Actual source code: ex58.c

petsc-3.5.2 2014-09-08
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  2: static char help[] = "Solves a tridiagonal linear system with KSP.\n\n";

  4: /*T
  5:    Concepts: KSP^solving a system of linear equations
  6:    Processors: 1
  7: T*/

  9: /*
 10:   Modified from ex1.c for testing matrix operations when matrix structure is changed.
 11:   Contributed by Jose E. Roman, Feb. 2012.
 12: */
 13: #include <petscksp.h>

 17: int main(int argc,char **args)
 18: {
 19:   Vec            x, b, u;      /* approx solution, RHS, exact solution */
 20:   Mat            A,B,C;        /* linear system matrix */
 21:   KSP            ksp;          /* linear solver context */
 22:   PC             pc;           /* preconditioner context */
 23:   PetscReal      norm;         /* norm of solution error */
 25:   PetscInt       i,n = 20,col[3],its;
 26:   PetscMPIInt    size;
 27:   PetscScalar    neg_one      = -1.0,one = 1.0,value[3];
 28:   PetscBool      nonzeroguess = PETSC_FALSE;

 30:   PetscInitialize(&argc,&args,(char*)0,help);
 31:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 32:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
 33:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
 34:   PetscOptionsGetBool(NULL,"-nonzero_guess",&nonzeroguess,NULL);


 37:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 38:          Compute the matrix and right-hand-side vector that define
 39:          the linear system, Ax = b.
 40:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 53:   /*
 54:      Create matrix.  When using MatCreate(), the matrix format can
 55:      be specified at runtime.

 57:      Performance tuning note:  For problems of substantial size,
 58:      preallocation of matrix memory is crucial for attaining good
 59:      performance. See the matrix chapter of the users manual for details.
 60:   */
 61:   MatCreate(PETSC_COMM_WORLD,&A);
 62:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
 63:   MatSetFromOptions(A);
 64:   MatSetUp(A);

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

 81:   /*
 82:      jroman: added matrices
 83:   */
 84:   MatCreate(PETSC_COMM_WORLD,&B);
 85:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
 86:   MatSetFromOptions(B);
 87:   MatSetUp(B);
 88:   for (i=0; i<n; i++) {
 89:     MatSetValue(B,i,i,value[1],INSERT_VALUES);
 90:     if (n-i+n/3<n) {
 91:       MatSetValue(B,n-i+n/3,i,value[0],INSERT_VALUES);
 92:       MatSetValue(B,i,n-i+n/3,value[0],INSERT_VALUES);
 93:     }
 94:   }
 95:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 96:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 97:   MatDuplicate(A,MAT_COPY_VALUES,&C);
 98:   MatAXPY(C,2.0,B,DIFFERENT_NONZERO_PATTERN);

100:   /*
101:      Set exact solution; then compute right-hand-side vector.
102:   */
103:   VecSet(u,one);
104:   MatMult(C,u,b);

106:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
107:                 Create the linear solver and set various options
108:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
109:   /*
110:      Create linear solver context
111:   */
112:   KSPCreate(PETSC_COMM_WORLD,&ksp);

114:   /*
115:      Set operators. Here the matrix that defines the linear system
116:      also serves as the preconditioning matrix.
117:   */
118:   KSPSetOperators(ksp,C,C);

120:   /*
121:      Set linear solver defaults for this problem (optional).
122:      - By extracting the KSP and PC contexts from the KSP context,
123:        we can then directly call any KSP and PC routines to set
124:        various options.
125:      - The following four statements are optional; all of these
126:        parameters could alternatively be specified at runtime via
127:        KSPSetFromOptions();
128:   */
129:   KSPGetPC(ksp,&pc);
130:   PCSetType(pc,PCJACOBI);
131:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

133:   /*
134:     Set runtime options, e.g.,
135:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
136:     These options will override those specified above as long as
137:     KSPSetFromOptions() is called _after_ any other customization
138:     routines.
139:   */
140:   KSPSetFromOptions(ksp);

142:   if (nonzeroguess) {
143:     PetscScalar p = .5;
144:     VecSet(x,p);
145:     KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
146:   }

148:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149:                       Solve the linear system
150:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
151:   /*
152:      Solve linear system
153:   */
154:   KSPSolve(ksp,b,x);

156:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157:                       Check solution and clean up
158:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
159:   /*
160:      Check the error
161:   */
162:   VecAXPY(x,neg_one,u);
163:   VecNorm(x,NORM_2,&norm);
164:   KSPGetIterationNumber(ksp,&its);
165:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);

167:   /*
168:      Free work space.  All PETSc objects should be destroyed when they
169:      are no longer needed.
170:   */
171:   VecDestroy(&x); VecDestroy(&u);
172:   VecDestroy(&b); MatDestroy(&A);
173:   MatDestroy(&B);
174:   MatDestroy(&C);
175:   KSPDestroy(&ksp);

177:   /*
178:      Always call PetscFinalize() before exiting a program.  This routine
179:        - finalizes the PETSc libraries as well as MPI
180:        - provides summary and diagnostic information if certain runtime
181:          options are chosen (e.g., -log_summary).
182:   */
183:   PetscFinalize();
184:   return 0;
185: }