SlabLU: a two-level sparse direct solver for elliptic PDEs

The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two-dimensional domain. The scheme decomposes the domain into thin subdomains, or “slabs” and uses a two-level approach that is designed with parallelization in mind. The sche...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Advances in computational mathematics Jg. 50; H. 4; S. 90
Hauptverfasser:	Yesypenko, Anna, Martinsson, Per-Gunnar
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.08.2024 Springer Nature B.V Springer
Schlagworte:	Computational mathematics Computational Mathematics and Numerical Analysis Computational Science and Engineering Discretization Domains Elliptic differential equations Graphics processing units Linear algebra Linear systems Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Matrix algebra Parabolic differential equations Partial differential equations Solvers Sparsity Visualization 65N35 Direct solver Sparse direct solver Randomized linear algebra Helmholtz equation High-order discretization GPU 65N22 65F05 Multifrontal solver
ISSN:	1019-7168, 1572-9044
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two-dimensional domain. The scheme decomposes the domain into thin subdomains, or “slabs” and uses a two-level approach that is designed with parallelization in mind. The scheme takes advantage of H 2 -matrix structure emerging during factorization and utilizes randomized algorithms to efficiently recover this structure. As opposed to multi-level nested dissection schemes that incorporate the use of H or H 2 matrices for a hierarchy of front sizes, SlabLU is a two-level scheme which only uses H 2 -matrix algebra for fronts of roughly the same size. The simplicity allows the scheme to be easily tuned for performance on modern architectures and GPUs. The solver described is compatible with a range of different local discretizations, and numerical experiments demonstrate its performance for regular discretizations of rectangular and curved geometries. The technique becomes particularly efficient when combined with very high-order accurate multidomain spectral collocation schemes. With this discretization, a Helmholtz problem on a domain of size 1000 λ × 1000 λ (for which N = 100 M ) is solved in 15 min to 6 correct digits on a high-powered desktop with GPU acceleration.
Bibliographie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 SC0022251 None USDOE Office of Science (SC)
ISSN:	1019-7168 1572-9044
DOI:	10.1007/s10444-024-10176-x