1: !
2: !
3: !/*T
4: ! Concepts: KSP^basic sequential example
5: ! Concepts: KSP^Laplacian, 2d
6: ! Concepts: Laplacian, 2d
7: ! Processors: 1
8: !T*/
9: ! -----------------------------------------------------------------------
11: program main
12: implicit none
14: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
15: ! Include files
16: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
17: !
18: ! The following include statements are required for KSP Fortran programs:
19: ! petscsys.h - base PETSc routines
20: ! petscvec.h - vectors
21: ! petscmat.h - matrices
22: ! petscksp.h - Krylov subspace methods
23: ! petscpc.h - preconditioners
24: !
25: #include <finclude/petscsys.h>
26: #include <finclude/petscvec.h>
27: #include <finclude/petscmat.h>
28: #include <finclude/petscksp.h>
29: #include <finclude/petscpc.h>
31: ! User-defined context that contains all the data structures used
32: ! in the linear solution process.
34: ! Vec x,b /* solution vector, right hand side vector and work vector */
35: ! Mat A /* sparse matrix */
36: ! KSP ksp /* linear solver context */
37: ! int m,n /* grid dimensions */
38: !
39: ! Since we cannot store Scalars and integers in the same context,
40: ! we store the integers/pointers in the user-defined context, and
41: ! the scalar values are carried in the common block.
42: ! The scalar values in this simplistic example could easily
43: ! be recalculated in each routine, where they are needed.
44: !
45: ! Scalar hx2,hy2 /* 1/(m+1)*(m+1) and 1/(n+1)*(n+1) */
47: ! Note: Any user-defined Fortran routines MUST be declared as external.
49: external UserInitializeLinearSolver
50: external UserFinalizeLinearSolver
51: external UserDoLinearSolver
53: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
54: ! Variable declarations
55: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
57: PetscScalar hx,hy,x,y
58: PetscFortranAddr userctx(6)
59: PetscErrorCode ierr
60: PetscInt m,n,t,tmax,i,j
61: PetscBool flg
62: PetscMPIInt size,rank
63: PetscReal enorm
64: PetscScalar cnorm
65: PetscScalar,ALLOCATABLE :: userx(:,:)
66: PetscScalar,ALLOCATABLE :: userb(:,:)
67: PetscScalar,ALLOCATABLE :: solution(:,:)
68: PetscScalar,ALLOCATABLE :: rho(:,:)
70: double precision hx2,hy2
71: common /param/ hx2,hy2
73: tmax = 2
74: m = 6
75: n = 7
77: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
78: ! Beginning of program
79: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
81: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
82: call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
83: if (size .ne. 1) then
84: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
85: if (rank .eq. 0) then
86: write(6,*) 'This is a uniprocessor example only!'
87: endif
88: SETERRQ(PETSC_COMM_WORLD,1,' ',ierr)
89: endif
91: ! The next two lines are for testing only; these allow the user to
92: ! decide the grid size at runtime.
94: call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-m',m,flg,ierr)
95: call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
97: ! Create the empty sparse matrix and linear solver data structures
99: call UserInitializeLinearSolver(m,n,userctx,ierr)
101: ! Allocate arrays to hold the solution to the linear system. This
102: ! approach is not normally done in PETSc programs, but in this case,
103: ! since we are calling these routines from a non-PETSc program, we
104: ! would like to reuse the data structures from another code. So in
105: ! the context of a larger application these would be provided by
106: ! other (non-PETSc) parts of the application code.
108: ALLOCATE (userx(m,n),userb(m,n),solution(m,n))
110: ! Allocate an array to hold the coefficients in the elliptic operator
112: ALLOCATE (rho(m,n))
114: ! Fill up the array rho[] with the function rho(x,y) = x; fill the
115: ! right-hand-side b[] and the solution with a known problem for testing.
117: hx = 1.0/(m+1)
118: hy = 1.0/(n+1)
119: y = hy
120: do 20 j=1,n
121: x = hx
122: do 10 i=1,m
123: rho(i,j) = x
124: solution(i,j) = sin(2.*PETSC_PI*x)*sin(2.*PETSC_PI*y)
125: userb(i,j) = -2.*PETSC_PI*cos(2.*PETSC_PI*x)* &
126: & sin(2.*PETSC_PI*y) + &
127: & 8*PETSC_PI*PETSC_PI*x* &
128: & sin(2.*PETSC_PI*x)*sin(2.*PETSC_PI*y)
129: x = x + hx
130: 10 continue
131: y = y + hy
132: 20 continue
134: ! Loop over a bunch of timesteps, setting up and solver the linear
135: ! system for each time-step.
