Testing performance with and without Block Low Rank Compression in MUMPS and the new PaStiX 6.0 for JOREK nonlinear MHD simulations

TL;DR

This paper evaluates the impact of Block Low Rank (BLR) compression on the performance and memory usage of MUMPS and PaStiX solvers within JOREK nonlinear MHD simulations, highlighting trade-offs in accuracy and efficiency.

Contribution

It introduces BLR support in MUMPS and PaStiX for JOREK, analyzes the effects of BLR parameters on simulation accuracy and performance, and provides insights into optimal configurations.

Findings

BLR reduces memory consumption by several tens of percent.

Performance improvements are observed in certain configurations.

Choosing the right BLR accuracy parameter $$ is critical for balancing speed and convergence.

Abstract

The interface to the MUMPS solver was updated in the JOREK MHD code to support Block Low Rank (BLR) compression and an interface to the new PaStiX solver version 6 has been implemented supporting BLR as well. First tests were carried out with JOREK, which solves a large sparse matrix system iteratively in each time step. For the preconditioning, a direct solver is applied in the code to sub-matrices, and at this point BLR was applied with the results being summarized in this report. For a simple case with a linearly growing mode, results with both solvers look promising with a considerable reduction of the memory consumption by several ten percent was obtained. A direct increase in performance was seen in particular configurations already. The choice of the BLR accuracy parameter $\epsilon$ proves to be critical in this simple test and also in more realistic simulations, which were carried out only with MUMPS due to the limited time available. The more realistic test showed an increase in run time when using BLR, which was mitigated when using larger values of $\epsilon$. However, the GMRes iterative solver does not reach convergence anymore when $\epsilon$ is too large, since the preconditioner becomes too inaccurate in that case. It is thus critical to use an $\epsilon$ as large as possible, while still reaching convergence. More tests regarding this optimum will be necessary in the future. BLR can also lead to an indirect speed-up in particular cases, when the simulation can be run on a smaller number of compute nodes due to the reduced memory consumption.