Concepts

Performance

To compare the sparse LU factorization we can consider the UMFPACK lu factorization from SuiteSparse, and the general LU sparse matrix factorization of Sparspak. The former is a multi-frontal algorithm, the latter is a super-nodal algorithm. Both rely quite heavily on dense algebra subroutines.

Some preliminary data was collected for one particular sparse matrix system, with a symmetric matrix, 63070 equations, 4.22 million non-zeros.

On a Surface Pro 7 with 16 GB of RAM, i7-1065G7 @ 1.30 GHz, the following results were gathered under Windows 10.

UMFPACKSparspak
Without MKL [sec]2231
With MKL [sec]1921

On the same machine with Windows Subsystem for Linux, WSL 2, running Ubuntu 22.04, the results were as

UMFPACKSparspak
Without MKL [sec]1939
With MKL [sec]1619

Clearly, MKL can make a huge difference