Comparison of $\mathcal{H}$-matrix- and FMM-based 3D-ACA for a time-domain boundary element method
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917361248894976 |
|---|---|
| author | Schanz, Martin Keshava, Vibudha Lakshmi de Gersem, Herbert |
| author_facet | Schanz, Martin Keshava, Vibudha Lakshmi de Gersem, Herbert |
| contents | The homogeneous wave equation is solved by a time-domain boundary element method (BEM) using low-order shape functions for spatial, and the generalised convolution quadrature method (gCQ) by Lopez-Fernandez and Sauter for temporal discretisation. The three-dimensional array of BEM matrices according to a set of complex frequencies in Laplace domain is approximated by generalised Adaptive Cross Approximation (3D-ACA). Its rank is increased adaptively until a prescribed accuracy is reached, relying on a pure algebraic error criterion. The data slices for the selected frequency points are further processed by either the standard $\mathcal{H}$-matrices approach with ACA or by a fast multipole method (FMM). This paper compares both approaches with respect to their demands in storage and computing time. Both techniques are illustrated for calculating the sound scattered by an electric machine, for which the proposed algebraic compression techniques make time-domain BEM feasible for the first time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00715 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparison of $\mathcal{H}$-matrix- and FMM-based 3D-ACA for a time-domain boundary element method Schanz, Martin Keshava, Vibudha Lakshmi de Gersem, Herbert Numerical Analysis 35L05, 65M38, 65R20 The homogeneous wave equation is solved by a time-domain boundary element method (BEM) using low-order shape functions for spatial, and the generalised convolution quadrature method (gCQ) by Lopez-Fernandez and Sauter for temporal discretisation. The three-dimensional array of BEM matrices according to a set of complex frequencies in Laplace domain is approximated by generalised Adaptive Cross Approximation (3D-ACA). Its rank is increased adaptively until a prescribed accuracy is reached, relying on a pure algebraic error criterion. The data slices for the selected frequency points are further processed by either the standard $\mathcal{H}$-matrices approach with ACA or by a fast multipole method (FMM). This paper compares both approaches with respect to their demands in storage and computing time. Both techniques are illustrated for calculating the sound scattered by an electric machine, for which the proposed algebraic compression techniques make time-domain BEM feasible for the first time. |
| title | Comparison of $\mathcal{H}$-matrix- and FMM-based 3D-ACA for a time-domain boundary element method |
| topic | Numerical Analysis 35L05, 65M38, 65R20 |
| url | https://arxiv.org/abs/2505.00715 |