Actual source code: ex11f.F90
1: !
2: ! Description: Solves a complex linear system in parallel with KSP (Fortran code).
3: !
5: !
6: ! The model problem:
7: ! Solve Helmholtz equation on the unit square: (0,1) x (0,1)
8: ! -delta u - sigma1*u + i*sigma2*u = f,
9: ! where delta = Laplace operator
10: ! Dirichlet b.c.'s on all sides
11: ! Use the 2-D, five-point finite difference stencil.
12: !
13: ! Compiling the code:
14: ! This code uses the complex numbers version of PETSc, so configure
15: ! must be run to enable this
16: !
17: !
18: ! -----------------------------------------------------------------------
20: program main
21: #include <petsc/finclude/petscksp.h>
22: use petscksp
23: implicit none
25: !
26: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
27: ! Variable declarations
28: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
29: !
30: ! Variables:
31: ! ksp - linear solver context
32: ! x, b, u - approx solution, right-hand-side, exact solution vectors
33: ! A - matrix that defines linear system
34: ! its - iterations for convergence
35: ! norm - norm of error in solution
36: ! rctx - random number context
37: !
39: KSP ksp
40: Mat A
41: Vec x,b,u
42: PetscRandom rctx
43: PetscReal norm,h2,sigma1
44: PetscScalar none,sigma2,v,pfive,czero
45: PetscScalar cone
46: PetscInt dim,its,n,Istart
47: PetscInt Iend,i,j,II,JJ,one
48: PetscErrorCode ierr
49: PetscMPIInt rank
50: PetscBool flg
51: logical use_random
53: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
54: ! Beginning of program
55: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
57: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
58: if (ierr .ne. 0) then
59: print*,'Unable to initialize PETSc'
60: stop
61: endif
63: none = -1.0
64: n = 6
65: sigma1 = 100.0
66: czero = 0.0
67: cone = PETSC_i
68: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
69: call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-sigma1',sigma1,flg,ierr)
70: call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
71: dim = n*n
73: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
74: ! Compute the matrix and right-hand-side vector that define
75: ! the linear system, Ax = b.
76: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
78: ! Create parallel matrix, specifying only its global dimensions.
79: ! When using MatCreate(), the matrix format can be specified at
80: ! runtime. Also, the parallel partitioning of the matrix is
81: ! determined by PETSc at runtime.
83: call MatCreate(PETSC_COMM_WORLD,A,ierr)
84: call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim,ierr)
85: call MatSetFromOptions(A,ierr)
86: call MatSetUp(A,ierr)
88: ! Currently, all PETSc parallel matrix formats are partitioned by
89: ! contiguous chunks of rows across the processors. Determine which
90: ! rows of the matrix are locally owned.
92: call MatGetOwnershipRange(A,Istart,Iend,ierr)
94: ! Set matrix elements in parallel.
95: ! - Each processor needs to insert only elements that it owns
96: ! locally (but any non-local elements will be sent to the
97: ! appropriate processor during matrix assembly).
98: ! - Always specify global rows and columns of matrix entries.
100: call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-norandom',flg,ierr)
101: if (flg) then
102: use_random = .false.
103: sigma2 = 10.0*PETSC_i
104: else
105: use_random = .true.
106: call PetscRandomCreate(PETSC_COMM_WORLD,rctx,ierr)
107: call PetscRandomSetFromOptions(rctx,ierr)
108: call PetscRandomSetInterval(rctx,czero,cone,ierr)
109: endif
110: h2 = 1.0/real((n+1)*(n+1))
112: one = 1
113: do 10, II=Istart,Iend-1
114: v = -1.0
115: i = II/n
116: j = II - i*n
117: if (i.gt.0) then
118: JJ = II - n
119: call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
120: endif
121: if (i.lt.n-1) then
122: JJ = II + n
123: call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
124: endif
125: if (j.gt.0) then
126: JJ = II - 1
127: call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
128: endif
129: if (j.lt.n-1) then
130: JJ = II + 1
131: call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
132: endif
133: if (use_random) call PetscRandomGetValue(rctx,sigma2,ierr)
134: v = 4.0 - sigma1*h2 + sigma2*h2
135: call MatSetValues(A,one,II,one,II,v,ADD_VALUES,ierr)
136: 10 continue
137: if (use_random) call PetscRandomDestroy(rctx,ierr)
139: ! Assemble matrix, using the 2-step process:
140: ! MatAssemblyBegin(), MatAssemblyEnd()
141: ! Computations can be done while messages are in transition
142: ! by placing code between these two statements.
144: call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
145: call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
147: ! Create parallel vectors.
148: ! - Here, the parallel partitioning of the vector is determined by
149: ! PETSc at runtime. We could also specify the local dimensions
150: ! if desired.
151: ! - Note: We form 1 vector from scratch and then duplicate as needed.
153: call VecCreate(PETSC_COMM_WORLD,u,ierr)
154: call VecSetSizes(u,PETSC_DECIDE,dim,ierr)
155: call VecSetFromOptions(u,ierr)
156: call VecDuplicate(u,b,ierr)
157: call VecDuplicate(b,x,ierr)
159: ! Set exact solution; then compute right-hand-side vector.
161: if (use_random) then
162: call PetscRandomCreate(PETSC_COMM_WORLD,rctx,ierr)
163: call PetscRandomSetFromOptions(rctx,ierr)
164: call VecSetRandom(u,rctx,ierr)
165: else
166: pfive = 0.5
167: call VecSet(u,pfive,ierr)
168: endif
169: call MatMult(A,u,b,ierr)
171: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
172: ! Create the linear solver and set various options
173: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: ! Create linear solver context
177: call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)
179: ! Set operators. Here the matrix that defines the linear system
180: ! also serves as the preconditioning matrix.
182: call KSPSetOperators(ksp,A,A,ierr)
184: ! Set runtime options, e.g.,
185: ! -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
187: call KSPSetFromOptions(ksp,ierr)
189: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: ! Solve the linear system
191: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193: call KSPSolve(ksp,b,x,ierr)
195: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196: ! Check solution and clean up
197: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: ! Check the error
201: call VecAXPY(x,none,u,ierr)
202: call VecNorm(x,NORM_2,norm,ierr)
203: call KSPGetIterationNumber(ksp,its,ierr)
204: if (rank .eq. 0) then
205: if (norm .gt. 1.e-12) then
206: write(6,100) norm,its
207: else
208: write(6,110) its
209: endif
210: endif
211: 100 format('Norm of error ',e11.4,',iterations ',i5)
212: 110 format('Norm of error < 1.e-12,iterations ',i5)
214: ! Free work space. All PETSc objects should be destroyed when they
215: ! are no longer needed.
217: if (use_random) call PetscRandomDestroy(rctx,ierr)
218: call KSPDestroy(ksp,ierr)
219: call VecDestroy(u,ierr)
220: call VecDestroy(x,ierr)
221: call VecDestroy(b,ierr)
222: call MatDestroy(A,ierr)
224: call PetscFinalize(ierr)
225: end
227: !
228: !/*TEST
229: !
230: ! build:
231: ! requires: complex
232: !
233: ! test:
234: ! args: -n 6 -norandom -pc_type none -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
235: ! output_file: output/ex11f_1.out
236: !
237: !TEST*/