Actual source code: ex38.c

petsc-3.6.4 2016-04-12
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  1: /*

  3: mpiexec -n 8 ./ex38 -ksp_type fbcgs -ksp_rtol 1.e-6 -sub_ksp_type bcgs -sub_ksp_rtol 1.e-3 -pc_type bjacobi -ksp_converged_reason -ksp_monitor -n1 64 -n2 64

  5:   Contributed by Jie Chen for testing flexible BiCGStab algorithm
  6: */

  8: static char help[] = "Solves the PDE (in 2D) -laplacian(u) + gamma x dot grad(u) + beta u = 1\n\
  9: with zero Dirichlet condition. The discretization is standard centered\n\
 10: difference. Input parameters include:\n\
 11:   -n1        : number of mesh points in 1st dimension (default 64)\n\
 12:   -n2        : number of mesh points in 2nd dimension (default 64)\n\
 13:   -h         : spacing between mesh points (default 1/n1)\n\
 14:   -gamma     : gamma (default 4/h)\n\
 15:   -beta      : beta (default 0.01/h^2)\n\n";

 17: /*T
 18:    Concepts: KSP^basic parallel example;
 19:    Concepts: KSP^Laplacian, 2d
 20:    Concepts: Laplacian, 2d
 21:    Processors: n
 22: T*/

 24: /*
 25:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 26:   automatically includes:
 27:      petscsys.h    - base PETSc routines   petscvec.h - vectors
 28:      petscmat.h    - matrices
 29:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 30:      petscviewer.h - viewers               petscpc.h  - preconditioners
 31: */
 32: #include <petscksp.h>

 36: int main(int argc,char **args)
 37: {
 38:   Vec            x,b,u;                 /* approx solution, RHS, working vector */
 39:   Mat            A;                     /* linear system matrix */
 40:   KSP            ksp;                   /* linear solver context */
 41:   PetscInt       n1, n2;                /* parameters */
 42:   PetscReal      h, gamma, beta;        /* parameters */
 43:   PetscInt       i,j,Ii,J,Istart,Iend;
 45:   PetscScalar    v, co1, co2;
 46: #if defined(PETSC_USE_LOG)
 47:   PetscLogStage stage;
 48: #endif

 50:   PetscInitialize(&argc,&args,(char*)0,help);

 52:   n1 = 64;
 53:   n2 = 64;

 55:   PetscOptionsGetInt(NULL,"-n1",&n1,NULL);
 56:   PetscOptionsGetInt(NULL,"-n2",&n2,NULL);

 58:   h     = 1.0/n1;
 59:   gamma = 4.0;
 60:   beta  = 0.01;

 62:   PetscOptionsGetReal(NULL,"-h",&h,NULL);
 63:   PetscOptionsGetReal(NULL,"-gamma",&gamma,NULL);
 64:   PetscOptionsGetReal(NULL,"-beta",&beta,NULL);
 65:   gamma = gamma/h;
 66:   beta  = beta/(h*h);

 68:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 69:          Compute the matrix and set right-hand-side vector.
 70:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 71:   /*
 72:      Create parallel matrix, specifying only its global dimensions.
 73:      When using MatCreate(), the matrix format can be specified at
 74:      runtime. Also, the parallel partitioning of the matrix is
 75:      determined by PETSc at runtime.

 77:      Performance tuning note:  For problems of substantial size,
 78:      preallocation of matrix memory is crucial for attaining good
 79:      performance. See the matrix chapter of the users manual for details.
 80:   */
 81:   MatCreate(PETSC_COMM_WORLD,&A);
 82:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n1*n2,n1*n2);
 83:   MatSetFromOptions(A);
 84:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
 85:   MatSeqAIJSetPreallocation(A,5,NULL);
 86:   MatSetUp(A);

 88:   /*
 89:      Currently, all PETSc parallel matrix formats are partitioned by
 90:      contiguous chunks of rows across the processors.  Determine which
 91:      rows of the matrix are locally owned.
 92:   */
 93:   MatGetOwnershipRange(A,&Istart,&Iend);

