[petsc-users] SLEPC/PETSC for large scale FEM generalised eigenvalue problem

[Jose E. Roman]

Most probably you want EPS_TARGET_MAGNITUDE with shift-and-invert, i.e.,

-st_type sinvert -eps_target 0 -eps_target_magnitude -st_ksp_type preonly -st_pc_type lu -st_pc_factor_mat_solver_type mumps

This will solve a linear system with your A matrix instead of your B matrix. If A is singular, try a nonzero target located on the left of your eigenvalues.

Jose

> El 9 dic 2024, a las 22:57, Barry Smith <bsmith at petsc.dev> escribió:
> 
> 
>   I'll leave it to Jose to provide a complete, comprehensive answer, but given your problem sizes, I think using a direct solver instead of an iterative solver may be the best bet.  So configure PETSc without debugging and with MUMPS
> 
>   ./configure --with-debugging=0 --download-mumps --download-scalapack --download-ptscotch
> 
> and use -ksp_type preconly -pc_type lu -pc_factor_mat_solver_type mumps
> 
>   Good luck
> 
> 
>> On Dec 9, 2024, at 4:50 PM, LUCA SCALIA <lscalia at pa.uc3m.es> wrote:
>> 
>> Dear group, 
>> 
>> I am using libraries PETSC and SLEPC for a Finite Element code written in c++ that I am developing, oriented to the solution of  generalised eigenvalue problems for large structural systems featuring up to 10^5 -10^6 degrees of freedom.
>> 
>> I manage to successfully run the code for a generalised eigenvalue problem of structures with around 10^4 degrees of freedom in a reasonable amount of time but the problem arises in the case of systems with a number of degrees of freedom from 10^5 or above.
>> 
>> The current test case I'm trying  has 120.000 degrees of freedom. The EPS solver gets slower and slower as the iterations pass. After a rough estimate, I would say it may take no less than 5-6 hours with 20 MPI processes ( allowing an unlimited number of iterations)
>> 
>> I need to compute the first 10 to 30 (nev) modes of the structure (EPS_SMALLEST_MAGNITUDE). I'm using the default KRYLOVSCHUR iterative solver. The problem is generalised Hermitian
>> 
>> 
>> I tried to play a little bit with different settings and options of the library, e.g.:
>> 
>> 1) ncv parameter. different  values of ncv, between 10*nev and 40*nev
>> 
>> 2) different solvers for the ksp object ( GMRES and CG ), and tolerance as well preconditioner (PCJACOBI and PCBJACOBI)
>> 
>> 3) Normalisation of matrices A and B with the respective Frobenius or Infinite norms.
>> 
>> ... but I wasn't able to solve the problem.
>> 
>> I kindly ask for advice on which strategies I should resort to in order to improve the speed of SLEPC for such large numbers of degrees of freedom, since I'm quite new to the solution of the generalised eigenvalue problem.
>> 
>> I also attach two files with the stiffness and mass matrix of one element to show the magnitude of the entries of the two matrices
>> 
>> Best regards,
>> 
>> Luca
>> <stiffness_matrix_A.txt><mass_matrix_B.txt>
>