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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/1903.02118 |
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| _version_ | 1866917351905034240 |
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| author | Sato, Dye SK Ando, Ryosuke |
| author_facet | Sato, Dye SK Ando, Ryosuke |
| contents | We present a fast and memory-efficient algorithm for transient, space-time-domain, and elastodynamic boundary-integral analysis. Associated data-sparse approximations and operations are named fast domain partitioning hierarchical matrices (FDP=H-matrices). The fast domain partitioning method (the FDPM) solves a known problem of hierarchical matrices (H-matrices) in compressing discretized elastodynamic kernel functions. A novel set of plane-wave approximations then unites the FDPM and H-matrices in an accurate analytic manner. Memory usage is $\mathcal O(N \log N)$ and computation time $\mathcal O(NM \log N)$ in our algorithm throughout one run with $N$ boundary elements and $M$ time steps. The amount of associated cost reduction is remarkable, as the memory usage and computational time have been originally $\mathcal O(N^2M)$ and $\mathcal O(N^2M^2)$, respectively, to run the orthodox time-marching implementation. Numerical experiments indicate that FDP=H-matrices achieve $\mathcal O(NM/\log N)$ times smaller memory and computation time while ensuring the accuracy of the analyses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_02118 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A log-linear time algorithm for the elastodynamic boundary integral equation method Sato, Dye SK Ando, Ryosuke Computational Physics We present a fast and memory-efficient algorithm for transient, space-time-domain, and elastodynamic boundary-integral analysis. Associated data-sparse approximations and operations are named fast domain partitioning hierarchical matrices (FDP=H-matrices). The fast domain partitioning method (the FDPM) solves a known problem of hierarchical matrices (H-matrices) in compressing discretized elastodynamic kernel functions. A novel set of plane-wave approximations then unites the FDPM and H-matrices in an accurate analytic manner. Memory usage is $\mathcal O(N \log N)$ and computation time $\mathcal O(NM \log N)$ in our algorithm throughout one run with $N$ boundary elements and $M$ time steps. The amount of associated cost reduction is remarkable, as the memory usage and computational time have been originally $\mathcal O(N^2M)$ and $\mathcal O(N^2M^2)$, respectively, to run the orthodox time-marching implementation. Numerical experiments indicate that FDP=H-matrices achieve $\mathcal O(NM/\log N)$ times smaller memory and computation time while ensuring the accuracy of the analyses. |
| title | A log-linear time algorithm for the elastodynamic boundary integral equation method |
| topic | Computational Physics |
| url | https://arxiv.org/abs/1903.02118 |