{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/bernstein-bezier-weight-adjusted","title":"Bernstein-Bézier weight-adjusted discontinuous Galerkin methods for wave propagation in heterogeneous media","arxiv_id":"1808.08645","date":"2018-08-27","proceeding":null,"authors":["Kaihang Guo","Jesse Chan"],"abstract":"This paper presents an efficient discontinuous Galerkin method to simulate wave propagation in heterogeneous media with sub-cell variations. This method is based on a weight-adjusted discontinuous Galerkin method (WADG), which achieves high order accuracy for arbitrary heterogeneous media. However, the computational cost of WADG grows rapidly with the order of approximation. In this work, we propose a Bernstein-B\\'ezier weight-adjusted discontinuous Galerkin method (BBWADG) to address this cost. By approximating sub-cell heterogeneities by a fixed degree polynomial, the main steps of WADG can be expressed as polynomial multiplication and $L^2$ projection, which we carry out using fast Bernstein algorithms. The proposed approach reduces the overall computational complexity from $O(N^{2d})$ to $O(N^{d+1})$ in $d$ dimensions. Numerical experiments illustrate the accuracy of the proposed approach, and computational experiments for a GPU implementation of BBWADG verify that this theoretical complexity is achieved in practice.","url_abs":"http://arxiv.org/abs/1808.08645v1","url_pdf":"http://arxiv.org/pdf/1808.08645v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"bernstein-bezier-weight-adjusted","repo_url":"https://github.com/KGuo26/bbwadg_public","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}