@Article{CiCP-31-5,
author = {Nadir-Alexandre, Messaï and Sebastien, Pernet and Bouguerra, Abdesselam},
title = {Directional $\mathcal{H}^2$ Compression Algorithm: Optimisations and Application to a Discontinuous Galerkin BEM for the Helmholtz Equation},
journal = {Communications in Computational Physics},
year = {2022},
volume = {31},
number = {5},
pages = {1585--1635},
abstract = {<p style="text-align: justify;">This study aimed to specialise a directional $\mathcal{H}^2
(\mathcal{D}\mathcal{H}^2)$ compression to matrices arising from the discontinuous Galerkin (DG) discretisation of the hypersingular
equation in acoustics. The significant finding is an algorithm that takes a DG stiffness matrix and finds a near-optimal $\mathcal{D}\mathcal{H}^2$ approximation for low and high-frequency
problems. We introduced the necessary special optimisations to make this algorithm
more efficient in the case of a DG stiffness matrix. Moreover, an automatic parameter
tuning strategy makes it easy to use and versatile. Numerical comparisons with a classical Boundary Element Method (BEM) show that a DG scheme combined with a $\mathcal{D}\mathcal{H}^2$ gives better computational efficiency than a classical BEM in the case of high-order finite elements and $hp$ heterogeneous meshes. The results indicate that DG is suitable
for an auto-adaptive context in integral equations.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2021-0241},
url = {https://global-sci.com/article/79558/directional-mathcalh2-compression-algorithm-optimisations-and-application-to-a-discontinuous-galerkin-bem-for-the-helmholtz-equation}
}