Match and Order: improving direct solvers for cardiac simulations

Organization

Principal investigator (Inria): Grégoire Pichon, Inria ROMA project-team
Principal investigator (Main team): Johannes Langguth, Simula Research Laboratory
Other participants from Inria ROMA: Bora Uçar (senior researcher), Somesh Singh (post-doc)
Other participants from Simula Research Laboratory: Xing Cai (professor), James Trotter (post-doc), Luk Burchard (PhD Student)

G. Pichon and B. Uçar are visiting SIMULA from September 25th, 2023 to September 29th, 2023
Meeting on 20 Oct, 2023 at 10h online (J. Langguth, G. Pichon, J. Trotter, B. Uçar).
Meeting on 1 December, 2023 at 10h online (J. Langguth, G. Pichon, J. Trotter, B. Uçar, Luk Burchard)..
Planned visit from the Simula team, the weeked of 15 January 2024.

We have developed an approximation algorithm for the weighted bipartite matching problem. This will be used within a direct solver to improve numerical behavior. We are currently testing this algorithm in isolation from the direct solvers for potential improvements. Later on we will test it in a direct solver before thinking about its potential parallelization.

We have made experiments with matrices arising in Simula cardiac simulations using the PaStiX sparse direct solvers and its low-rank functionalities. The most impressive achievement was the possibility to solve a 8x8x8 cells problem on a node made of 128 GB of RAM. The use of low-rank compression allowed to solve the problem while it would have required more that 550 GB of RAM using regular approaches. For smaller problems that would have fit in memory before, we managed to reduce execution time by a factor of three, while maintaining a suitable accuracy for the final application. We are planning a large scale experimental evaluation of low rank solvers for the cardiac simulations. This is currently the task with the highest priority for the MODS team. One aim of the planned January 2024 meeting is to define precisely the context of the study.

Locally the Inria team works on ordering for low rank (LR) solvers. Once the appropriateness of LR solvers for cardiac simulations are established, we can use this improved ordering scheme inside the simulators.