Actual source code: ex1f.F90
1: !
2: ! Solves the time dependent Bratu problem using pseudo-timestepping
3: !
4: ! This code demonstrates how one may solve a nonlinear problem
5: ! with pseudo-timestepping. In this simple example, the pseudo-timestep
6: ! is the same for all grid points, i.e., this is equivalent to using
7: ! the backward Euler method with a variable timestep.
8: !
9: ! Note: This example does not require pseudo-timestepping since it
10: ! is an easy nonlinear problem, but it is included to demonstrate how
11: ! the pseudo-timestepping may be done.
12: !
13: ! See snes/tutorials/ex4.c[ex4f.F] and
14: ! snes/tutorials/ex5.c[ex5f.F] where the problem is described
15: ! and solved using the method of Newton alone.
16: !
17: !
18: !23456789012345678901234567890123456789012345678901234567890123456789012
19: program main
20: #include <petsc/finclude/petscts.h>
21: use petscts
22: implicit none
24: !
25: ! Create an application context to contain data needed by the
26: ! application-provided call-back routines, FormJacobian() and
27: ! FormFunction(). We use a double precision array with three
28: ! entries indexed by param, lmx, lmy.
29: !
30: PetscReal user(3)
31: PetscInt param,lmx,lmy,i5
32: parameter (param = 1,lmx = 2,lmy = 3)
33: !
34: ! User-defined routines
35: !
36: external FormJacobian,FormFunction
37: !
38: ! Data for problem
39: !
40: TS ts
41: Vec x,r
42: Mat J
43: PetscInt its,N,i1000,itmp
44: PetscBool flg
45: PetscErrorCode ierr
46: PetscReal param_max,param_min,dt
47: PetscReal tmax
48: PetscReal ftime
49: TSConvergedReason reason
51: i5 = 5
52: param_max = 6.81
53: param_min = 0
55: PetscCallA(PetscInitialize(ierr))
56: user(lmx) = 4
57: user(lmy) = 4
58: user(param) = 6.0
60: !
61: ! Allow user to set the grid dimensions and nonlinearity parameter at run-time
62: !
63: PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-mx',user(lmx),flg,ierr))
64: itmp = 4
65: PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my',itmp,flg,ierr))
66: user(lmy) = itmp
67: PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-param',user(param),flg,ierr))
68: if (user(param) .ge. param_max .or. user(param) .le. param_min) then
69: print*,'Parameter is out of range'
70: endif
71: if (user(lmx) .gt. user(lmy)) then
72: dt = .5/user(lmx)
73: else
74: dt = .5/user(lmy)
75: endif
76: PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-dt',dt,flg,ierr))
77: N = int(user(lmx)*user(lmy))
79: !
80: ! Create vectors to hold the solution and function value
81: !
82: PetscCallA(VecCreateSeq(PETSC_COMM_SELF,N,x,ierr))
83: PetscCallA(VecDuplicate(x,r,ierr))
85: !
86: ! Create matrix to hold Jacobian. Preallocate 5 nonzeros per row
87: ! in the sparse matrix. Note that this is not the optimal strategy see
88: ! the Performance chapter of the users manual for information on
89: ! preallocating memory in sparse matrices.
90: !
91: i5 = 5
92: PetscCallA(MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,i5,PETSC_NULL_INTEGER_ARRAY,J,ierr))
94: !
95: ! Create timestepper context
96: !
98: PetscCallA(TSCreate(PETSC_COMM_WORLD,ts,ierr))
99: PetscCallA(TSSetProblemType(ts,TS_NONLINEAR,ierr))
101: !
102: ! Tell the timestepper context where to compute solutions
103: !
105: PetscCallA(TSSetSolution(ts,x,ierr))
107: !
108: ! Provide the call-back for the nonlinear function we are
109: ! evaluating. Thus whenever the timestepping routines need the
110: ! function they will call this routine. Note the final argument
111: ! is the application context used by the call-back functions.
112: !
114: PetscCallA(TSSetRHSFunction(ts,PETSC_NULL_VEC,FormFunction,user,ierr))
116: !
