| Autor: |
Yesypenko, Anna, Martinsson, Per-Gunnar |
| Rok vydání: |
2022 |
| Předmět: |
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| DOI: |
10.48550/arxiv.2211.07572 |
| Popis: |
The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a rectangular domains. The scheme decomposes the domain into thin subdomains, or ``slabs''. Within each slab, a local factorization is executed that exploits the geometry of the local domain. A global factorization is then obtained through the LU factorization of a block-tridiagonal reduced system. The general two-level framework is easier to implement and optimize for modern latency-bound architectures than traditional multi-frontal schemes based on hierarchical nested dissection orderings. The solver has complexity $O(N^{5/3})$ for the factorization step, and $O(N^{7/6})$ for each solve once the factorization is completed. The solver described is compatible with a range of different local discretizations, and numerical experiments demonstrate its high performance for standard finite difference discretizations on a regular grid. The technique becomes particularly efficient when combined with very high-order convergent multi-domain spectral collocation schemes. With this discretization, a Helmholtz problem on a domain of size $1000 \lambda \times 1000 \lambda$ (for which $N$=100M) is solved in 15 minutes to 6 correct digits on a high-powered desktop. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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