Actual source code: ex7.c
petsc-3.8.4 2018-03-24
2: static char help[] = ".\n";
4: /*
6: u_t = u_xx + R(u)
8: Where u(t,x,i) for i=0, .... N-1 where i+1 represents the void size
10: ex9.c is the 2d version of this code
11: */
13: #include <petscdm.h>
14: #include <petscdmda.h>
15: #include <petscts.h>
17: /*
18: User-defined data structures and routines
19: */
21: /* AppCtx */
22: typedef struct {
23: PetscInt N; /* number of dofs */
24: } AppCtx;
26: extern PetscErrorCode IFunction(TS,PetscReal,Vec,Vec,Vec,void*);
27: extern PetscErrorCode InitialConditions(DM,Vec);
28: extern PetscErrorCode IJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*);
31: int main(int argc,char **argv)
32: {
33: TS ts; /* nonlinear solver */
34: Vec U; /* solution, residual vectors */
35: Mat J; /* Jacobian matrix */
37: DM da;
38: AppCtx user;
39: PetscInt i;
40: char Name[16];
42: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
43: Initialize program
44: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
45: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
46: user.N = 1;
47: PetscOptionsGetInt(NULL,NULL,"-N",&user.N,NULL);
49: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
50: Create distributed array (DMDA) to manage parallel grid and vectors
51: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
52: DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_MIRROR,-8,user.N,1,NULL,&da);
53: DMSetFromOptions(da);
54: DMSetUp(da);
56: for (i=0; i<user.N; i++) {
57: PetscSNPrintf(Name,16,"Void size %d",(int)(i+1));
58: DMDASetFieldName(da,i,Name);
59: }
61: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
62: Extract global vectors from DMDA; then duplicate for remaining
63: vectors that are the same types
64: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
65: DMCreateGlobalVector(da,&U);
66: DMSetMatType(da,MATAIJ);
67: DMCreateMatrix(da,&J);
69: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
70: Create timestepping solver context
71: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
72: TSCreate(PETSC_COMM_WORLD,&ts);
73: TSSetType(ts,TSARKIMEX);
74: TSSetDM(ts,da);
75: TSSetProblemType(ts,TS_NONLINEAR);
76: TSSetIFunction(ts,NULL,IFunction,&user);
77: TSSetIJacobian(ts,J,J,IJacobian,&user);
80: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
81: Set initial conditions
82: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
83: InitialConditions(da,U);
84: TSSetSolution(ts,U);
86: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
87: Set solver options
88: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
89: TSSetTimeStep(ts,.001);
90: TSSetMaxTime(ts,1.0);
91: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
92: TSSetFromOptions(ts);
94: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
95: Solve nonlinear system
96: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
97: TSSolve(ts,U);
99: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100: Free work space. All PETSc objects should be destroyed when they
101: are no longer needed.
102: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
103: VecDestroy(&U);
104: MatDestroy(&J);
105: TSDestroy(&ts);
106: DMDestroy(&da);
108: PetscFinalize();
109: return(0);
110: }
111: /* ------------------------------------------------------------------- */
112: /*
113: IFunction - Evaluates nonlinear function, F(U).
115: Input Parameters:
116: . ts - the TS context
117: . U - input vector
118: . ptr - optional user-defined context, as set by SNESSetFunction()
120: Output Parameter:
121: . F - function vector
122: */
123: PetscErrorCode IFunction(TS ts,PetscReal ftime,Vec U,Vec Udot,Vec F,void *ptr)
124: {
125: DM da;
127: PetscInt i,c,Mx,xs,xm,N;
128: PetscReal hx,sx,x;
129: PetscScalar uxx;
130: PetscScalar **u,**f,**udot;
131: Vec localU;
134: TSGetDM(ts,&da);
135: DMGetLocalVector(da,&localU);
136: DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,&N,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
138: hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
140: /*
141: Scatter ghost points to local vector,using the 2-step process
142: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
143: By placing code between these two statements, computations can be
144: done while messages are in transition.
