I am looking for libraries for solving large scale linear system (10e5) of equations using parallelization and shared memory. 1. Sparse, complex symmetric, SPD. 2. Suitable for higher order FEM ,DGFEM using Domain decomposition. 3. Suitable for iterative solvers with built in preconditioners. 4. Suitable for C++ and/or MATLAB. OS preferred- Ubuntu. Intel compiler. ( Paradiso does not support intel Mkl)
4$\begingroup$ How large is large? Are there any other properties of the matrices, i.e. sparse, SPD, etc. $\endgroup$– SteveAug 22, 2017 at 8:34
$\begingroup$ You might also want to note that unless things have changed recently, most of PETSc is geared towards a distributed memory model, qv. mcs.anl.gov/petsc/miscellaneous/petscthreads.html $\endgroup$– origimboAug 22, 2017 at 10:25
$\begingroup$ Are your matrices sparse or dense ? $\endgroup$– BrunoLevyAug 23, 2017 at 15:26
1$\begingroup$ Sparse, SPD, complex symmetric, DOF's are usually in the range of 1e5 $\endgroup$– BulletAug 24, 2017 at 7:41
2$\begingroup$ In fact, a version of Pardiso is supplied with the MKL. So, if you are already using MKL, that would probably be the best solution for you. $\endgroup$– Bill GreeneAug 26, 2017 at 20:00
Eigen does not use parallelism for solving linear systems (see comment in http://eigen.tuxfamily.org/index.php?title=FAQ#How_does_Eigen_compare_to_BLAS.2FLAPACK.3F ).
Trilinos provides different linear solvers (direct, preconditioners, iterative).
Pardiso and MUMPS are other direct solvers that can run in parallel.
$\begingroup$ I would add PETSC to that list. Both PETSC (in C) and Trilinos (in C++) provide a large array of direct and iterative (Krylov, etc.) linear solver for large sparse matrices in a distributed memory environment. Both libraries are at the top of their game IMO... $\endgroup$– BlaBAug 24, 2017 at 12:59
For dense linear algebra, the LAPACK and BLAS libraries are nearly always the way to go. There are a number of C++ packages that interface to LAPACK and BLAS.
Some other packages in this space that might be of use:
UMFPACK: unsymmetric multifrontal method, sequential but robust
SuperLU: supernodal sparse LU, has parallel variants (both sharedmem and distmem)
TAUCS: sharedmem parallel multifrontal, can exploit complex-symmetry (I think)
MyraMath: sharedmem parallel multifrontal, can exploit complex-symmetry, has some interesting algorithms to support substructuring/DDM (disclaimer: I authored this one)
In my experience, PARDISO is generally the fastest.
$\begingroup$ In my experience, SuperLU performs very poorly and I would not recommend it. $\endgroup$– cfhAug 29, 2017 at 10:46
This page offers comparisons between various linear solvers http://www.netlib.org/utk/people/JackDongarra/la-sw.html
For a distributed, C++ based solver which can handle SPD specifically for sparse matrices along with built-in preconditioning, I would strongly recommend Elemental
For sparse systems, you can use my own library OpenNL: https://gforge.inria.fr/frs/?group_id=1252
It has no dependency, simple API for matrix assembly, it is parallel, works also on the GPU. It has built-in iterative algorithms (CG, preCG, BiCG, GMRES) and supports sparse direct solvers (SuperLU, CHOLMOD) with a plugin.
Documentation of OpenNL: http://alice.loria.fr/software/geogram/doc/html/nl_8h.html#details