Actual source code: ex67.c

petsc-master 2019-06-26
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  2: static char help[] = "Krylov methods to solve u''  = f in parallel with periodic boundary conditions,\n\
  3:                       with a singular, inconsistent system.\n\n";

  5: /*T
  6:    Concepts: KSP^basic parallel example
  7:    Concepts: periodic boundary conditions
  8:    Processors: n
  9: T*/



 13: /*

 15:    This tests solving singular inconsistent systems with GMRES

 17:    Default: Solves a symmetric system
 18:    -symmetric false: Solves a non-symmetric system where nullspace(A) != nullspace(A')

 20:   -ksp_pc_side left or right

 22:    See the KSPSolve() for a discussion of when right preconditioning with nullspace(A) != nullspace(A') can fail to produce the
 23:    norm minimizing solution.

 25:    Note that though this example does solve the system with right preconditioning and nullspace(A) != nullspace(A') it does not produce the
 26:    norm minimizing solution, that is the computed solution is not orthogonal to the nullspace(A).


 29:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
 30:    Include "petscksp.h" so that we can use KSP solvers.  Note that this
 31:    file automatically includes:
 32:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 33:      petscmat.h - matrices
 34:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 35:      petscviewer.h - viewers               petscpc.h  - preconditioners
 36:      petscksp.h   - linear solvers
 37: */

 39:  #include <petscdm.h>
 40:  #include <petscdmda.h>
 41:  #include <petscsnes.h>
 42:  #include <petsc/private/kspimpl.h>

 44: PetscBool symmetric = PETSC_TRUE;

 46: PetscErrorCode FormMatrix(Mat,void*);
 47: PetscErrorCode FormRightHandSide(Vec,void*);

 49: int main(int argc,char **argv)
 50: {
 51:   KSP            ksp;
 52:   Mat            J;
 53:   DM             da;
 54:   Vec            x,r;              /* vectors */
 56:   PetscInt       M = 10;
 57:   MatNullSpace   constants,nconstants;

 59:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 60:   PetscOptionsGetInt(NULL,NULL,"-M",&M,NULL);
 61:   PetscOptionsGetBool(NULL,NULL,"-symmetric",&symmetric,NULL);

 63:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 64:      Create linear solver context
 65:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 67:   KSPCreate(PETSC_COMM_WORLD,&ksp);

 69:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 70:      Create vector data structures; set function evaluation routine
 71:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 73:   /*
 74:      Create distributed array (DMDA) to manage parallel grid and vectors
 75:   */
 76:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,M,1,2,NULL,&da);
 77:   DMSetFromOptions(da);
 78:   DMSetUp(da);

 80:   /*
 81:      Extract global and local vectors from DMDA; then duplicate for remaining
 82:      vectors that are the same types
 83:   */
 84:   DMCreateGlobalVector(da,&x);
 85:   VecDuplicate(x,&r);

 87:   /*
 88:      Set function evaluation routine and vector.  Whenever the nonlinear
 89:      solver needs to compute the nonlinear function, it will call this
 90:      routine.
 91:       - Note that the final routine argument is the user-defined
 92:         context that provides application-specific data for the
 93:         function evaluation routine.
 94:   */
 95:   FormRightHandSide(r,da);

 97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 98:      Create matrix data structure;
 99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
100:   DMCreateMatrix(da,&J);
101:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,NULL,&constants);
102:   if (symmetric) {
103:     MatSetOption(J,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
104:     MatSetOption(J,MAT_SYMMETRIC,PETSC_TRUE);
105:   } else {
106:     Vec         n;
107:     PetscInt    zero = 0;
108:     PetscScalar zeros = 0.0;
109:     VecDuplicate(x,&n);
110:     /* the nullspace(A') is the constant vector but with a zero in the very first entry; hence nullspace(A') != nullspace(A) */
111:     VecSet(n,1.0);
112:     VecSetValues(n,1,&zero,&zeros,INSERT_VALUES);
113:     VecAssemblyBegin(n);
114:     VecAssemblyEnd(n);
115:     VecNormalize(n,NULL);
116:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_FALSE,1,&n,&nconstants);
117:     MatSetTransposeNullSpace(J,nconstants);
118:     MatNullSpaceDestroy(&nconstants);
119:     VecDestroy(&n);
120:   }
121:   MatSetNullSpace(J,constants);
122:   FormMatrix(J,da);

124:   KSPSetOperators(ksp,J,J);

126:   KSPSetFromOptions(ksp);
127:   KSPSolve(ksp,r,x);
128:   KSPSolveTranspose(ksp,r,x);

130:   VecDestroy(&x);
131:   VecDestroy(&r);
132:   MatDestroy(&J);
133:   MatNullSpaceDestroy(&constants);
134:   KSPDestroy(&ksp);
135:   DMDestroy(&da);
136:   PetscFinalize();
137:   return ierr;
138: }

140: /*

142:      This intentionally includes something in the right hand side that is not in the range of the matrix A.
143:      Since MatSetNullSpace() is called and the matrix is symmetric; the Krylov method automatically removes this
144:      portion of the right hand side before solving the linear system.
145: */
146: PetscErrorCode FormRightHandSide(Vec f,void *ctx)
147: {
148:   DM             da    = (DM) ctx;
149:   PetscScalar    *ff;
151:   PetscInt       i,M,xs,xm;
152:   PetscReal      h;

