Actual source code: ex12.c

petsc-master 2019-12-15
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  2: static char help[] = "Solves a linear system in parallel with KSP,\n\
  3: demonstrating how to register a new preconditioner (PC) type.\n\
  4: Input parameters include:\n\
  5:   -m <mesh_x>       : number of mesh points in x-direction\n\
  6:   -n <mesh_n>       : number of mesh points in y-direction\n\n";

  8: /*T
  9:    Concepts: KSP^solving a system of linear equations
 10:    Concepts: KSP^Laplacian, 2d
 11:    Concepts: PC^registering preconditioners
 12:    Processors: n
 13: T*/

 15: /*
 16:    Demonstrates registering a new preconditioner (PC) type.

 18:    To register a PC type whose code is linked into the executable,
 19:    use PCRegister(). To register a PC type in a dynamic library use PCRegister()

 21:    Also provide the prototype for your PCCreate_XXX() function. In
 22:    this example we use the PETSc implementation of the Jacobi method,
 23:    PCCreate_Jacobi() just as an example.

 25:    See the file src/ksp/pc/impls/jacobi/jacobi.c for details on how to
 26:    write a new PC component.

 28:    See the manual page PCRegister() for details on how to register a method.
 29: */

 31: /*
 32:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 33:   automatically includes:
 34:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 35:      petscmat.h - matrices
 36:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 37:      petscviewer.h - viewers               petscpc.h  - preconditioners
 38: */
 39:  #include <petscksp.h>

 41: PETSC_EXTERN PetscErrorCode PCCreate_Jacobi(PC);

 43: int main(int argc,char **args)
 44: {
 45:   Vec            x,b,u;  /* approx solution, RHS, exact solution */
 46:   Mat            A;        /* linear system matrix */
 47:   KSP            ksp;     /* linear solver context */
 48:   PetscReal      norm;     /* norm of solution error */
 49:   PetscInt       i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
 51:   PetscScalar    v,one = 1.0;
 52:   PC             pc;      /* preconditioner context */

 54:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 55:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 56:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

 58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 59:          Compute the matrix and right-hand-side vector that define
 60:          the linear system, Ax = b.
 61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 62:   /*
 63:      Create parallel matrix, specifying only its global dimensions.
 64:      When using MatCreate(), the matrix format can be specified at
 65:      runtime. Also, the parallel partitioning of the matrix can be
 66:      determined by PETSc at runtime.
 67:   */
 68:   MatCreate(PETSC_COMM_WORLD,&A);
 69:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 70:   MatSetFromOptions(A);
 71:   MatSetUp(A);

 73:   /*
 74:      Currently, all PETSc parallel matrix formats are partitioned by
 75:      contiguous chunks of rows across the processors.  Determine which
 76:      rows of the matrix are locally owned.
 77:   */
 78:   MatGetOwnershipRange(A,&Istart,&Iend);

 80:   /*
 81:      Set matrix elements for the 2-D, five-point stencil in parallel.
 82:       - Each processor needs to insert only elements that it owns
 83:         locally (but any non-local elements will be sent to the
 84:         appropriate processor during matrix assembly).
 85:       - Always specify global rows and columns of matrix entries.
 86:    */
 87:   for (Ii=Istart; Ii<Iend; Ii++) {
 88:     v = -1.0; i = Ii/n; j = Ii - i*n;
 89:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 90:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 91:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 92:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 93:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 94:   }

 96:   /*
 97:      Assemble matrix, using the 2-step process:
 98:        MatAssemblyBegin(), MatAssemblyEnd()
 99:      Computations can be done while messages are in transition
100:      by placing code between these two statements.
101:   */
102:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
103:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

105:   /*
106:      Create parallel vectors.
107:       - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
108:       we specify only the vector's global
109:         dimension; the parallel partitioning is determined at runtime.
110:       - When solving a linear system, the vectors and matrices MUST
111:         be partitioned accordingly.  PETSc automatically generates
112:         appropriately partitioned matrices and vectors when MatCreate()
113:         and VecCreate() are used with the same communicator.
114:       - Note: We form 1 vector from scratch and then duplicate as needed.
115:   */
116:   VecCreate(PETSC_COMM_WORLD,&u);
117:   VecSetSizes(u,PETSC_DECIDE,m*n);
118:   VecSetFromOptions(u);
119:   VecDuplicate(u,&b);
120:   VecDuplicate(b,&x);

122:   /*
123:      Set exact solution; then compute right-hand-side vector.
124:      Use an exact solution of a vector with all elements of 1.0;
125:   */
126:   VecSet(u,one);
127:   MatMult(A,u,b);

129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130:                 Create the linear solver and set various options
131:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

133:   /*
134:      Create linear solver context
135:   */
136:   KSPCreate(PETSC_COMM_WORLD,&ksp);

138:   /*
139:      Set operators. Here the matrix that defines the linear system
140:      also serves as the preconditioning matrix.
141:   */
142:   KSPSetOperators(ksp,A,A);

144:   /*
145:        First register a new PC type with the command PCRegister()
146:   */
147:   PCRegister("ourjacobi",PCCreate_Jacobi);

149:   /*
150:      Set the PC type to be the new method
151:   */
152:   KSPGetPC(ksp,&pc);
153:   PCSetType(pc,"ourjacobi");

155:   /*
156:     Set runtime options, e.g.,
157:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
158:     These options will override those specified above as long as
159:     KSPSetFromOptions() is called _after_ any other customization
160:     routines.
161:   */
162:   KSPSetFromOptions(ksp);

164:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165:                       Solve the linear system
166:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

168:   KSPSolve(ksp,b,x);

170:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171:                       Check solution and clean up
172:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

174:   /*
175:      Check the error
176:   */
177:   VecAXPY(x,-1.0,u);
178:   VecNorm(x,NORM_2,&norm);
179:   KSPGetIterationNumber(ksp,&its);

181:   /*
182:      Print convergence information.  PetscPrintf() produces a single
183:      print statement from all processes that share a communicator.
184:   */
185:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

187:   /*
188:      Free work space.  All PETSc objects should be destroyed when they
189:      are no longer needed.
190:   */
191:   KSPDestroy(&ksp);
192:   VecDestroy(&u);  VecDestroy(&x);
193:   VecDestroy(&b);  MatDestroy(&A);

195:   /*
196:      Always call PetscFinalize() before exiting a program.  This routine
197:        - finalizes the PETSc libraries as well as MPI
198:        - provides summary and diagnostic information if certain runtime
199:          options are chosen (e.g., -log_view).
200:   */
201:   PetscFinalize();
202:   return ierr;
203: }


206: /*TEST

208:    test:
209:       args: -ksp_gmres_cgs_refinement_type refine_always

211: TEST*/