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We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

Numerical Analysis · Mathematics 2016-05-04 Alex. H. Barnett , Bradley J. Nelson , J. Matthew Mahoney

We propose time-domain boundary integral and coupled boundary integral and variational formulations for acoustic scattering by linearly elastic obstacles. Well posedness along with stability and error bounds with explicit time dependence…

Numerical Analysis · Mathematics 2018-04-23 George C. Hsiao , Tonatiuh Sanchez-Vizuet , Francisco--Javier Sayas

We present several versions of Regularized Combined Field Integral Equation (CFIER) formulations for the solution of three dimensional frequency domain electromagnetic scattering problems with Perfectly Electric Conducting (PEC) boundary…

Numerical Analysis · Mathematics 2014-04-08 Yassine Boubendir , Catalin Turc

This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lam\'e coefficients in the form of a bounded domain of arbitrary shape surrounded…

Numerical Analysis · Mathematics 2021-03-08 Benjamin Stamm , Shuyang Xiang

In this paper, we discuss the stable discretisation of the double layer boundary integral operator for the wave equation in $1d$. For this, we show that the boundary integral formulation is $L^2$-elliptic and also inf-sup stable in standard…

Numerical Analysis · Mathematics 2025-02-04 Daniel Hoonhout , Carolina Urzúa-Torres

Isogeometric analysis with the boundary element method (IGABEM) has recently gained interest. In this paper, the approximability of IGABEM on 3D acoustic scattering problems will be investigated and a new improved BeTSSi submarine will be…

Numerical Analysis · Mathematics 2022-04-21 Jon Vegard Venås , Trond Kvamsdal

The structure and function of biological molecules are strongly influenced by the water and dissolved ions that surround them. This aqueous solution (solvent) exerts significant electrostatic forces in response to the biomolecule's…

Numerical Analysis · Mathematics 2015-12-29 Matthew G. Knepley , Jaydeep P. Bardhan

An original boundary integral formulation is proposed for the problem of a semi-infinite crack at the interface between two dissimilar elastic materials in the presence of heat flows and mass diffusion. Symmetric and skew-symmetric weight…

Mathematical Physics · Physics 2016-02-17 L. Morini , A. Piccolroaz

A system of Boundary-Domain Integral Equations is derived from the mixed (Dirichlet-Neumann) boundary value problem for the diffusion equation in inhomogeneous media defined on an unbounded domain. Boundary-domain integral equations are…

Analysis of PDEs · Mathematics 2020-11-23 C. Fresneda-Portillo

In this paper, we make the first attempt to apply the boundary integrated neural networks (BINNs) for the numerical solution of two-dimensional (2D) elastostatic and piezoelectric problems. BINNs combine artificial neural networks with the…

Computational Engineering, Finance, and Science · Computer Science 2023-08-03 Peijun Zhang , Chuanzeng Zhang , Yan Gu , Wenzhen Qu , Shengdong Zhao

Conventionally, piecewise polynomials have been used in the boundary elements method (BEM) to approximate unknown boundary values. Since infinitely smooth radial basis functions (RBFs) are more stable and accurate than the polynomials for…

Numerical Analysis · Mathematics 2023-09-13 Hossein Hosseinzadeh , Zeinab Sedaghatjoo

Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy…

Computational Physics · Physics 2012-08-21 David J. Chappell , Gregor Tanner , Stefano Giani

We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…

Numerical Analysis · Mathematics 2025-03-25 Roman Chapko , Leonidas Mindrinos

This paper is concerned with the application of time domain boundary integral methods(TDBIMs) to a non-stationary boundary value problem for the thermo-elasto-dynamic equations, based on the Lubich approach via the Laplace transform.…

Numerical Analysis · Mathematics 2021-05-28 George Hsiao , Tonatiuh Sánchez-Vizuet

The Scaled Boundary Finite Element Method is a novel semi-analytical method jointly developed by Chongmin Song and John P Wolf to solve problems in elastodynamics and allied problems in civil engineering. This novel method has been recently…

Computational Physics · Physics 2007-05-23 V. S. Prasanna Rajan

A mixed boundary value problem for the diffusion equation in non-homogeneous media partial differential equation is reduced to a system of direct segregated parametrix-based Boundary-Domain Integral Equations (BDIEs). We use a parametrix…

Analysis of PDEs · Mathematics 2020-11-23 Carlos Fresneda-Portillo , Sergey E. Mikhailov

This paper is the direct-formulation companion to [Burbano-Gallegos, P\'erez-Arancibia, and Turc, ESAIM: M2AN, 60(1):273--315, 2026], which developed indirect combined-field-only boundary integral equations (BIEs) for time-harmonic…

Numerical Analysis · Mathematics 2026-05-07 Carlos Pérez-Arancibia , Catalin Turc

This paper discusses the practical development of space-time boundary element methods for the wave equation in three spatial dimensions. The employed trial spaces stem from simplex meshes of the lateral boundary of the space-time cylinder.…

Numerical Analysis · Mathematics 2021-08-25 Dominik Pölz , Martin Schanz

A mixed boundary value problem for the partial differential equation of diffusion in an inhomogeneous medium in a Lipschitz domain is reduced to a system of direct segregated parametrix-based Boundary-Domain Integral Equations (BDIEs). We…

Analysis of PDEs · Mathematics 2020-11-23 S. E. Mikhailov , C. F. Portillo

A second-order accurate kernel-free boundary integral method is presented for Stokes and Navier boundary value problems on three-dimensional irregular domains. It solves equations in the framework of boundary integral equations, whose…

Numerical Analysis · Mathematics 2023-06-28 Zhongshu Zhao , Haixia Dong , Wenjun Ying