136: ! Note that this loop is somewhat artificial. It is intended to
137: ! demonstrate how one may reuse the linear solvers in each time-step.
139: do 100 t=1,tmax
140: call UserDoLinearSolver(rho,userctx,userb,userx,ierr)
142: ! Compute error: Note that this could (and usually should) all be done
143: ! using the PETSc vector operations. Here we demonstrate using more
144: ! standard programming practices to show how they may be mixed with
145: ! PETSc.
146: cnorm = 0.0
147: do 90 j=1,n
148: do 80 i=1,m
149: cnorm = cnorm + &
150: & PetscConj(solution(i,j)-userx(i,j))* &
151: & (solution(i,j)-userx(i,j))
152: 80 continue
153: 90 continue
154: enorm = PetscRealPart(cnorm*hx*hy)
155: write(6,115) m,n,enorm
156: 115 format ('m = ',I2,' n = ',I2,' error norm = ',1PE11.4)
157: 100 continue
159: ! We are finished solving linear systems, so we clean up the
160: ! data structures.
162: DEALLOCATE (userx,userb,solution,rho)
164: call UserFinalizeLinearSolver(userctx,ierr)
165: call PetscFinalize(ierr)
166: end
168: ! ----------------------------------------------------------------
169: subroutine UserInitializeLinearSolver(m,n,userctx,ierr)
171: implicit none
173: #include <finclude/petscsys.h>
174: #include <finclude/petscvec.h>
175: #include <finclude/petscmat.h>
176: #include <finclude/petscksp.h>
177: #include <finclude/petscpc.h>
179: PetscInt m,n
180: PetscErrorCode ierr
181: PetscFortranAddr userctx(*)
183: common /param/ hx2,hy2
184: double precision hx2,hy2
186: ! Local variable declararions
187: Mat A
188: Vec b,x
189: KSP ksp
190: PetscInt Ntot,five,one
193: ! Here we assume use of a grid of size m x n, with all points on the
194: ! interior of the domain, i.e., we do not include the points corresponding
195: ! to homogeneous Dirichlet boundary conditions. We assume that the domain
196: ! is [0,1]x[0,1].
198: hx2 = (m+1)*(m+1)
199: hy2 = (n+1)*(n+1)
200: Ntot = m*n
202: five = 5
203: one = 1
205: ! Create the sparse matrix. Preallocate 5 nonzeros per row.
207: call MatCreateSeqAIJ(PETSC_COMM_SELF,Ntot,Ntot,five, &
208: & PETSC_NULL_INTEGER,A,ierr)
209: !
210: ! Create vectors. Here we create vectors with no memory allocated.
211: ! This way, we can use the data structures already in the program
212: ! by using VecPlaceArray() subroutine at a later stage.
213: !
214: call VecCreateSeqWithArray(PETSC_COMM_SELF,one,Ntot, &
215: & PETSC_NULL_SCALAR,b,ierr)
216: call VecDuplicate(b,x,ierr)
218: ! Create linear solver context. This will be used repeatedly for all
219: ! the linear solves needed.
221: call KSPCreate(PETSC_COMM_SELF,ksp,ierr)
223: userctx(1) = x
224: userctx(2) = b
225: userctx(3) = A
226: userctx(4) = ksp
227: userctx(5) = m
228: userctx(6) = n
230: return
231: end
232: ! -----------------------------------------------------------------------
234: ! Solves -div (rho grad psi) = F using finite differences.
235: ! rho is a 2-dimensional array of size m by n, stored in Fortran
236: ! style by columns. userb is a standard one-dimensional array.
238: subroutine UserDoLinearSolver(rho,userctx,userb,userx,ierr)
240: implicit none
242: #include <finclude/petscsys.h>
243: #include <finclude/petscvec.h>
244: #include <finclude/petscmat.h>
245: #include <finclude/petscksp.h>
246: #include <finclude/petscpc.h>
248: PetscErrorCode ierr
249: PetscFortranAddr userctx(*)
250: PetscScalar rho(*),userb(*),userx(*)
253: common /param/ hx2,hy2
254: double precision hx2,hy2
256: PC pc
257: KSP ksp
258: Vec b,x
259: Mat A
260: PetscInt m,n,one
261: PetscInt i,j,II,JJ
262: PetscScalar v
264: ! PetscScalar tmpx(*),tmpb(*)
266: one = 1
267: x = userctx(1)
268: b = userctx(2)
269: A = userctx(3)
270: ksp = userctx(4)
271: m = int(userctx(5))
272: n = int(userctx(6))
274: ! This is not the most efficient way of generating the matrix,
275: ! but let's not worry about it. We should have separate code for
276: ! the four corners, each edge and then the interior. Then we won't
277: ! have the slow if-tests inside the loop.
