2: /* Program usage:  mpiexec -n <procs> ex12 [-help] [all PETSc options] */

  4: static char help[] = "Solves a linear system in parallel with KSP.\n\
  5: Input parameters include:\n\
  6:   -m <mesh_x>       : number of mesh points in x-direction\n\
  7:   -n <mesh_n>       : number of mesh points in y-direction\n\n";

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

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

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

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

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

 29:    See the manual page PCRegisterDynamic() for details on how to register a method.
 30: */

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

 42: EXTERN_C_BEGIN
 43: extern PetscErrorCode PCCreate_Jacobi(PC);
 44: EXTERN_C_END

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

 59:   PetscInitialize(&argc,&args,(char *)0,help);
 60:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
 61:   PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);

 63:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 64:          Compute the matrix and right-hand-side vector that define
 65:          the linear system, Ax = b.
 66:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 67:   /* 
 68:      Create parallel matrix, specifying only its global dimensions.
 69:      When using MatCreate(), the matrix format can be specified at
 70:      runtime. Also, the parallel partitioning of the matrix can be
 71:      determined by PETSc at runtime.
 72:   */
 73:   MatCreate(PETSC_COMM_WORLD,&A);
 74:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 75:   MatSetFromOptions(A);
 76:   MatSetUp(A);

 78:   /* 
 79:      Currently, all PETSc parallel matrix formats are partitioned by
 80:      contiguous chunks of rows across the processors.  Determine which
 81:      rows of the matrix are locally owned. 
 82:   */
 83:   MatGetOwnershipRange(A,&Istart,&Iend);

 85:   /* 
 86:      Set matrix elements for the 2-D, five-point stencil in parallel.
 87:       - Each processor needs to insert only elements that it owns
 88:         locally (but any non-local elements will be sent to the
 89:         appropriate processor during matrix assembly). 
 90:       - Always specify global rows and columns of matrix entries.
 91:    */
 92:   for (Ii=Istart; Ii<Iend; Ii++) {
 93:     v = -1.0; i = Ii/n; j = Ii - i*n;
 94:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 95:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 96:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 97:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 98:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 99:   }

101:   /* 
102:      Assemble matrix, using the 2-step process:
103:        MatAssemblyBegin(), MatAssemblyEnd()
104:      Computations can be done while messages are in transition
105:      by placing code between these two statements.
106:   */
107:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
108:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

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

127:   /* 
128:      Set exact solution; then compute right-hand-side vector.
129:      Use an exact solution of a vector with all elements of 1.0;  
130:   */
131:   VecSet(u,one);
132:   MatMult(A,u,b);

134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
135:                 Create the linear solver and set various options
136:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

138:   /* 
139:      Create linear solver context
140:   */
141:   KSPCreate(PETSC_COMM_WORLD,&ksp);

143:   /* 
144:      Set operators. Here the matrix that defines the linear system
145:      also serves as the preconditioning matrix.
146:   */
147:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);

149:   /*
150:        First register a new PC type with the command PCRegister()
151:   */
152:   PCRegister("ourjacobi",0,"PCCreate_Jacobi",PCCreate_Jacobi);
153: 
154:   /* 
155:      Set the PC type to be the new method
156:   */
157:   KSPGetPC(ksp,&pc);
158:   PCSetType(pc,"ourjacobi");

160:   /* 
161:     Set runtime options, e.g.,
162:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
163:     These options will override those specified above as long as
164:     KSPSetFromOptions() is called _after_ any other customization
165:     routines.
166:   */
167:   KSPSetFromOptions(ksp);

169:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
170:                       Solve the linear system
171:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

173:   KSPSolve(ksp,b,x);

175:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
176:                       Check solution and clean up
177:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

179:   /* 
180:      Check the error
181:   */
182:   VecAXPY(x,neg_one,u);
183:   VecNorm(x,NORM_2,&norm);
184:   KSPGetIterationNumber(ksp,&its);
185:   /* Scale the norm */
186:   /*  norm *= sqrt(1.0/((m+1)*(n+1))); */

188:   /*
189:      Print convergence information.  PetscPrintf() produces a single 
190:      print statement from all processes that share a communicator.
191:   */
192:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G iterations %D\n",norm,its);

194:   /* 
195:      Free work space.  All PETSc objects should be destroyed when they
196:      are no longer needed.
197:   */
198:   KSPDestroy(&ksp);
199:   VecDestroy(&u);  VecDestroy(&x);
200:   VecDestroy(&b);  MatDestroy(&A);

202:   /*
203:      Always call PetscFinalize() before exiting a program.  This routine
204:        - finalizes the PETSc libraries as well as MPI
205:        - provides summary and diagnostic information if certain runtime
206:          options are chosen (e.g., -log_summary). 
207:   */
208:   PetscFinalize();
209:   return 0;
210: }