145: */
146: DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
147: DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);
149: /*
150: Get pointers to vector data
151: */
152: DMDAVecGetArrayDOF(da,localU,&u);
153: DMDAVecGetArrayDOF(da,Udot,&udot);
154: DMDAVecGetArrayDOF(da,F,&f);
156: /*
157: Get local grid boundaries
158: */
159: DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
161: /*
162: Compute function over the locally owned part of the grid
163: */
164: for (i=xs; i<xs+xm; i++) {
165: x = i*hx;
167: /* diffusion term */
168: for (c=0; c<N; c++) {
169: uxx = (-2.0*u[i][c] + u[i-1][c] + u[i+1][c])*sx;
170: f[i][c] = udot[i][c] - uxx;
171: }
173: /* reaction terms */
175: for (c=0; c<N/3; c++) {
176: f[i][c] += 500*u[i][c]*u[i][c] + 500*u[i][c]*u[i][c+1];
177: f[i][c+1] += -500*u[i][c]*u[i][c] + 500*u[i][c]*u[i][c+1];
178: f[i][c+2] -= 500*u[i][c]*u[i][c+1];
179: }
182: /* forcing term */
184: f[i][0] -= 5*PetscExpScalar((1.0 - x)*(1.0 - x));
186: }
188: /*
189: Restore vectors
190: */
191: DMDAVecRestoreArrayDOF(da,localU,&u);
192: DMDAVecRestoreArrayDOF(da,Udot,&udot);
193: DMDAVecRestoreArrayDOF(da,F,&f);
194: DMRestoreLocalVector(da,&localU);
195: return(0);
196: }
198: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat J,Mat Jpre,void *ctx)
199: {
201: PetscInt i,c,Mx,xs,xm,nc;
202: DM da;
203: MatStencil col[3],row;
204: PetscScalar vals[3],hx,sx;
205: AppCtx *user = (AppCtx*)ctx;
206: PetscInt N = user->N;
207: PetscScalar **u;
210: TSGetDM(ts,&da);
211: DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
212: DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
214: hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
216: DMDAVecGetArrayDOF(da,U,&u);
218: MatZeroEntries(Jpre);
219: for (i=xs; i<xs+xm; i++) {
220: for (c=0; c<N; c++) {
221: nc = 0;
222: row.c = c; row.i = i;
223: col[nc].c = c; col[nc].i = i-1; vals[nc++] = -sx;
224: col[nc].c = c; col[nc].i = i; vals[nc++] = 2.0*sx + a;
225: col[nc].c = c; col[nc].i = i+1; vals[nc++] = -sx;
226: MatSetValuesStencil(Jpre,1,&row,nc,col,vals,ADD_VALUES);
227: }
229: for (c=0; c<N/3; c++) {
230: nc = 0;
231: row.c = c; row.i = i;
232: col[nc].c = c; col[nc].i = i; vals[nc++] = 1000*u[i][c] + 500*u[i][c+1];
233: col[nc].c = c+1; col[nc].i = i; vals[nc++] = 500*u[i][c];
234: MatSetValuesStencil(Jpre,1,&row,nc,col,vals,ADD_VALUES);
236: nc = 0;
237: row.c = c+1; row.i = i;
238: col[nc].c = c; col[nc].i = i; vals[nc++] = -1000*u[i][c] + 500*u[i][c+1];
239: col[nc].c = c+1; col[nc].i = i; vals[nc++] = 500*u[i][c];
240: MatSetValuesStencil(Jpre,1,&row,nc,col,vals,ADD_VALUES);
242: nc = 0;
243: row.c = c+2; row.i = i;
244: col[nc].c = c; col[nc].i = i; vals[nc++] = -500*u[i][c+1];
245: col[nc].c = c+1; col[nc].i = i; vals[nc++] = -500*u[i][c];
246: MatSetValuesStencil(Jpre,1,&row,nc,col,vals,ADD_VALUES);
248: }
249: }
250: MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
251: MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
252: if (J != Jpre) {
253: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
254: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
255: }
256: DMDAVecRestoreArrayDOF(da,U,&u);
257: return(0);
258: }
260: /* ------------------------------------------------------------------- */
261: PetscErrorCode InitialConditions(DM da,Vec U)
262: {
264: PetscInt i,c,xs,xm,Mx,N;
265: PetscScalar **u;
266: PetscReal hx,x;
269: DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,&N,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
271: hx = 1.0/(PetscReal)(Mx-1);
273: /*
274: Get pointers to vector data
275: */
276: DMDAVecGetArrayDOF(da,U,&u);
278: /*
279: Get local grid boundaries
280: */
281: DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
283: /*
284: Compute function over the locally owned part of the grid
285: */
286: for (i=xs; i<xs+xm; i++) {
287: x = i*hx;
288: for (c=0; c<N; c++) u[i][c] = 0.0; /*PetscCosScalar(PETSC_PI*x);*/
289: }
291: /*
292: Restore vectors
293: */
294: DMDAVecRestoreArrayDOF(da,U,&u);
295: return(0);
296: }