278: !
279: ! Compute the operator
280: ! -div rho grad
281: ! on an m by n grid with zero Dirichlet boundary conditions. The rho
282: ! is assumed to be given on the same grid as the finite difference
283: ! stencil is applied. For a staggered grid, one would have to change
284: ! things slightly.
286: II = 0
287: do 110 j=1,n
288: do 100 i=1,m
289: if (j .gt. 1) then
290: JJ = II - m
291: v = -0.5*(rho(II+1) + rho(JJ+1))*hy2
292: call MatSetValues(A,one,II,one,JJ,v,INSERT_VALUES,ierr)
293: endif
294: if (j .lt. n) then
295: JJ = II + m
296: v = -0.5*(rho(II+1) + rho(JJ+1))*hy2
297: call MatSetValues(A,one,II,one,JJ,v,INSERT_VALUES,ierr)
298: endif
299: if (i .gt. 1) then
300: JJ = II - 1
301: v = -0.5*(rho(II+1) + rho(JJ+1))*hx2
302: call MatSetValues(A,one,II,one,JJ,v,INSERT_VALUES,ierr)
303: endif
304: if (i .lt. m) then
305: JJ = II + 1
306: v = -0.5*(rho(II+1) + rho(JJ+1))*hx2
307: call MatSetValues(A,one,II,one,JJ,v,INSERT_VALUES,ierr)
308: endif
309: v = 2*rho(II+1)*(hx2+hy2)
310: call MatSetValues(A,one,II,one,II,v,INSERT_VALUES,ierr)
311: II = II+1
312: 100 continue
313: 110 continue
314: !
315: ! Assemble matrix
316: !
317: call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
318: call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
320: !
321: ! Set operators. Here the matrix that defines the linear system
322: ! also serves as the preconditioning matrix. Since all the matrices
323: ! will have the same nonzero pattern here, we indicate this so the
324: ! linear solvers can take advantage of this.
325: !
326: call KSPSetOperators(ksp,A,A,SAME_NONZERO_PATTERN,ierr)
328: !
329: ! Set linear solver defaults for this problem (optional).
330: ! - Here we set it to use direct LU factorization for the solution
331: !
332: call KSPGetPC(ksp,pc,ierr)
333: call PCSetType(pc,PCLU,ierr)
335: !
336: ! Set runtime options, e.g.,
337: ! -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
338: ! These options will override those specified above as long as
339: ! KSPSetFromOptions() is called _after_ any other customization
340: ! routines.
341: !
342: ! Run the program with the option -help to see all the possible
343: ! linear solver options.
344: !
345: call KSPSetFromOptions(ksp,ierr)
347: !
348: ! This allows the PETSc linear solvers to compute the solution
349: ! directly in the user's array rather than in the PETSc vector.
350: !
351: ! This is essentially a hack and not highly recommend unless you
352: ! are quite comfortable with using PETSc. In general, users should
353: ! write their entire application using PETSc vectors rather than
354: ! arrays.
355: !
356: call VecPlaceArray(x,userx,ierr)
357: call VecPlaceArray(b,userb,ierr)
359: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
360: ! Solve the linear system
361: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
363: call KSPSolve(ksp,b,x,ierr)
365: call VecResetArray(x,ierr)
366: call VecResetArray(b,ierr)
368: return
369: end
371: ! ------------------------------------------------------------------------
373: subroutine UserFinalizeLinearSolver(userctx,ierr)
375: implicit none
377: #include <finclude/petscsys.h>
378: #include <finclude/petscvec.h>
379: #include <finclude/petscmat.h>
380: #include <finclude/petscksp.h>
381: #include <finclude/petscpc.h>
383: PetscErrorCode ierr
384: PetscFortranAddr userctx(*)
386: ! Local variable declararions
388: Vec x,b
389: Mat A
390: KSP ksp
391: !
392: ! We are all done and don't need to solve any more linear systems, so
393: ! we free the work space. All PETSc objects should be destroyed when
394: ! they are no longer needed.
395: !
396: x = userctx(1)
397: b = userctx(2)
398: A = userctx(3)
399: ksp = userctx(4)
401: call VecDestroy(x,ierr)
402: call VecDestroy(b,ierr)
403: call MatDestroy(A,ierr)
404: call KSPDestroy(ksp,ierr)
406: return
407: end