117: ! Set the Jacobian matrix and the function used to compute
118: ! Jacobians.
119: !
121: PetscCallA(TSSetRHSJacobian(ts,J,J,FormJacobian,user,ierr))
123: !
124: ! For the initial guess for the problem
125: !
127: PetscCallA(FormInitialGuess(x,user,ierr))
129: !
130: ! This indicates that we are using pseudo timestepping to
131: ! find a steady state solution to the nonlinear problem.
132: !
134: PetscCallA(TSSetType(ts,TSPSEUDO,ierr))
136: !
137: ! Set the initial time to start at (this is arbitrary for
138: ! steady state problems and the initial timestep given above
139: !
141: PetscCallA(TSSetTimeStep(ts,dt,ierr))
143: !
144: ! Set a large number of timesteps and final duration time
145: ! to insure convergence to steady state.
146: !
147: i1000 = 1000
148: tmax = 1.e12
149: PetscCallA(TSSetMaxSteps(ts,i1000,ierr))
150: PetscCallA(TSSetMaxTime(ts,tmax,ierr))
151: PetscCallA(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER,ierr))
153: !
154: ! Set any additional options from the options database. This
155: ! includes all options for the nonlinear and linear solvers used
156: ! internally the timestepping routines.
157: !
159: PetscCallA(TSSetFromOptions(ts,ierr))
161: PetscCallA(TSSetUp(ts,ierr))
163: !
164: ! Perform the solve. This is where the timestepping takes place.
165: !
166: PetscCallA(TSSolve(ts,x,ierr))
167: PetscCallA(TSGetSolveTime(ts,ftime,ierr))
168: PetscCallA(TSGetStepNumber(ts,its,ierr))
169: PetscCallA(TSGetConvergedReason(ts,reason,ierr))
171: write(6,100) its,ftime,reason
172: 100 format('Number of pseudo time-steps ',i5,' final time ',1pe9.2,' reason ',i3)
174: !
175: ! Free the data structures constructed above
176: !
178: PetscCallA(VecDestroy(x,ierr))
179: PetscCallA(VecDestroy(r,ierr))
180: PetscCallA(MatDestroy(J,ierr))
181: PetscCallA(TSDestroy(ts,ierr))
182: PetscCallA(PetscFinalize(ierr))
183: end
185: !
186: ! -------------------- Form initial approximation -----------------
187: !
188: subroutine FormInitialGuess(X,user,ierr)
189: use petscts
190: implicit none
192: Vec X
193: PetscReal user(3)
194: PetscInt i,j,row,mx,my
195: PetscErrorCode ierr
196: PetscReal one,lambda
197: PetscReal temp1,temp,hx,hy
198: PetscScalar,pointer :: xx(:)
199: PetscInt param,lmx,lmy
200: parameter (param = 1,lmx = 2,lmy = 3)
202: one = 1.0
204: mx = int(user(lmx))
205: my = int(user(lmy))
206: lambda = user(param)
208: hy = one / (my-1)
209: hx = one / (mx-1)
211: PetscCall(VecGetArrayF90(X,xx,ierr))
212: temp1 = lambda/(lambda + one)
213: do 10, j=1,my
214: temp = min(j-1,my-j)*hy
215: do 20 i=1,mx
216: row = i + (j-1)*mx
217: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
218: xx(row) = 0.0
219: else
220: xx(row) = temp1*sqrt(min(min(i-1,mx-i)*hx,temp))
221: endif
222: 20 continue
223: 10 continue
224: PetscCall(VecRestoreArrayF90(X,xx,ierr))
225: end
226: !
227: ! -------------------- Evaluate Function F(x) ---------------------
228: !
