$\mathcal{H}^2$-matrices for translation-invariant kernel functions
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913380615323648 |
|---|---|
| author | Börm, Steffen Henningsen, Janne |
| author_facet | Börm, Steffen Henningsen, Janne |
| contents | Boundary element methods for elliptic partial differential equations typically lead to boundary integral operators with translation-invariant kernel functions. Taking advantage of this property is fairly simple for particle methods, e.g., Nystrom-type discretizations, but more challenging if the supports of basis functions have to be taken into account.
In this article, we present a modified construction for $\mathcal{H}^2$-matrices that uses translation-invariance to significantly reduce the storage requirements. Due to the uniformity of the boxes used for the construction, we need only a few uncomplicated assumptions to prove estimates for the resulting storage complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_16609 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | $\mathcal{H}^2$-matrices for translation-invariant kernel functions Börm, Steffen Henningsen, Janne Numerical Analysis 65N38, 65R20, 65D05, 41A10 Boundary element methods for elliptic partial differential equations typically lead to boundary integral operators with translation-invariant kernel functions. Taking advantage of this property is fairly simple for particle methods, e.g., Nystrom-type discretizations, but more challenging if the supports of basis functions have to be taken into account. In this article, we present a modified construction for $\mathcal{H}^2$-matrices that uses translation-invariance to significantly reduce the storage requirements. Due to the uniformity of the boxes used for the construction, we need only a few uncomplicated assumptions to prove estimates for the resulting storage complexity. |
| title | $\mathcal{H}^2$-matrices for translation-invariant kernel functions |
| topic | Numerical Analysis 65N38, 65R20, 65D05, 41A10 |
| url | https://arxiv.org/abs/2210.16609 |