Well-posed boundary integral equation formulations and Nyström discretizations for the solution of Helmholtz transmission problems in two-dimensional Lipschitz domains
University of New Hampshire（新罕布什尔大学）；New Jersey Institute of Technology（新泽西理工学院）
We present a comparison between the performance of solvers based on Nyström discretizations of several well-posed boundary integral equation formulations of Helmholtz transmission problems in two-dimensional Lipschitz domains. Specifically, we focus on the following four classes of boundary integral formulations of Helmholtz transmission problems (1) the classical first kind integral equations for transmission problems, (2) the classical second kind integral equations for transmission problems, (3) the {\em single} integral equation formulations, and (4) certain direct counterparts of recently introduced Generalized Combined Source Integral Equations. The former two formulations were the only formulations whose well-posedness in Lipschitz domains was rigorously established. We establish the well-posedness of the latter two formulations in appropriate functional spaces of boundary traces of solutions of transmission Helmholtz problems in Lipschitz domains. We give ample numerical evidence that Nyström solvers based on formulations (3) and (4) are computationally more advantageous than solvers based on the classical formulations (1) and (2), especially in the case of high-contrast transmission problems at high frequencies.
Well-conditioned boundary integral equation formulations and Nyström discretizations for the solution of Helmholtz problems with impedance boundary conditions in two-dimensional Lipschitz domains
Stability estimates of Nyström discretizations of Helmholtz decomposition boundary integral equation formulations for the solution of Navier scattering problems in two dimensions with Dirichlet boundary conditions
High-Order Nyström/Convolution-Quadrature Solution of Time-Domain Scattering from Closed and Open Lipschitz Boundaries with Dirichlet and Neumann Boundary Conditions
Inverse boundary value problem for the Helmholtz equation: Multi-level approach and iterative reconstruction
Politecnico di Milano（米兰理工大学）；Universita’ di Roma ”La Sapienza”（罗马第一大学）；Purdue University（普渡大学）；University of Minnesota（明尼苏达大学）；University of Vienna（维也纳大学）
Proxy-surface-based fast direct solver for TE-mode scattering problems on distributed memory systems
Center for Information Infrastructure, Institute of Science Tokyo（科学技术研究所信息基础设施中心）；Institute of Integrated Research, Institute of Science Tokyo（科学技术研究所综合研究机构）
Extension of the G{ü}nter derivatives to Lipschitz domains and application to the boundary potentials of elastic waves
Université de Toulouse, Institut Mathématique de Toulouse, Département de Génie Mathématique, INSA（图卢兹大学，图卢兹数学研究所，数学工程系，国立应用科学学院）；University of Pau (France)（波尔多大学（法国））
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）
On Closed and Exact Grad-grad- and div-Div-Complexes, Corresponding Compact Embeddings for Tensor Rotations, and a Related Decomposition Result for Biharmonic Problems in 3D
Universität Duisburg-Essen（杜伊斯堡-埃森大学）；Johannes Kepler Universität Linz（约翰·开普勒林茨大学）
Convolution quadrature methods for time-domain scattering from unbounded penetrable interfaces
Institute for Mathematical and Computational Engineering, School of Engineering and Faculty of Mathematics, Pontificia Universidad Católica de Chile（智利天主教大学工程学院与数学学院计算与数学工程研究所）；Department of Mathematics, Massachusetts Institute of Technology（麻省理工学院数学系）
Pressure-robust $hp$-a posteriori error estimates of $\boldsymbol{H}(\mathrm{div})$-conforming discontinuous Galerkin methods for the Stokes equations
Inria（法国国家数字技术研究院）；CERMICS, CNRS, ENPC, Institut Polytechnique de Paris（巴黎高等师范学院、国立信息与自动化研究所、巴黎理工学院）；School of Mathematical Sciences（东方理工学院数学科学学院）；Eastern Institute of Technology（香港城市大学数学系）；Department of Mathematics, City University of Hong Kong
