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.
UMFPACK | Sparspak | |
---|---|---|
Without MKL [sec] | 22 | 31 |
With MKL [sec] | 19 | 21 |
On the same machine with Windows Subsystem for Linux, WSL 2, running Ubuntu 22.04, the results were as
UMFPACK | Sparspak | |
---|---|---|
Without MKL [sec] | 19 | 39 |
With MKL [sec] | 16 | 19 |
Clearly, MKL can make a huge difference