 95:   /*
 96:      Set matrix elements for the 2-D, five-point stencil in parallel.
 97:       - Each processor needs to insert only elements that it owns
 98:         locally (but any non-local elements will be sent to the
 99:         appropriate processor during matrix assembly).
100:       - Always specify global rows and columns of matrix entries.
101:    */
102:   PetscLogStageRegister("Assembly", &stage);
103:   PetscLogStagePush(stage);
104:   co1  = gamma * h * h / 2.0;
105:   co2  = beta * h * h;
106:   for (Ii=Istart; Ii<Iend; Ii++) {
107:     i = Ii/n2; j = Ii - i*n2;
108:     if (i>0) {
109:       J    = Ii - n2;  v = -1.0 + co1*(PetscScalar)i;
110:       MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
111:     }
112:     if (i<n1-1) {
113:       J    = Ii + n2;  v = -1.0 + co1*(PetscScalar)i;
114:       MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
115:     }
116:     if (j>0) {
117:       J    = Ii - 1;  v = -1.0 + co1*(PetscScalar)j;
118:       MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
119:     }
120:     if (j<n2-1) {
121:       J    = Ii + 1;  v = -1.0 + co1*(PetscScalar)j;
122:       MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
123:     }
124:     v    = 4.0 + co2;
125:     MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
126:   }

128:   /*
129:      Assemble matrix, using the 2-step process:
130:        MatAssemblyBegin(), MatAssemblyEnd()
131:      Computations can be done while messages are in transition
132:      by placing code between these two statements.
133:   */
134:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
135:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
136:   PetscLogStagePop();

138:   /*
139:      Create parallel vectors.
140:       - We form 1 vector from scratch and then duplicate as needed.
141:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
142:         in this example, we specify only the
143:         vector's global dimension; the parallel partitioning is determined
144:         at runtime.
145:       - When solving a linear system, the vectors and matrices MUST
146:         be partitioned accordingly.  PETSc automatically generates
147:         appropriately partitioned matrices and vectors when MatCreate()
148:         and VecCreate() are used with the same communicator.
149:       - The user can alternatively specify the local vector and matrix
150:         dimensions when more sophisticated partitioning is needed
151:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
152:         below).
153:   */
154:   VecCreate(PETSC_COMM_WORLD,&b);
155:   VecSetSizes(b,PETSC_DECIDE,n1*n2);
156:   VecSetFromOptions(b);
157:   VecDuplicate(b,&x);
158:   VecDuplicate(b,&u);

160:   /*
161:      Set right-hand side.
162:   */
163:   VecSet(b,1.0);

165:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
166:                 Create the linear solver and set various options
167:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
168:   /*
169:      Create linear solver context
170:   */
171:   KSPCreate(PETSC_COMM_WORLD,&ksp);

173:   /*
174:      Set operators. Here the matrix that defines the linear system
175:      also serves as the preconditioning matrix.
176:   */
177:   KSPSetOperators(ksp,A,A);

179:   /*
180:      Set linear solver defaults for this problem (optional).
181:      - By extracting the KSP and PC contexts from the KSP context,
182:        we can then directly call any KSP and PC routines to set
183:        various options.
184:   */
185:   KSPSetTolerances(ksp,1.e-6,1.e-50,PETSC_DEFAULT,200);

187:   /*
188:     Set runtime options, e.g.,
189:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
190:     These options will override those specified above as long as
191:     KSPSetFromOptions() is called _after_ any other customization
192:     routines.
193:   */
194:   KSPSetFromOptions(ksp);

196:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
197:                       Solve the linear system
198:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

200:   KSPSolve(ksp,b,x);

202:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
203:                       Clean up
204:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
205:   /*
206:      Free work space.  All PETSc objects should be destroyed when they
207:      are no longer needed.
208:   */
209:   KSPDestroy(&ksp);
210:   VecDestroy(&u);  VecDestroy(&x);
211:   VecDestroy(&b);  MatDestroy(&A);

213:   /*
214:      Always call PetscFinalize() before exiting a program.  This routine
215:        - finalizes the PETSc libraries as well as MPI
216:        - provides summary and diagnostic information if certain runtime
217:          options are chosen (e.g., -log_summary).
218:   */
219:   PetscFinalize();
220:   return 0;
221: }