We present Nyström discretizations of multitrace formulations and non-overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz transmission problems for bounded composite scatterers with piecewise constant material properties. We investigate the performance of DDM with both classical Robin and generalized Robin boundary conditions. The generalized Robin boundary conditions incorporate square root Fourier multiplier approximations of Dirichlet to Neumann operators. While the classical version of DDM is not particularly well suited for Krylov subspace iterative solvers, we show that the associated DDM linear system can be efficiently solved by hierarchical elimination via Schur complements of the Robin data. We show through numerical examples that the latter version of DDM gives rise to small numbers of Krylov subspace iterations that depend mildly on the frequency and number of subdomains.
Integral equation methods for acoustic scattering by fractals
Universidade de Aveiro（阿威罗大学）；University of Reading（雷丁大学）；Sorbonne Université（索邦大学）；University College London（伦敦大学学院）；Università degli studi di Pavia（帕维亚大学）
Convergence of overlapping domain decomposition methods with PML transmission conditions applied to nontrapping Helmholtz problems
University College London（伦敦大学学院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Research Institute of Big Data（深圳大数据研究院）；University of Bath（巴斯大学）；CNRS and Institut de Mathématiques de Toulouse, UMR5219（法国国家科学研究中心与图卢兹数学研究所；图卢兹大学）；Université de Toulouse
High-Order Nyström/Convolution-Quadrature Solution of Time-Domain Scattering from Closed and Open Lipschitz Boundaries with Dirichlet and Neumann Boundary Conditions
A Trefftz Discontinuous Galerkin Method for Time Harmonic Waves with Generalized Impedance Boundary Conditions
Institute for Mathematics and its Applications, College of Science and Engineering（数学及其应用研究所，科学与工程学院）；Department of Mathematical Sciences, University of Delaware（特拉华大学数学科学系）；Departamento de Matemáticas, Universidad de Oviedo（奥维耶多大学数学系）
