Memory‐efficient compression of 𝒟ℋ2‐matrices for high‐frequency Helmholtz problems
Fuente:
Wiley Open Access
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Artículo Open Access |
| Veröffentlicht: |
Wiley
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1867009844948500480 |
|---|---|
| author | Steffen Börm Janne Henningsen |
| author_facet | Steffen Börm Janne Henningsen Steffen Börm Janne Henningsen |
| collection | Wiley Open Access |
| contents | Memory‐efficient compression of 𝒟ℋ2‐matrices for high‐frequency Helmholtz problems Steffen Börm Janne Henningsen Numerical Linear Algebra with Applications AbstractDirectional interpolation is a fast and efficient compression technique for high‐frequency Helmholtz boundary integral equations, but requires a very large amount of storage in its original form. Algebraic recompression can significantly reduce the storage requirements and speed up the solution process accordingly. During the recompression process, weight matrices are required to correctly measure the influence of different basis vectors on the final result, and for highly accurate approximations, these weight matrices require more storage than the final compressed matrix. We present a compression method for the weight matrices and demonstrate that it introduces only a controllable error to the overall approximation. Numerical experiments show that the new method leads to a significant reduction in storage requirements. 10.1002/nla.2575 http://creativecommons.org/licenses/by-nc/4.0/ |
| doi_str_mv | 10.1002/nla.2575 |
| format | Artículo Open Access |
| id | wiley_oa_10_1002_nla_2575 |
| institution | Wiley Open Access |
| license_str_mv | http://creativecommons.org/licenses/by-nc/4.0/ |
| publishDate | 2024 |
| publisher | Wiley |
| record_format | wiley_oa |
| spellingShingle | Memory‐efficient compression of 𝒟ℋ2‐matrices for high‐frequency Helmholtz problems Steffen Börm Janne Henningsen Numerical Linear Algebra with Applications Memory‐efficient compression of 𝒟ℋ2‐matrices for high‐frequency Helmholtz problems Steffen Börm Janne Henningsen Numerical Linear Algebra with Applications AbstractDirectional interpolation is a fast and efficient compression technique for high‐frequency Helmholtz boundary integral equations, but requires a very large amount of storage in its original form. Algebraic recompression can significantly reduce the storage requirements and speed up the solution process accordingly. During the recompression process, weight matrices are required to correctly measure the influence of different basis vectors on the final result, and for highly accurate approximations, these weight matrices require more storage than the final compressed matrix. We present a compression method for the weight matrices and demonstrate that it introduces only a controllable error to the overall approximation. Numerical experiments show that the new method leads to a significant reduction in storage requirements. 10.1002/nla.2575 http://creativecommons.org/licenses/by-nc/4.0/ |
| title | Memory‐efficient compression of 𝒟ℋ2‐matrices for high‐frequency Helmholtz problems |
| topic | Numerical Linear Algebra with Applications |
| url | https://onlinelibrary.wiley.com/doi/10.1002/nla.2575 |