229: subroutine FormFunction(ts,t,X,F,user,ierr)
230: use petscts
231: implicit none
233: TS ts
234: PetscReal t
235: Vec X,F
236: PetscReal user(3)
237: PetscErrorCode ierr
238: PetscInt i,j,row,mx,my
239: PetscReal two,lambda
240: PetscReal hx,hy,hxdhy,hydhx
241: PetscScalar ut,ub,ul,ur,u
242: PetscScalar uxx,uyy,sc
243: PetscScalar,pointer :: xx(:), ff(:)
244: PetscInt param,lmx,lmy
245: parameter (param = 1,lmx = 2,lmy = 3)
247: two = 2.0
249: mx = int(user(lmx))
250: my = int(user(lmy))
251: lambda = user(param)
253: hx = 1.0 / real(mx-1)
254: hy = 1.0 / real(my-1)
255: sc = hx*hy
256: hxdhy = hx/hy
257: hydhx = hy/hx
259: PetscCall(VecGetArrayReadF90(X,xx,ierr))
260: PetscCall(VecGetArrayF90(F,ff,ierr))
261: do 10 j=1,my
262: do 20 i=1,mx
263: row = i + (j-1)*mx
264: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
265: ff(row) = xx(row)
266: else
267: u = xx(row)
268: ub = xx(row - mx)
269: ul = xx(row - 1)
270: ut = xx(row + mx)
271: ur = xx(row + 1)
272: uxx = (-ur + two*u - ul)*hydhx
273: uyy = (-ut + two*u - ub)*hxdhy
274: ff(row) = -uxx - uyy + sc*lambda*exp(u)
275: endif
276: 20 continue
277: 10 continue
279: PetscCall(VecRestoreArrayReadF90(X,xx,ierr))
280: PetscCall(VecRestoreArrayF90(F,ff,ierr))
281: end
282: !
283: ! -------------------- Evaluate Jacobian of F(x) --------------------
284: !
285: subroutine FormJacobian(ts,ctime,X,JJ,B,user,ierr)
286: use petscts
287: implicit none
289: TS ts
290: Vec X
291: Mat JJ,B
292: PetscReal user(3),ctime
293: PetscErrorCode ierr
294: Mat jac
295: PetscInt i,j,row(1),mx,my
296: PetscInt col(5),i1,i5
297: PetscScalar two,one,lambda
298: PetscScalar v(5),sc
299: PetscScalar,pointer :: xx(:)
300: PetscReal hx,hy,hxdhy,hydhx
302: PetscInt param,lmx,lmy
303: parameter (param = 1,lmx = 2,lmy = 3)
305: i1 = 1
306: i5 = 5
307: jac = B
308: two = 2.0
309: one = 1.0
311: mx = int(user(lmx))
312: my = int(user(lmy))
313: lambda = user(param)
315: hx = 1.0 / real(mx-1)
316: hy = 1.0 / real(my-1)
317: sc = hx*hy
318: hxdhy = hx/hy
319: hydhx = hy/hx
321: PetscCall(VecGetArrayReadF90(X,xx,ierr))
322: do 10 j=1,my
323: do 20 i=1,mx
324: !
325: ! When inserting into PETSc matrices, indices start at 0
326: !
327: row(1) = i - 1 + (j-1)*mx
328: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
329: PetscCall(MatSetValues(jac,i1,[row],i1,[row],[one],INSERT_VALUES,ierr))
330: else
331: v(1) = hxdhy
332: col(1) = row(1) - mx
333: v(2) = hydhx
334: col(2) = row(1) - 1
335: v(3) = -two*(hydhx+hxdhy)+sc*lambda*exp(xx(row(1)))
336: col(3) = row(1)
337: v(4) = hydhx
338: col(4) = row(1) + 1
339: v(5) = hxdhy
340: col(5) = row(1) + mx
341: PetscCall(MatSetValues(jac,i1,[row],i5,col,v,INSERT_VALUES,ierr))
342: endif
343: 20 continue
344: 10 continue
345: PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr))
346: PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr))
347: PetscCall(VecRestoreArrayF90(X,xx,ierr))
348: end
350: !/*TEST
351: !
352: ! test:
353: ! TODO: broken
354: ! args: -ksp_gmres_cgs_refinement_type refine_always -snes_type newtonls -ts_monitor_pseudo -ts_max_snes_failures 3 -ts_pseudo_frtol 1.e-5 -snes_stol 1e-5
355: !
356: !TEST*/