Discretization in Multilayered Media with High Contrasts: Is It All About the Boundaries?
INSA Lyon（里昂高等师范学院）；CNRS（法国国家科学研究中心）；Ecole Centrale de Lyon（里昂中央理工学院）；Universite Claude Bernard Lyon 1（里昂第一大学）；Université Jean Monnet（让·莫内大学）；ICJ UMR5208（计算几何研究所）；University of California, Merced（加州大学默塞德分校）；Laboratoire POEMS（POEMS实验室）；CNRS-ENSTA-INRIA（CNRS-ENSTA-INRIA联合实验室）；Institut Polytechnique de Paris（巴黎理工学院）
Wave propagation in multilayered media with high material contrasts poses significant numerical challenges, as large variations in wavenumbers lead to strong reflections and complex transmission of the incoming wave field. To address these difficulties, we employ a boundary integral formulation thereby avoiding volumetric discretization. In this framework, the accuracy of the numerical solution depends strongly on how the material interfaces are discretized. In this work, we demonstrate that standard meshing strategies based on resolving the maximum wavenumber across the domain become computationally inefficient in multilayered configurations, where high wavenumbers are confined to localized subdomains. Through a systematic study of multilayer transmission problems, we show that no simple discretization rule based on the maximum wavenumber or material contrasts emerges. Instead, the wavenumber of the background (exterior) medium plays a dominant role in determining the optimal boundary resolution. Building on these insights, we propose an adaptive approach that achieves uniform accuracy and efficient computation across multiple layers. Numerical experiments for a range of multilayer configurations demonstrate the scalability and robustness of the proposed approach.
High-Order Nyström/Convolution-Quadrature Solution of Time-Domain Scattering from Closed and Open Lipschitz Boundaries with Dirichlet and Neumann Boundary Conditions
High-order DLM-ALE discretizations with robust operator preconditioning for fluid-rigid-body interaction
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen International Center for Industrial and Applied Mathematics, Shenzhen Research Institute of Big Data（深圳市工业与应用数学国际中心，深圳大数据研究院）；Shenzhen Raymind Biotechnology Co., Ltd.（深圳睿医生物科技有限公司）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
Very high order treatment of embedded curved boundaries in compressible flows: ADER discontinuous Galerkin with a space-time Reconstruction for Off-site data
针对非贴合网格上弯曲边界的高阶边界条件一致性难题，将 ROD 融入 ADER 间断 Galerkin 的时空预测器，实现单次时空多项式重构，并通过后验限制支持激波与弯曲边界相互作用计算。
A Finite Volume Method for Elastic Waves in Heterogeneous, Anisotropic and Fractured Media
Center for Modeling of Coupled Subsurface, Dynamics, Department of Mathematics, University of Bergen（卑尔根大学耦合地下动力学中心数学系）；NORCE Norwegian Research Centre AS（挪威研究中心有限公司）
Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad-Shafranov equation by extension from polygonal subdomains
New York University, Courant Institute of Mathematical Sciences（纽约大学 库朗数学科学研究所）；Universidad de Concepción, Department of Mathematical Engineering（康塞普西翁大学 数学工程系）；Universidad de Concepción, Center for Research in Mathematical Engineering（康塞普西翁大学 数学工程研究中心）
Minimization-based polynomial corrections for high-order curved boundaries on fixed and moving domains: assessment on finite volume and discontinuous Galerkin schemes
Université Paris Cité and Sorbonne Université, CNRS, LJLL（巴黎西岱大学与索邦大学，法国国家科学研究中心，拉格朗日分析与应用数学实验室）；Laboratoire de Mathématiques, Université Savoie Mont Blanc, CNRS, UMR 5127（萨瓦-蒙布朗大学数学实验室，法国国家科学研究中心）；Department of Mathematics and Computer Science, University of Ferrara（费拉拉大学数学与计算机科学系）