155:   DMDAVecGetArray(da,f,&ff);

157:   /*
158:      Get local grid boundaries (for 1-dimensional DMDA):
159:        xs, xm  - starting grid index, width of local grid (no ghost points)
160:   */
161:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
162:   DMDAGetInfo(da,NULL,&M,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);

164:   /*
165:      Compute function over locally owned part of the grid
166:      Note the [i-1] and [i+1] will automatically access the ghost points from other processes or the periodic points.
167:   */
168:   h = 1.0/M;
169:   for (i=xs; i<xs+xm; i++) ff[i] = - PetscSinReal(2.0*PETSC_PI*i*h) + 1.0;

171:   /*
172:      Restore vectors
173:   */
174:   DMDAVecRestoreArray(da,f,&ff);
175:   return(0);
176: }
177: /* ------------------------------------------------------------------- */
178: PetscErrorCode FormMatrix(Mat jac,void *ctx)
179: {
180:   PetscScalar    A[3];
182:   PetscInt       i,M,xs,xm;
183:   DM             da = (DM) ctx;
184:   MatStencil     row,cols[3];
185:   PetscReal      h;

188:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

190:   /*
191:     Get range of locally owned matrix
192:   */
193:   DMDAGetInfo(da,NULL,&M,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);

195:   MatZeroEntries(jac);
196:   h = 1.0/M;
197:   /* because of periodic boundary conditions we can simply loop over all local nodes and access to the left and right */
198:   if (symmetric) {
199:     for (i=xs; i<xs+xm; i++) {
200:       row.i = i;
201:       cols[0].i = i - 1;
202:       cols[1].i = i;
203:       cols[2].i = i + 1;
204:       A[0] = A[2] = 1.0/(h*h); A[1] = -2.0/(h*h);
205:       MatSetValuesStencil(jac,1,&row,3,cols,A,ADD_VALUES);
206:     }
207:   } else {
208:     MatStencil  *acols;
209:     PetscScalar *avals;

211:     /* only works for one process */
212:     MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
213:     row.i = 0;
214:     PetscMalloc1(M,&acols);
215:     PetscMalloc1(M,&avals);
216:     for (i=0; i<M; i++) {
217:       acols[i].i = i;
218:       avals[i]  = (i % 2) ? 1 : -1;
219:     }
220:     MatSetValuesStencil(jac,1,&row,M,acols,avals,ADD_VALUES);
221:     PetscFree(acols);
222:     PetscFree(avals);
223:     row.i = 1;
224:     cols[0].i = - 1;
225:     cols[1].i = 1;
226:     cols[2].i = 1 + 1;
227:     A[0] = A[2] = 1.0/(h*h); A[1] = -2.0/(h*h);
228:     MatSetValuesStencil(jac,1,&row,3,cols,A,ADD_VALUES);
229:     for (i=2; i<xs+xm-1; i++) {
230:       row.i = i;
231:       cols[0].i = i - 1;
232:       cols[1].i = i;
233:       cols[2].i = i + 1;
234:       A[0] = A[2] = 1.0/(h*h); A[1] = -2.0/(h*h);
235:       MatSetValuesStencil(jac,1,&row,3,cols,A,ADD_VALUES);
236:     }
237:     row.i = M - 1 ;
238:     cols[0].i = M-2;
239:     cols[1].i = M-1;
240:     cols[2].i = M+1;
241:     A[0] = A[2] = 1.0/(h*h); A[1] = -2.0/(h*h);
242:     MatSetValuesStencil(jac,1,&row,3,cols,A,ADD_VALUES);
243:   }
244:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
245:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
246:   return(0);
247: }


250: /*TEST

252:    test:
253:       suffix: nonsymmetric_left
254:       args: -symmetric false -ksp_view -ksp_converged_reason -pc_type jacobi -mat_no_inode -ksp_monitor_true_residual -ksp_rtol 1.e-14 -ksp_max_it 12 -ksp_pc_side left
255:       filter: sed 's/ATOL/RTOL/g'
256:       requires: !single

258:    test:
259:       suffix: nonsymmetric_right
260:       args: -symmetric false -ksp_view -ksp_converged_reason -pc_type jacobi -mat_no_inode -ksp_monitor_true_residual -ksp_rtol 1.e-14 -ksp_max_it 12 -ksp_pc_side right
261:       filter: sed 's/ATOL/RTOL/g'
262:       requires: !single

264:    test:
265:       suffix: symmetric_left
266:       args: -ksp_view -ksp_converged_reason -pc_type sor -mat_no_inode -ksp_monitor_true_residual -ksp_rtol 1.e-14 -ksp_max_it 12 -ksp_pc_side left
267:       requires: !single

269:    test:
270:       suffix: symmetric_right
271:       args: -ksp_view -ksp_converged_reason -pc_type sor -mat_no_inode -ksp_monitor_true_residual -ksp_rtol 1.e-14 -ksp_max_it 12 -ksp_pc_side right
272:       filter: sed 's/ATOL/RTOL/g'
273:       requires: !single

275:    test:
276:       suffix: transpose_asm
277:       args: -symmetric false -ksp_monitor -ksp_view -pc_type asm -sub_pc_type lu -sub_pc_factor_zeropivot 1.e-33 -ksp_converged_reason
278:       filter: sed 's/ATOL/RTOL/g'

280: TEST*/