Bernstein-Bezier weight-adjusted discontinuous Galerkin methods for wave propagation in heterogeneous media

JOURNAL OF COMPUTATIONAL PHYSICS

卷:400

Article

Guo, Kaihang¹  Chan, Jesse¹ 

[1] Rice Univ, Dept Computat & Appl Math, 6100 Main St, Houston, TX 77005 USA

关键词: Discontinuous Galerkin;    Bernstein;    High order;    Heterogeneous media;    GPU;   

DOI  :  10.1016/j.jcp.2019.108971

来源: Elsevier

【 摘 要 】

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 [1]. However, the computational cost of WADG grows rapidly with the order of approximation. In this work, we propose a Bernstein-Bezier weight-adjusted discontinuous Galerkin method (BBWADG) to address this cost. By approx-imating 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 (Nd+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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free