Actual source code: ex48.c

petsc-3.12.0 2019-09-29
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  2: static char help[] = "Solves a tridiagonal linear system with KSP.\n\n";

  4: /*
  5:     Test example that demonstrates how MINRES can produce a dp of zero
  6:     but still converge.

  8:     Provided by: Mark Filipiak <mjf@staffmail.ed.ac.uk>
  9: */
 10:  #include <petscksp.h>

 12: int main(int argc,char **args)
 13: {
 14:   Vec            x, b, u;      /* approx solution, RHS, exact solution */
 15:   Mat            A;            /* linear system matrix */
 16:   KSP            ksp;         /* linear solver context */
 17:   PC             pc;           /* preconditioner context */
 18:   PetscReal      norm;
 20:   PetscInt       i,n = 2,col[3],its;
 21:   PetscMPIInt    size;
 22:   PetscScalar    one = 1.0,value[3];
 23:   PetscBool      nonzeroguess = PETSC_FALSE;

 25:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 26:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 27:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
 28:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 29:   PetscOptionsGetBool(NULL,NULL,"-nonzero_guess",&nonzeroguess,NULL);


 32:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 33:          Compute the matrix and right-hand-side vector that define
 34:          the linear system, Ax = b.
 35:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 37:   /*
 38:      Create vectors.  Note that we form 1 vector from scratch and
 39:      then duplicate as needed.
 40:   */
 41:   VecCreate(PETSC_COMM_WORLD,&x);
 42:   PetscObjectSetName((PetscObject) x, "Solution");
 43:   VecSetSizes(x,PETSC_DECIDE,n);
 44:   VecSetFromOptions(x);
 45:   VecDuplicate(x,&b);
 46:   VecDuplicate(x,&u);

 48:   /*
 49:      Create matrix.  When using MatCreate(), the matrix format can
 50:      be specified at runtime.

 52:      Performance tuning note:  For problems of substantial size,
 53:      preallocation of matrix memory is crucial for attaining good
 54:      performance. See the matrix chapter of the users manual for details.
 55:   */
 56:   MatCreate(PETSC_COMM_WORLD,&A);
 57:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
 58:   MatSetFromOptions(A);
 59:   MatSetUp(A);

 61:   /*
 62:      Assemble matrix
 63:   */
 64:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
 65:   for (i=1; i<n-1; i++) {
 66:     col[0] = i-1; col[1] = i; col[2] = i+1;
 67:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 68:   }
 69:   i    = n - 1; col[0] = n - 2; col[1] = n - 1;
 70:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 71:   i    = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
 72:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 73:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 74:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 76:   /*
 77:      Set constant right-hand-side vector.
 78:   */
 79:   VecSet(b,one);
 80:   /*
 81:      Solution = RHS for the matrix [[2 -1] [-1 2]] and RHS [1 1]
 82:   */
 83:   VecSet(u,one);

 85:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 86:                 Create the linear solver and set various options
 87:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 88:   /*
 89:      Create linear solver context
 90:   */
 91:   KSPCreate(PETSC_COMM_WORLD,&ksp);

 93:   /*
 94:      Set operators. Here the matrix that defines the linear system
 95:      also serves as the preconditioning matrix.
 96:   */
 97:   KSPSetOperators(ksp,A,A);

 99:   /*
100:      Set linear solver defaults for this problem (optional).
101:      - By extracting the KSP and PC contexts from the KSP context,
102:        we can then directly call any KSP and PC routines to set
103:        various options.
104:      - The following four statements are optional; all of these
105:        parameters could alternatively be specified at runtime via
106:        KSPSetFromOptions();
107:   */
108:   KSPGetPC(ksp,&pc);
109:   PCSetType(pc,PCJACOBI);
110:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

112:   /*
113:     Set runtime options, e.g.,
114:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
115:     These options will override those specified above as long as
116:     KSPSetFromOptions() is called _after_ any other customization
117:     routines.
118:   */
119:   KSPSetFromOptions(ksp);

121:   if (nonzeroguess) {
122:     PetscScalar p = .5;
123:     VecSet(x,p);
124:     KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
125:   }

127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128:                       Solve the linear system
129:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
130:   /*
131:      Solve linear system
132:   */
133:   KSPSolve(ksp,b,x);

135:   /*
136:      View solver info; we could instead use the option -ksp_view to
137:      print this info to the screen at the conclusion of KSPSolve().
138:   */
139:   KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);

141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142:                       Check solution and clean up
143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144:   /*
145:      Check the error
146:   */
147:   VecAXPY(x,-1.0,u);
148:   VecNorm(x,NORM_2,&norm);
149:   KSPGetIterationNumber(ksp,&its);
150:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);


153:   /*
154:      Free work space.  All PETSc objects should be destroyed when they
155:      are no longer needed.
156:   */
157:   VecDestroy(&x); VecDestroy(&u);
158:   VecDestroy(&b); MatDestroy(&A);
159:   KSPDestroy(&ksp);

161:   /*
162:      Always call PetscFinalize() before exiting a program.  This routine
163:        - finalizes the PETSc libraries as well as MPI
164:        - provides summary and diagnostic information if certain runtime
165:          options are chosen (e.g., -log_view).
166:   */
167:   PetscFinalize();
168:   return ierr;
169: }


172: /*TEST

174:    test:
175:       args: -ksp_monitor_short -ksp_converged_reason -ksp_type minres -pc_type jacobi -ksp_error_if_not_converged

177: TEST*/