", (double)PetscRealPart(v[k]));
220: }
221: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
222: }
223: }
224: }
226: /*
227: Assemble matrix, using the 2-step process:
228: MatAssemblyBegin(), MatAssemblyEnd().
229: */
230: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
231: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
232: /*
233: Tell the matrix we will never add a new nonzero location to the
234: matrix. If we do, it will generate an error.
235: */
236: MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
237: return(0);
238: }
240: /*TEST
242: test:
243: args: -snes_view -snes_monitor_short -da_refine 1 -pc_type mg -ksp_type fgmres -pc_mg_type full -mg_levels_ksp_chebyshev_esteig 0.5,1.1
245: test:
246: suffix: ew_1
247: args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 1
248: requires: !single
250: test:
251: suffix: ew_2
252: args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 2
254: test:
255: suffix: ew_3
256: args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 3
257: requires: !single
259: test:
260: suffix: fm_rise_2
261: args: -K 3 -m 1 -D 0.2 -snes_monitor_short -snes_type ngmres -snes_npc_side right -npc_snes_type newtonls -npc_snes_linesearch_type basic -snes_ngmres_restart_it 1 -snes_ngmres_restart_fm_rise
262: requires: !single
264: test:
265: suffix: fm_rise_4
266: args: -K 3 -m 1 -D 0.2 -snes_monitor_short -snes_type ngmres -snes_npc_side right -npc_snes_type newtonls -npc_snes_linesearch_type basic -snes_ngmres_restart_it 2 -snes_ngmres_restart_fm_rise -snes_rtol 1.e-2 -snes_max_it 5
268: TEST*/