Actual source code: ex2.c
petsc-3.6.4 2016-04-12
1: /*
2: Formatted test for TS routines.
4: Solves U_t=F(t,u)
5: Where:
7: [2*u1+u2
8: F(t,u)= [u1+2*u2+u3
9: [ u2+2*u3
10: We can compare the solutions from euler, beuler and SUNDIALS to
11: see what is the difference.
13: */
15: static char help[] = "Solves a nonlinear ODE. \n\n";
17: #include <petscts.h>
18: #include <petscpc.h>
20: extern PetscErrorCode RHSFunction(TS,PetscReal,Vec,Vec,void*);
21: extern PetscErrorCode RHSJacobian(TS,PetscReal,Vec,Mat,Mat,void*);
22: extern PetscErrorCode Monitor(TS,PetscInt,PetscReal,Vec,void*);
23: extern PetscErrorCode Initial(Vec,void*);
25: extern PetscReal solx(PetscReal);
26: extern PetscReal soly(PetscReal);
27: extern PetscReal solz(PetscReal);
31: int main(int argc,char **argv)
32: {
34: PetscInt time_steps = 100,steps;
35: PetscMPIInt size;
36: Vec global;
37: PetscReal dt,ftime;
38: TS ts;
39: Mat A = 0;
41: PetscInitialize(&argc,&argv,(char*)0,help);
42: MPI_Comm_size(PETSC_COMM_WORLD,&size);
44: PetscOptionsGetInt(NULL,"-time",&time_steps,NULL);
46: /* set initial conditions */
47: VecCreate(PETSC_COMM_WORLD,&global);
48: VecSetSizes(global,PETSC_DECIDE,3);
49: VecSetFromOptions(global);
50: Initial(global,NULL);
52: /* make timestep context */
53: TSCreate(PETSC_COMM_WORLD,&ts);
54: TSSetProblemType(ts,TS_NONLINEAR);
55: TSMonitorSet(ts,Monitor,NULL,NULL);
57: dt = 0.1;
59: /*
60: The user provides the RHS and Jacobian
61: */
62: TSSetRHSFunction(ts,NULL,RHSFunction,NULL);
63: MatCreate(PETSC_COMM_WORLD,&A);
64: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,3,3);
65: MatSetFromOptions(A);
66: MatSetUp(A);
67: RHSJacobian(ts,0.0,global,A,A,NULL);
68: TSSetRHSJacobian(ts,A,A,RHSJacobian,NULL);
70: TSSetFromOptions(ts);
72: TSSetInitialTimeStep(ts,0.0,dt);
73: TSSetDuration(ts,time_steps,1);
74: TSSetSolution(ts,global);
76: TSSolve(ts,global);
77: TSGetSolveTime(ts,&ftime);
78: TSGetTimeStepNumber(ts,&steps);
81: /* free the memories */
83: TSDestroy(&ts);
84: VecDestroy(&global);
85: MatDestroy(&A);
87: PetscFinalize();
88: return 0;
89: }
91: /* -------------------------------------------------------------------*/
94: /* this test problem has initial values (1,1,1). */
95: PetscErrorCode Initial(Vec global,void *ctx)
96: {
97: PetscScalar *localptr;
98: PetscInt i,mybase,myend,locsize;
101: /* determine starting point of each processor */
102: VecGetOwnershipRange(global,&mybase,&myend);
103: VecGetLocalSize(global,&locsize);
105: /* Initialize the array */
106: VecGetArray(global,&localptr);
107: for (i=0; i<locsize; i++) localptr[i] = 1.0;
109: if (mybase == 0) localptr[0]=1.0;
111: VecRestoreArray(global,&localptr);
112: return 0;
113: }
117: PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec global,void *ctx)
118: {
119: VecScatter scatter;
120: IS from,to;
121: PetscInt i,n,*idx;
122: Vec tmp_vec;
123: PetscErrorCode ierr;
124: const PetscScalar *tmp;
126: /* Get the size of the vector */
127: VecGetSize(global,&n);
129: /* Set the index sets */
130: PetscMalloc1(n,&idx);
131: for (i=0; i<n; i++) idx[i]=i;
133: /* Create local sequential vectors */
134: VecCreateSeq(PETSC_COMM_SELF,n,&tmp_vec);
136: /* Create scatter context */
137: ISCreateGeneral(PETSC_COMM_SELF,n,idx,PETSC_COPY_VALUES,&from);
138: ISCreateGeneral(PETSC_COMM_SELF,n,idx,PETSC_COPY_VALUES,&to);
139: VecScatterCreate(global,from,tmp_vec,to,&scatter);
140: VecScatterBegin(scatter,global,tmp_vec,INSERT_VALUES,SCATTER_FORWARD);
141: VecScatterEnd(scatter,global,tmp_vec,INSERT_VALUES,SCATTER_FORWARD);
143: VecGetArrayRead(tmp_vec,&tmp);
144: PetscPrintf(PETSC_COMM_WORLD,"At t =%14.6e u = %14.6e %14.6e %14.6e \n",
145: time,PetscRealPart(tmp[0]),PetscRealPart(tmp[1]),PetscRealPart(tmp[2]));
146: PetscPrintf(PETSC_COMM_WORLD,"At t =%14.6e errors = %14.6e %14.6e %14.6e \n",
