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

[Michael Werner]

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.