Brief Announcement: Communication Optimal Sparse LU Factorization for Planar Matrices
We introduce a new parallel algorithm for solving sparse LU factorization of planar matrices, which commonly arise in the finite element method for 2D PDEs. Existing scalable methods, such as the multifrontal approach with subtree-to-subcube mapping by Gupta et al. [1] and right-looking with 3D mapping by Sao et al. [2] fail to achieve optimal communication costs for these matrices. Our new algorithm combines 3D mapping and subtree-to-subcube mapping to minimize communication costs while allowing trade-offs between extra memory and reduced communication. We demonstrate that our proposed algorithm attains the communication lower bound up to a factor of O(log log n) in the memory-optimal case and up to a factor of O(log P) in the memory-independent case for an n-dimensional planar sparse matrix on P processors.
- Research Organization:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- AC05-00OR22725
- OSTI ID:
- 1999008
- Resource Relation:
- Conference: SPAA23: 35th ACM Symposium on Parallelism in Algorithms and Architectures - Orlando, Florida, United States of America - 6/17/2023 12:00:00 PM-6/19/2023 12:00:00 PM
- Country of Publication:
- United States
- Language:
- English
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