[petsc-users] slepc4py - Using shell matrix and explicit preconditioning matrix to solve EPS

[Michael Werner]

Interesting, I will have a look at those papers, thank you. I'm 
still trying to get the Davidson methods to work, because for big 
matrices I can't use the krylov methods anymore due to limited 
memory.

Kind regards,
Michael

Jose E. Roman writes:

> If Krylov methods work for you then no need to worry about 
> Davidson methods. JD has many parameters that influence 
> convergence. Also, it relies on having a good preconditioner, 
> maybe ASM is not enough for your problem. Some time ago with we 
> used the pARMS preconditioner, see 
> https://doi.org/10.1016/j.cpc.2011.12.018 - but the results are 
> problem dependent. Also, you can try GD instead of JD, which is 
> simpler and often gives better performance. See a detailed 
> explanation here: https://doi.org/10.1145/2543696
>
> Jose
>
>> El 1 ago 2018, a las 10:43, Michael Werner 
>> <michael.werner at dlr.de> escribió:
>> 
>> 
>> Thanks for the quick reply, your suggestion worked 
>> perfect. Concerning your remark about Davidson-type methods: I 
>> already tried that, however I had problems getting them to 
>> converge to the expected eigenvalues. Even when I was using the 
>> full explicit system matrix and the options suggested in the 
>> slepc manual (-st_type precond -eps_type jd -st_pc_type asm 
>> -st_ksp_type bcgsl -st_ksp_rtol 0.001 -eps_target 0.01 
>> -eps_target_real), the results were always "hit-and-miss", the 
>> results didn't reliably converge towards the eigenvalues 
>> suggested by the exact shift-and-invert.
>> 
>> Kind regards,
>> Michael
>> 
>> Jose E. Roman writes:
>> 
>>> Try calling E.setUp() before replacing the matrix. But note 
>>> that E.setUp() will try to build the preconditioner, so you 
>>> will have to set PC=none and later change it to lu.
>>> 
>>> Also note that in Krylov methods with exact shift-and-invert 
>>> (LU) the preconditioner matrix should be exactly the same as 
>>> A-sigma*B, otherwise you may get unexpected 
>>> results. Davidson-type methods allow using a different 
>>> preconditioner.
>>> 
>>> Jose
>>> 
>>>> El 1 ago 2018, a las 10:11, Michael Werner 
>>>> <michael.werner at dlr.de> escribió:
>>>> Hello,
>>>> I'm trying to find the smallest eigenvalues of a linear 
>>>> system created by CFD simulations. To reduce memory 
>>>> requirements, I want to use a shell matrix (A_Shell) to 
>>>> provide the matrix-vector product, and a lower-order explicit 
>>>> matrix (P) as preconditioner. As I'm solving a generalized 
>>>> problem, I'm also passing a second explicit matrix (B) to the 
>>>> EPS. However, I don't see a way to provide the explicit 
>>>> preconditioning matrix to the EPS.
>>>> I'm using the following options: -st_type sinvert -st_pc_type 
>>>> lu -st_matmode shell -eps_target 0.01 -eps_target_real  My 
>>>> Python code looks like this:
>>>> E = SLEPc.EPS().create(comm=PETSc.COMM_WORLD)
>>>> E.setOperators(A_Shell, B)
>>>> E.setProblemType(SLEPc.EPS.ProblemType.GNHEP)
>>>> st = E.getST()
>>>> ksp = st.getKSP()
>>>> pc = ksp.getPC()
>>>> pc.setOperators(A_Shell, P)
>>>> E.setFromOptions()
>>>> E.solve()
>>>> If I run this, I get the following error:
>>>>> Error: error code 92
>>>>> [2] EPSSolve() line 135 in 
>>>>> /home/conda/feedstock_root/build_artifacts/slepc_1531127798016/work/src/eps/interface/epssolve.c
>>>>> [2] EPSSetUp() line 263 in 
>>>>> /home/conda/feedstock_root/build_artifacts/slepc_1531127798016/work/src/eps/interface/epssetup.c
>>>>> [2] STSetUp() line 271 in 
>>>>> /home/conda/feedstock_root/build_artifacts/slepc_1531127798016/work/src/sys/classes/st/interface/stsolve.c
>>>>> [2] STSetUp_Sinvert() line 132 in 
>>>>> /home/conda/feedstock_root/build_artifacts/slepc_1531127798016/work/src/sys/classes/st/impls/sinvert/sinvert.c
>>>>> [2] KSPSetUp() line 381 in 
>>>>> /home/conda/feedstock_root/build_artifacts/petsc_1530637062977/work/src/ksp/ksp/interface/itfunc.c
>>>>> [2] PCSetUp() line 923 in 
>>>>> /home/conda/feedstock_root/build_artifacts/petsc_1530637062977/work/src/ksp/pc/interface/precon.c
>>>>> [2] PCSetUp_LU() line 113 in 
>>>>> /home/conda/feedstock_root/build_artifacts/petsc_1530637062977/work/src/ksp/pc/impls/factor/lu/lu.c
>>>>> [2] MatGetFactor() line 4332 in 
>>>>> /home/conda/feedstock_root/build_artifacts/petsc_1530637062977/work/src/mat/interface/matrix.c
>>>>> [2] See 
>>>>> http://www.mcs.anl.gov/petsc/documentation/linearsolvertable.html 
>>>>> for possible LU and Cholesky solvers
>>>>> [2] MatSolverType mumps does not support matrix type shell
>>>> I also tried setting up the preconditioner in advance, but 
>>>> that didn't work either and produced the same errors as 
>>>> above:
>>>> pc = PETSc.PC().create(comm=PETSc.COMM_WORLD)
>>>> pc.setOperators(A_Shell, P)
>>>> pc.setFromOptions()
>>>> pc.setUp()
>>>> E = SLEPc.EPS().create(comm=PETSc.COMM_WORLD)
>>>> E.setOperators(A_Shell, B)
>>>> E.setProblemType(SLEPc.EPS.ProblemType.GNHEP)
>>>> ksp = E.getKSP()
>>>> ksp.setPC(pc)
>>>> E.setFromOptions()
>>>> E.solve()
>>>> If I simply try to solve a KSP with those two matrices, it 
>>>> works without any problems.
>>