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Related papers: Discrete FEM-BEM coupling with the Generalized Opt…

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Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…

Numerical Analysis · Mathematics 2024-02-21 Elwin van 't Wout

We consider solving the exterior Dirichlet problem for the Helmholtz equation with the $h$-version of the boundary element method (BEM) using the standard second-kind combined-field integral equations. We prove a new, sharp bound on how the…

Numerical Analysis · Mathematics 2019-02-25 Jeffrey Galkowski , Eike H. Müller , Euan A. Spence

In this paper, we present a fast boundary integral method accelerated by the fast multipole method (FMM) for acoustic wave scattering governed by the scalar Helmholtz equation in multi-layered two-dimensional media. Multiple scatterers are…

Numerical Analysis · Mathematics 2025-11-18 Linfeng Xia , Heng Yuan , Bo Wang , Wei Cai

Generalized Bose-Einstein (BE) and Fermi-Dirac (FD) distributions in nonextensive quantum statistics have been discussed by the maximum-entropy method (MEM) with the optimum Lagrange multiplier based on the exact integral representation…

Statistical Mechanics · Physics 2009-07-21 Hideo Hasegawa

We analyze a multilevel diagonal additive Schwarz preconditioner for the adaptive coupling of FEM and BEM for a linear 2D Laplace transmission problem. We rigorously prove that the condition number of the preconditioned system stays…

Numerical Analysis · Mathematics 2017-12-04 Michael Feischl , Thomas Führer , Dirk Praetorius , Ernst P. Stephan

The Wave Based Method (WBM) is a Trefftz method for the simulation of wave problems in vibroacoustics. Like other Trefftz methods, it employs a non-standard discretisation basis consisting of solutions of the partial differential equation…

Numerical Analysis · Mathematics 2018-02-06 Daan Huybrechs , Anda-Elena Olteanu

While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber agrees with an eigenvalue of the interior Dirichlet problem.…

Numerical Analysis · Mathematics 2025-08-19 Théophile Chaumont-Frelet , Gregor Gantner

We analyze a discontinuous Galerkin FEM-BEM scheme for a second order elliptic transmission problem posed in the three-dimensional space. The symmetric variational formulation is discretized by nonconforming Raviart-Thomas finite elements…

Numerical Analysis · Mathematics 2013-10-14 Norbert Heuer , Salim Meddahi , Francisco-Javier Sayas

To mitigate pollution effects in high-frequency Helmholtz problems, Learning-based Numerical Methods (LbNM) reconstruct solution operators using complete systems of exact solutions. However, the previously used fundamental-solution (FS)…

Numerical Analysis · Mathematics 2026-03-17 Lifu Song , Tingyue Li , Jin Cheng

The use of boundary integral equations in modeling boundary value problems-such as elastic, acoustic, or electromagnetic ones-is well established in the literature and widespread in practical applications. These equations are typically…

Computational Engineering, Finance, and Science · Computer Science 2025-05-28 Viviana Giunzioni , Adrien Merlini , Francesco P. Andriulli

Dirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method…

Numerical Analysis · Mathematics 2013-02-06 Luca Heltai , Francesco Costanzo

We describe a new finite element method (FEM) to construct continuous equilibrium distribution functions of stellar systems. The method is a generalization of Schwarzschild's orbit superposition method from the space of discrete functions…

Instrumentation and Methods for Astrophysics · Physics 2015-05-19 Mir Abbas Jalali , Scott Tremaine

We investigate the parallel one-level overlapping Schwarz method for solving finite element discretization of high-frequency Helmholtz equations. The resulting linear systems are large, indefinite, ill-conditioned, and complex-valued. We…

Numerical Analysis · Mathematics 2026-02-03 Yan Xie , Shihua Gong , Ivan G. Graham , Euan A. Spence , Chen-Song Zhang

We model time-harmonic acoustic scattering by an object composed of piece-wise homogeneous parts and an arbitrarily heterogeneous part. We propose and analyze new formulations that couple, adopting a Costabel-type approach, boundary…

Numerical Analysis · Mathematics 2024-08-06 Marcella Bonazzoli , Xavier Claeys

This paper presents and evaluates an approach for coupling together subdomain-local reduced order models (ROMs) constructed via non-intrusive operator inference (OpInf) with each other and with subdomain-local full order models (FOMs),…

Numerical Analysis · Mathematics 2024-10-15 Ian Moore , Christopher Wentland , Anthony Gruber , Irina Tezaur

In this paper, a three-dimensional Dirichlet-to-Neumann (DtN) finite element method (FEM) is developed to analyze the scattering of Lamb and SH guided waves due to a symmetric cavity defect in an isotropic infinite plate. During the finite…

Numerical Analysis · Mathematics 2025-01-09 Chen Yang , Junichi Nakaoka , Sohichi Hirose

A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…

Numerical Analysis · Mathematics 2026-05-22 Benedikt Gräßle , Stefan A. Sauter

In this paper, a two-dimensional Dirichlet-to-Neumann (DtN) finite element method (FEM) is developed to analyze the scattering of SH guided waves due to an interface delamination in a bi-material plate. During the finite element analysis,…

Numerical Analysis · Mathematics 2024-07-23 Chen Yang , Ruigang Qin , Sohichi Hirose , Bin Wang , Zhenghua Qian

The accurate electromagnetic modeling of both low- and high-frequency physics is crucial in the signal and power integrity analysis of electrical interconnects. The boundary element method (BEM) is appealing for lossy conductor modeling…

Computational Engineering, Finance, and Science · Computer Science 2022-08-31 Shashwat Sharma , Piero Triverio

This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of fixed, arbitrary order and the preconditioner is…

Numerical Analysis · Mathematics 2020-03-23 Marcella Bonazzoli , Victorita Dolean , Ivan G. Graham , Euan A. Spence , Pierre-Henri Tournier