Actual source code: ex11f.F90

petsc-master 2020-11-24
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```  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*/

11: !
12: !  The model problem:
13: !     Solve Helmholtz equation on the unit square: (0,1) x (0,1)
14: !          -delta u - sigma1*u + i*sigma2*u = f,
15: !           where delta = Laplace operator
16: !     Dirichlet b.c.'s on all sides
17: !     Use the 2-D, five-point finite difference stencil.
18: !
19: !     Compiling the code:
20: !      This code uses the complex numbers version of PETSc, so configure
21: !      must be run to enable this
22: !
23: !
24: ! -----------------------------------------------------------------------

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

31: !
32: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
33: !                   Variable declarations
34: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
35: !
36: !  Variables:
37: !     ksp     - linear solver context
38: !     x, b, u  - approx solution, right-hand-side, exact solution vectors
39: !     A        - matrix that defines linear system
40: !     its      - iterations for convergence
41: !     norm     - norm of error in solution
42: !     rctx     - random number context
43: !

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

59: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60: !                 Beginning of program
61: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

79: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
80: !      Compute the matrix and right-hand-side vector that define
81: !      the linear system, Ax = b.
82: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

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

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

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

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

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

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

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

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

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

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

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

177: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: !         Create the linear solver and set various options
179: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

181: !  Create linear solver context

183:       call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)

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

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

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

193:       call KSPSetFromOptions(ksp,ierr)

195: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196: !                      Solve the linear system
197: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

201: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
202: !                     Check solution and clean up
203: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

205: !  Check the error

207:       call VecAXPY(x,none,u,ierr)
208:       call VecNorm(x,NORM_2,norm,ierr)
209:       call KSPGetIterationNumber(ksp,its,ierr)
210:       if (rank .eq. 0) then
211:         if (norm .gt. 1.e-12) then
212:            write(6,100) norm,its
213:         else
214:            write(6,110) its
215:         endif
216:       endif
217:   100 format('Norm of error ',e11.4,',iterations ',i5)
218:   110 format('Norm of error < 1.e-12,iterations ',i5)

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

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

230:       call PetscFinalize(ierr)
231:       end

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