[petsc-users] Doubts on direct solver with mumps

[Emmanuel Ayala]

OK, I see.

Thank you very much for the quick response and explanation.

Regards.

El mar, 4 mar 2025 a la(s) 1:27 p.m., Jed Brown (jed at jedbrown.org) escribió:

> Yup, this is expected for direct solvers: numeric factorization for a 3D
> problem scales as O(n^2) while solving with the factors is only O(n^{4/3}).
> So you expect it to be slow to factor and fast to solve.
>
> Iterative methods with good preconditioners can be O(n), and tend to be
> the choice for large problems any time they can be sufficiently robust
> (which is both a science and an art, but is available for many problem
> classes).
>
> Emmanuel Ayala <juaneah at gmail.com> writes:
>
> > Hello everyone.
> >
> > I'm trying to solve a linear system (which comes from 3D FEM with
> > structured DM mesh) with a direct solver. I configured petsc installation
> > with mumps (–download-mumps –download-scalapack –download-parmetis
> > –download-metis, --download-hwloc, without ptscotch) and I have the
> > following functions:
> >
> >     // K is the stiffness matrix, assembly correctly
> >     // U is the solution vector
> >     // RHS is the right hand side of the linear equation
> >
> >     Mat Kfactor;
> >
> >     ierr = MatGetFactor(K,MATSOLVERMUMPS, MAT_FACTOR_CHOLESKY, &Kfactor);
> > CHKERRQ(ierr);
> >     ierr = MatCholeskyFactorSymbolic(Kfactor,K,0,0); CHKERRQ(ierr);
> >     ierr = MatCholeskyFactorNumeric(Kfactor,K,0); CHKERRQ(ierr);
> >     ierr = MatSolve(Kfactor,RHS,U);
> >
> >     and run with options:
> >     -pc_type cholesky -pc_factor_mat_solver_type mumps
> -mat_mumps_icntl_1 1
> > -mat_mumps_icntl_13 0 -mat_mumps_icntl_28 2 -mat_mumps_icntl_29 2
> >
> > PROBLEM:
> > I got the correct solution, but the function MatCholeskyFactorNumeric( )
> > takes too much time to be completed. MatCholeskyFactorSymbolic() and
> > MatSolve() are very fast. The test uses a square K matrix of 700k dofs,
> and
> > the MatCholeskyFactorNumeric() takes around 14 minutes, while an
> iterative
> > solver (KSPCG/PCJACOBI) takes 5 seconds to get the solution. Any
> > suggestions?
> >
> > Thanks in advance.
>
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