Actual source code: ex11f.F
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*/
9: !
10: ! The model problem:
11: ! Solve Helmholtz equation on the unit square: (0,1) x (0,1)
12: ! -delta u - sigma1*u + i*sigma2*u = f,
13: ! where delta = Laplace operator
14: ! Dirichlet b.c.'s on all sides
15: ! Use the 2-D, five-point finite difference stencil.
16: !
17: ! Compiling the code:
18: ! This code uses the complex numbers version of PETSc, so one of the
19: ! following values of BOPT must be used for compiling the PETSc libraries
20: ! and this example:
21: ! BOPT=g_complex - debugging version
22: ! BOPT=O_complex - optimized version
23: ! BOPT=Opg_complex - profiling version
24: !
25: ! -----------------------------------------------------------------------
27: program main
28: implicit none
30: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
31: ! Include files
32: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
33: !
34: ! The following include statements are required for KSP Fortran programs:
35: ! petsc.h - base PETSc routines
36: ! petscvec.h - vectors
37: ! petscmat.h - matrices
38: ! petscpc.h - preconditioners
39: ! petscksp.h - Krylov subspace methods
40: ! Include the following to use PETSc random numbers:
41: ! petscsys.h - system routines
42: ! Additional include statements may be needed if using other PETSc
43: ! routines in a Fortran program, e.g.,
44: ! petscviewer.h - viewers
45: ! petscis.h - index sets
46: !
47: #include include/finclude/petsc.h
48: #include include/finclude/petscvec.h
49: #include include/finclude/petscmat.h
50: #include include/finclude/petscpc.h
51: #include include/finclude/petscksp.h
52: #include include/finclude/petscsys.h
53: !
54: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55: ! Variable declarations
56: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
57: !
58: ! Variables:
59: ! ksp - linear solver context
60: ! x, b, u - approx solution, right-hand-side, exact solution vectors
61: ! A - matrix that defines linear system
62: ! its - iterations for convergence
63: ! norm - norm of error in solution
64: ! rctx - random number context
65: !
67: KSP ksp
68: Mat A
69: Vec x,b,u
70: PetscRandom rctx
71: double precision norm,h2,sigma1
72: PetscScalar none,sigma2,v,pfive
73: PetscInt dim,its,n,Istart,Iend,i,j,II,JJ,one
74: PetscErrorCode ierr
75: PetscMPIInt rank
76: PetscTruth flg
77: logical use_random
79: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
80: ! Beginning of program
81: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
83: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
84: #if !defined(PETSC_USE_COMPLEX)
85: write(6,*) "This example requires complex numbers."
86: goto 200
87: #endif
89: none = -1.0
90: n = 6
91: sigma1 = 100.0
92: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
93: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-sigma1',sigma1, &
94: & flg,ierr)
95: call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
96: dim = n*n
98: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
99: ! Compute the matrix and right-hand-side vector that define
100: ! the linear system, Ax = b.
101: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103: ! Create parallel matrix, specifying only its global dimensions.
104: ! When using MatCreate(), the matrix format can be specified at
105: ! runtime. Also, the parallel partitioning of the matrix is
106: ! determined by PETSc at runtime.
108: call MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,dim, &
109: & dim,A,ierr)
110: call MatSetFromOptions(A,ierr)
112: ! Currently, all PETSc parallel matrix formats are partitioned by
113: ! contiguous chunks of rows across the processors. Determine which
114: ! rows of the matrix are locally owned.
116: call MatGetOwnershipRange(A,Istart,Iend,ierr)
118: ! Set matrix elements in parallel.
119: ! - Each processor needs to insert only elements that it owns
120: ! locally (but any non-local elements will be sent to the
121: ! appropriate processor during matrix assembly).
122: ! - Always specify global rows and columns of matrix entries.
124: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-norandom', &
125: & flg,ierr)
126: if (flg .eq. 1) then
127: use_random = .false.
128: sigma2 = 10.0*PETSC_i
129: else
130: use_random = .true.
131: call PetscRandomCreate(PETSC_COMM_WORLD, &
132: & RANDOM_DEFAULT_IMAGINARY,rctx,ierr)
133: endif
134: h2 = 1.0/((n+1)*(n+1))
136: one = 1
137: do 10, II=Istart,Iend-1
138: v = -1.0
139: i = II/n
140: j = II - i*n
141: if (i.gt.0) then
142: JJ = II - n
143: call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
144: endif
145: if (i.lt.n-1) then
146: JJ = II + n
147: call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
148: endif
149: if (j.gt.0) then
150: JJ = II - 1
151: call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
152: endif
153: if (j.lt.n-1) then
154: JJ = II + 1
155: call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
156: endif
157: if (use_random) call PetscRandomGetValue(rctx,sigma2,ierr)
158: v = 4.0 - sigma1*h2 + sigma2*h2
159: call MatSetValues(A,one,II,one,II,v,ADD_VALUES,ierr)
160: 10 continue
161: if (use_random) call PetscRandomDestroy(rctx,ierr)
163: ! Assemble matrix, using the 2-step process:
164: ! MatAssemblyBegin(), MatAssemblyEnd()
165: ! Computations can be done while messages are in transition
166: ! by placing code between these two statements.
168: call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
169: call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
171: ! Create parallel vectors.
172: ! - Here, the parallel partitioning of the vector is determined by
173: ! PETSc at runtime. We could also specify the local dimensions
174: ! if desired.
175: ! - Note: We form 1 vector from scratch and then duplicate as needed.
177: call VecCreate(PETSC_COMM_WORLD,u,ierr)
178: call VecSetSizes(u,PETSC_DECIDE,dim,ierr)
179: call VecSetFromOptions(u,ierr)
180: call VecDuplicate(u,b,ierr)
181: call VecDuplicate(b,x,ierr)
183: ! Set exact solution; then compute right-hand-side vector.
185: if (use_random) then
186: call PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT, &
187: & rctx,ierr)
188: call VecSetRandom(rctx,u,ierr)
189: else
190: pfive = 0.5
191: call VecSet(pfive,u,ierr)
192: endif
193: call MatMult(A,u,b,ierr)
195: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196: ! Create the linear solver and set various options
197: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: ! Create linear solver context
201: call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)
203: ! Set operators. Here the matrix that defines the linear system
204: ! also serves as the preconditioning matrix.
206: call KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN,ierr)
208: ! Set runtime options, e.g.,
209: ! -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
211: call KSPSetFromOptions(ksp,ierr)
213: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
214: ! Solve the linear system
215: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
217: call KSPSolve(ksp,b,x,ierr)
219: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
220: ! Check solution and clean up
221: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
223: ! Check the error
225: call VecAXPY(none,u,x,ierr)
226: call VecNorm(x,NORM_2,norm,ierr)
227: call KSPGetIterationNumber(ksp,its,ierr)
228: if (rank .eq. 0) then
229: if (norm .gt. 1.e-12) then
230: write(6,100) norm,its
231: else
232: write(6,110) its
233: endif
234: endif
235: 100 format('Norm of error ',e10.4,',iterations ',i5)
236: 110 format('Norm of error < 1.e-12,iterations ',i5)
238: ! Free work space. All PETSc objects should be destroyed when they
239: ! are no longer needed.
241: if (use_random) call PetscRandomDestroy(rctx,ierr)
242: call KSPDestroy(ksp,ierr)
243: call VecDestroy(u,ierr)
244: call VecDestroy(x,ierr)
245: call VecDestroy(b,ierr)
246: call MatDestroy(A,ierr)
248: 200 continue
249: call PetscFinalize(ierr)
250: end