2017/12/20 by Chao Chen, Hadi Pouransari, Chen, Chao +7
Computer Science · Engineering · Physics and Astronomy · #65F50 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1712.07297
openalex publication_date 2017/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by every processor. We present various numerical results to demonstrate the versatility and scalability of the parallel algorithm.