التفاصيل البيبلوغرافية
| العنوان: |
Sparse Approximate Multifrontal Factorization with Composite Compression Methods. |
| المؤلفون: |
CLAUS, LISA, GHYSELS, PIETER, LIU, YANG, NHAN, THAI ANH, THIRUMALAISAMY, RAMAKRISHNAN, BHALLA, AMNEET PAL SINGH, LI, SHERRY |
| المصدر: |
ACM Transactions on Mathematical Software; Sep2023, Vol. 49 Issue 3, p1-28, 28p |
| مصطلحات موضوعية: |
FACTORIZATION, LINEAR systems, WAVE equation, BUTTERFLIES |
| مستخلص: |
This article presents a fast and approximate multifrontal solver for large sparse linear systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver leveraging the butterfly algorithm and its hierarchical matrix extension, HODBF (hierarchical off-diagonal butterfly) compression to compress large frontal matrices. The resulting multifrontal solver can attain quasi-linear computation and memory complexity when applied to sparse linear systems arising from spatial discretization of high-frequency wave equations. To further reduce the overall number of operations and especially the factorization memory usage to scale to larger problem sizes, in this article we develop a composite multifrontal solver that employs the HODBF format for large-sized fronts, a reduced-memory version of the nonhierarchical block low-rank format for medium-sized fronts, and a lossy compression format for small-sized fronts. This allows us to solve sparse linear systems of dimension up to 2.7 × larger than before and leads to a memory consumption that is reduced by 70% while ensuring the same execution time. The code is made publicly available in GitHub. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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