Actual source code: ex11f.F90

  1: !
  2: !  Description: Solves a complex linear system in parallel with KSP (Fortran code).
  3: !
  4: !!/*T
  5: !  Concepts: KSP^solving a Helmholtz equation
  6: !  Concepts: complex numbers
  7: !  Processors: n
  8: !T*/

 10: !
 11: !  The model problem:
 12: !     Solve Helmholtz equation on the unit square: (0,1) x (0,1)
 13: !          -delta u - sigma1*u + i*sigma2*u = f,
 14: !           where delta = Laplace operator
 15: !     Dirichlet b.c.'s on all sides
 16: !     Use the 2-D, five-point finite difference stencil.
 17: !
 18: !     Compiling the code:
 19: !      This code uses the complex numbers version of PETSc, so configure
 20: !      must be run to enable this
 21: !
 22: !
 23: ! -----------------------------------------------------------------------

 25:       program main
 26: #include <petsc/finclude/petscksp.h>
 27:       use petscksp
 28:       implicit none

 30: !
 31: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 32: !                   Variable declarations
 33: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 34: !
 35: !  Variables:
 36: !     ksp     - linear solver context
 37: !     x, b, u  - approx solution, right-hand-side, exact solution vectors
 38: !     A        - matrix that defines linear system
 39: !     its      - iterations for convergence
 40: !     norm     - norm of error in solution
 41: !     rctx     - random number context
 42: !

 44:       KSP             ksp
 45:       Mat              A
 46:       Vec              x,b,u
 47:       PetscRandom      rctx
 48:       PetscReal norm,h2,sigma1
 49:       PetscScalar  none,sigma2,v,pfive,czero
 50:       PetscScalar  cone
 51:       PetscInt dim,its,n,Istart
 52:       PetscInt Iend,i,j,II,JJ,one
 53:       PetscErrorCode ierr
 54:       PetscMPIInt rank
 55:       PetscBool  flg
 56:       logical          use_random

 58: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 59: !                 Beginning of program
 60: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 62:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 63:       if (ierr .ne. 0) then
 64:         print*,'Unable to initialize PETSc'
 65:         stop
 66:       endif

 68:       none   = -1.0
 69:       n      = 6
 70:       sigma1 = 100.0
 71:       czero  = 0.0
 72:       cone   = PETSC_i
 73:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
 74:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-sigma1',sigma1,flg,ierr)
 75:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
 76:       dim    = n*n

 78: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 79: !      Compute the matrix and right-hand-side vector that define
 80: !      the linear system, Ax = b.
 81: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 83: !  Create parallel matrix, specifying only its global dimensions.
 84: !  When using MatCreate(), the matrix format can be specified at
 85: !  runtime. Also, the parallel partitioning of the matrix is
 86: !  determined by PETSc at runtime.

 88:       call MatCreate(PETSC_COMM_WORLD,A,ierr)
 89:       call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim,ierr)
 90:       call MatSetFromOptions(A,ierr)
 91:       call MatSetUp(A,ierr)

 93: !  Currently, all PETSc parallel matrix formats are partitioned by
 94: !  contiguous chunks of rows across the processors.  Determine which
 95: !  rows of the matrix are locally owned.

 97:       call MatGetOwnershipRange(A,Istart,Iend,ierr)

 99: !  Set matrix elements in parallel.
100: !   - Each processor needs to insert only elements that it owns
101: !     locally (but any non-local elements will be sent to the
102: !     appropriate processor during matrix assembly).
103: !   - Always specify global rows and columns of matrix entries.

105:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-norandom',flg,ierr)
106:       if (flg) then
107:          use_random = .false.
108:          sigma2 = 10.0*PETSC_i
109:       else
110:          use_random = .true.
111:          call PetscRandomCreate(PETSC_COMM_WORLD,rctx,ierr)
112:          call PetscRandomSetFromOptions(rctx,ierr)
113:          call PetscRandomSetInterval(rctx,czero,cone,ierr)
114:       endif
115:       h2 = 1.0/real((n+1)*(n+1))

117:       one = 1
118:       do 10, II=Istart,Iend-1
119:         v = -1.0
120:         i = II/n
121:         j = II - i*n
122:         if (i.gt.0) then
123:           JJ = II - n
124:           call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
125:         endif
126:         if (i.lt.n-1) then
127:           JJ = II + n
128:           call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
129:         endif
130:         if (j.gt.0) then
131:           JJ = II - 1
132:           call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
133:         endif
134:         if (j.lt.n-1) then
135:           JJ = II + 1
136:           call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
137:         endif
138:         if (use_random) call PetscRandomGetValue(rctx,sigma2,ierr)
139:         v = 4.0 - sigma1*h2 + sigma2*h2
140:         call  MatSetValues(A,one,II,one,II,v,ADD_VALUES,ierr)
141:  10   continue
142:       if (use_random) call PetscRandomDestroy(rctx,ierr)

144: !  Assemble matrix, using the 2-step process:
145: !       MatAssemblyBegin(), MatAssemblyEnd()
146: !  Computations can be done while messages are in transition
147: !  by placing code between these two statements.

149:       call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
150:       call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)

152: !  Create parallel vectors.
153: !   - Here, the parallel partitioning of the vector is determined by
154: !     PETSc at runtime.  We could also specify the local dimensions
155: !     if desired.
156: !   - Note: We form 1 vector from scratch and then duplicate as needed.

158:       call VecCreate(PETSC_COMM_WORLD,u,ierr)
159:       call VecSetSizes(u,PETSC_DECIDE,dim,ierr)
160:       call VecSetFromOptions(u,ierr)
161:       call VecDuplicate(u,b,ierr)
162:       call VecDuplicate(b,x,ierr)

164: !  Set exact solution; then compute right-hand-side vector.

166:       if (use_random) then
167:          call PetscRandomCreate(PETSC_COMM_WORLD,rctx,ierr)
168:          call PetscRandomSetFromOptions(rctx,ierr)
169:          call VecSetRandom(u,rctx,ierr)
170:       else
171:          pfive = 0.5
172:          call VecSet(u,pfive,ierr)
173:       endif
174:       call MatMult(A,u,b,ierr)

176: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177: !         Create the linear solver and set various options
178: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

180: !  Create linear solver context

182:       call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)

184: !  Set operators. Here the matrix that defines the linear system
185: !  also serves as the preconditioning matrix.

187:       call KSPSetOperators(ksp,A,A,ierr)

189: !  Set runtime options, e.g.,
190: !      -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>

192:       call KSPSetFromOptions(ksp,ierr)

194: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195: !                      Solve the linear system
196: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

198:       call KSPSolve(ksp,b,x,ierr)

200: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
201: !                     Check solution and clean up
202: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

204: !  Check the error

206:       call VecAXPY(x,none,u,ierr)
207:       call VecNorm(x,NORM_2,norm,ierr)
208:       call KSPGetIterationNumber(ksp,its,ierr)
209:       if (rank .eq. 0) then
210:         if (norm .gt. 1.e-12) then
211:            write(6,100) norm,its
212:         else
213:            write(6,110) its
214:         endif
215:       endif
216:   100 format('Norm of error ',e11.4,',iterations ',i5)
217:   110 format('Norm of error < 1.e-12,iterations ',i5)

219: !  Free work space.  All PETSc objects should be destroyed when they
220: !  are no longer needed.

222:       if (use_random) call PetscRandomDestroy(rctx,ierr)
223:       call KSPDestroy(ksp,ierr)
224:       call VecDestroy(u,ierr)
225:       call VecDestroy(x,ierr)
226:       call VecDestroy(b,ierr)
227:       call MatDestroy(A,ierr)

229:       call PetscFinalize(ierr)
230:       end

232: !
233: !/*TEST
234: !
235: !   build:
236: !      requires: complex
237: !
238: !   test:
239: !      args: -n 6 -norandom -pc_type none -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
240: !      output_file: output/ex11f_1.out
241: !
242: !TEST*/