This project has been created (2023--2025) to improve direct solvers for cardiac simulations. Its focus is on matchings, sparse solvers, and ordering.
We have developed an approximation algorithm for the weighted bipartite perfect matching problem. This will be used within sparse solvers to improve numerical behavior. The algorithm needs to be tested for different solvers (B. Uçar and J. Langguth).
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 (G. Pichon and J. Trotter).
Locally the Inria team has worked on ordering for low rank (LR) solvers. The choices made in the PasTiX solver were justified, and a slight improvement (to fend off worst cases) has been incorporated (G. Pichon and B. Uçar).