Actual source code: ex46.c
petsc-3.8.4 2018-03-24
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*);
32: int main(int argc,char **argv)
33: {
34: SNES snes; /* nonlinear solver */
35: AppCtx user; /* user-defined work context */
36: PetscInt its; /* iterations for convergence */
38: DM da;
40: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
41: Initialize program
42: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
44: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
46: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
47: Initialize problem parameters
48: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
49: PetscOptionsBegin(PETSC_COMM_WORLD, "", "Surface Process Problem Options", "SNES");
50: user.D = 1.0;
51: PetscOptionsReal("-D", "The diffusion coefficient D", __FILE__, user.D, &user.D, NULL);
52: user.K = 1.0;
53: PetscOptionsReal("-K", "The advection coefficient K", __FILE__, user.K, &user.K, NULL);
54: user.m = 1;
55: PetscOptionsInt("-m", "The exponent for A", __FILE__, user.m, &user.m, NULL);
56: PetscOptionsEnd();
58: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
59: Create distributed array (DMDA) to manage parallel grid and vectors
60: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
61: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
62: DMSetFromOptions(da);
63: DMSetUp(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 ierr;
100: }
102: PetscScalar funcU(DMDACoor2d *coords)
103: {
104: return coords->x + coords->y;
105: }
107: PetscScalar funcA(PetscScalar z, AppCtx *user)
108: {
109: PetscScalar v = 1.0;
110: PetscInt i;
112: for (i = 0; i < user->m; ++i) v *= z;
113: return v;
114: }
116: PetscScalar funcADer(PetscScalar z, AppCtx *user)
117: {
118: PetscScalar v = 1.0;
119: PetscInt i;
121: for (i = 0; i < user->m-1; ++i) v *= z;
122: return (PetscScalar)user->m*v;
123: }
125: /*
126: FormFunctionLocal - Evaluates nonlinear function, F(x).
127: */
128: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
129: {
130: DM coordDA;
131: Vec coordinates;
132: DMDACoor2d **coords;
133: PetscScalar u, ux, uy, uxx, uyy;
134: PetscReal D, K, hx, hy, hxdhy, hydhx;
135: PetscInt i,j;
139: D = user->D;
140: K = user->K;
141: hx = 1.0/(PetscReal)(info->mx-1);
142: hy = 1.0/(PetscReal)(info->my-1);
143: hxdhy = hx/hy;
144: hydhx = hy/hx;
145: /*
146: Compute function over the locally owned part of the grid
147: */
148: DMGetCoordinateDM(info->da, &coordDA);
149: DMGetCoordinates(info->da, &coordinates);
150: DMDAVecGetArray(coordDA, coordinates, &coords);
151: for (j=info->ys; j<info->ys+info->ym; j++) {
152: for (i=info->xs; i<info->xs+info->xm; i++) {
153: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) f[j][i] = x[j][i];
154: else {
155: u = x[j][i];
156: ux = (x[j][i+1] - x[j][i])/hx;
157: uy = (x[j+1][i] - x[j][i])/hy;
158: uxx = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx;
159: uyy = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy;
160: f[j][i] = D*(uxx + uyy) - (K*funcA(x[j][i], user)*PetscSqrtScalar(ux*ux + uy*uy) + funcU(&coords[j][i]))*hx*hy;
161: if (PetscIsInfOrNanScalar(f[j][i])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", PetscRealPart(f[j][i]));
162: }
163: }
164: }
165: DMDAVecRestoreArray(coordDA, coordinates, &coords);
166: PetscLogFlops(11*info->ym*info->xm);
167: return(0);
168: }
170: /*
171: FormJacobianLocal - Evaluates Jacobian matrix.
172: */
173: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,AppCtx *user)
174: {
175: MatStencil col[5], row;
176: PetscScalar D, K, A, v[5], hx, hy, hxdhy, hydhx, ux, uy;
177: PetscReal normGradZ;
178: PetscInt i, j,k;
182: D = user->D;
183: K = user->K;
184: hx = 1.0/(PetscReal)(info->mx-1);
185: hy = 1.0/(PetscReal)(info->my-1);
186: hxdhy = hx/hy;
187: hydhx = hy/hx;
189: /*
190: Compute entries for the locally owned part of the Jacobian.
191: - Currently, all PETSc parallel matrix formats are partitioned by
192: contiguous chunks of rows across the processors.
193: - Each processor needs to insert only elements that it owns
194: locally (but any non-local elements will be sent to the
195: appropriate processor during matrix assembly).
196: - Here, we set all entries for a particular row at once.
197: - We can set matrix entries either using either
198: MatSetValuesLocal() or MatSetValues(), as discussed above.
199: */
200: for (j=info->ys; j<info->ys+info->ym; j++) {
201: for (i=info->xs; i<info->xs+info->xm; i++) {
202: row.j = j; row.i = i;
203: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
204: /* boundary points */
205: v[0] = 1.0;
206: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
207: } else {
208: /* interior grid points */
209: ux = (x[j][i+1] - x[j][i])/hx;
210: uy = (x[j+1][i] - x[j][i])/hy;
211: normGradZ = PetscRealPart(PetscSqrtScalar(ux*ux + uy*uy));
212: /* PetscPrintf(PETSC_COMM_SELF, "i: %d j: %d normGradZ: %g\n", i, j, normGradZ); */
213: if (normGradZ < 1.0e-8) normGradZ = 1.0e-8;
214: A = funcA(x[j][i], user);
216: v[0] = -D*hxdhy; col[0].j = j - 1; col[0].i = i;
217: v[1] = -D*hydhx; col[1].j = j; col[1].i = i-1;
218: 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;
219: v[3] = -D*hydhx + K*A*hx*hy/(2.0*normGradZ); col[3].j = j; col[3].i = i+1;
220: v[4] = -D*hxdhy + K*A*hx*hy/(2.0*normGradZ); col[4].j = j + 1; col[4].i = i;
221: for (k = 0; k < 5; ++k) {
222: if (PetscIsInfOrNanScalar(v[k])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", PetscRealPart(v[k]));
223: }
224: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
225: }
226: }
227: }
229: /*
230: Assemble matrix, using the 2-step process:
231: MatAssemblyBegin(), MatAssemblyEnd().
232: */
233: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
234: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
235: /*
236: Tell the matrix we will never add a new nonzero location to the
237: matrix. If we do, it will generate an error.
238: */
239: MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
240: return(0);
241: }