147: time,PetscRealPart(tmp[0]-solx(time)),PetscRealPart(tmp[1]-soly(time)),PetscRealPart(tmp[2]-solz(time)));
148: VecRestoreArrayRead(tmp_vec,&tmp);
149: VecScatterDestroy(&scatter);
150: ISDestroy(&from);
151: ISDestroy(&to);
152: PetscFree(idx);
153: VecDestroy(&tmp_vec);
154: return 0;
155: }
159: PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec globalin,Vec globalout,void *ctx)
160: {
161: PetscScalar *outptr;
162: const PetscScalar *inptr;
163: PetscInt i,n,*idx;
164: PetscErrorCode ierr;
165: IS from,to;
166: VecScatter scatter;
167: Vec tmp_in,tmp_out;
169: /* Get the length of parallel vector */
170: VecGetSize(globalin,&n);
172: /* Set the index sets */
173: PetscMalloc1(n,&idx);
174: for (i=0; i<n; i++) idx[i]=i;
176: /* Create local sequential vectors */
177: VecCreateSeq(PETSC_COMM_SELF,n,&tmp_in);
178: VecDuplicate(tmp_in,&tmp_out);
180: /* Create scatter context */
181: ISCreateGeneral(PETSC_COMM_SELF,n,idx,PETSC_COPY_VALUES,&from);
182: ISCreateGeneral(PETSC_COMM_SELF,n,idx,PETSC_COPY_VALUES,&to);
183: VecScatterCreate(globalin,from,tmp_in,to,&scatter);
184: VecScatterBegin(scatter,globalin,tmp_in,INSERT_VALUES,SCATTER_FORWARD);
185: VecScatterEnd(scatter,globalin,tmp_in,INSERT_VALUES,SCATTER_FORWARD);
186: VecScatterDestroy(&scatter);
188: /*Extract income array */
189: VecGetArrayRead(tmp_in,&inptr);
191: /* Extract outcome array*/
192: VecGetArray(tmp_out,&outptr);
194: outptr[0] = 2.0*inptr[0]+inptr[1];
195: outptr[1] = inptr[0]+2.0*inptr[1]+inptr[2];
196: outptr[2] = inptr[1]+2.0*inptr[2];
198: VecRestoreArrayRead(tmp_in,&inptr);
199: VecRestoreArray(tmp_out,&outptr);
201: VecScatterCreate(tmp_out,from,globalout,to,&scatter);
202: VecScatterBegin(scatter,tmp_out,globalout,INSERT_VALUES,SCATTER_FORWARD);
203: VecScatterEnd(scatter,tmp_out,globalout,INSERT_VALUES,SCATTER_FORWARD);
205: /* Destroy idx aand scatter */
206: ISDestroy(&from);
207: ISDestroy(&to);
208: VecScatterDestroy(&scatter);
209: VecDestroy(&tmp_in);
210: VecDestroy(&tmp_out);
211: PetscFree(idx);
212: return 0;
213: }
217: PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec x,Mat A,Mat BB,void *ctx)
218: {
219: PetscScalar v[3];
220: const PetscScalar *tmp;
221: PetscInt idx[3],i;
222: PetscErrorCode ierr;
224: idx[0]=0; idx[1]=1; idx[2]=2;
225: VecGetArrayRead(x,&tmp);
227: i = 0;
228: v[0] = 2.0; v[1] = 1.0; v[2] = 0.0;
229: MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
231: i = 1;
232: v[0] = 1.0; v[1] = 2.0; v[2] = 1.0;
233: MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
235: i = 2;
236: v[0] = 0.0; v[1] = 1.0; v[2] = 2.0;
237: MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
239: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
240: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
242: VecRestoreArrayRead(x,&tmp);
244: return 0;
245: }
247: /*
248: The exact solutions
249: */
250: PetscReal solx(PetscReal t)
251: {
252: return PetscExpReal((2.0 - PetscSqrtReal(2.0))*t)/2.0 - PetscExpReal((2.0 - PetscSqrtReal(2.0))*t)/(2.0*PetscSqrtReal(2.0)) +
253: PetscExpReal((2.0 + PetscSqrtReal(2.0))*t)/2.0 + PetscExpReal((2.0 + PetscSqrtReal(2.0))*t)/(2.0*PetscSqrtReal(2.0));
254: }
256: PetscReal soly(PetscReal t)
257: {
258: return PetscExpReal((2.0 - PetscSqrtReal(2.0))*t)/2.0 - PetscExpReal((2.0 - PetscSqrtReal(2.0))*t)/PetscSqrtReal(2.0) +
259: PetscExpReal((2.0 + PetscSqrtReal(2.0))*t)/2.0 + PetscExpReal((2.0 + PetscSqrtReal(2.0))*t)/PetscSqrtReal(2.0);
260: }
262: PetscReal solz(PetscReal t)
263: {
264: return PetscExpReal((2.0 - PetscSqrtReal(2.0))*t)/2.0 - PetscExpReal((2.0 - PetscSqrtReal(2.0))*t)/(2.0*PetscSqrtReal(2.0)) +
265: PetscExpReal((2.0 + PetscSqrtReal(2.0))*t)/2.0 + PetscExpReal((2.0 + PetscSqrtReal(2.0))*t)/(2.0*PetscSqrtReal(2.0));
266: }