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In this work a novel approach is presented for the isogeometric Boundary Element analysis of domains that contain inclusions with different elastic properties than the ones used for computing the fundamental solutions. In addition the…

Numerical Analysis · Computer Science 2016-08-24 Gernot Beer , Benjamin Marussig , Jürgen Zechner , Christian Dünser , Thomas-Peter Fries

This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…

Numerical Analysis · Mathematics 2024-09-12 Van Chien Le , Kristof Cools

We study the strongly singular volume integral equation that describes the scattering of time-harmonic electromagnetic waves by a penetrable obstacle. We consider the case of a cylindrical obstacle and fields invariant along the axis of the…

Analysis of PDEs · Mathematics 2015-09-30 Martin Costabel , Eric Darrigrand , Hamdi Sakly

Boundary element methods (BEM) reduce a partial differential equation in a domain to an integral equation on the domain's boundary. They are particularly attractive for solving problems on unbounded domains, but handling the dense matrices…

Numerical Analysis · Mathematics 2020-06-30 Steffen Börm

Consider an isotropic elastic medium $\Omega \subset \mathbb{R}^3$ whose Lam\'e parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave equation, but only…

Analysis of PDEs · Mathematics 2019-03-14 Peter Caday , Maarten V. de Hoop , Vitaly Katsnelson , Gunther Uhlmann

This paper deals with a special class of parametrizations for Isogeometric Analysis (IGA). The so-called scaled boundary parametrizations are easy to construct and particularly attractive if only a boundary description of the computational…

Numerical Analysis · Mathematics 2017-11-22 Clarissa Arioli , Alexander Shamanskiy , Sven Klinkel , Bernd Simeon

We consider the variational formulation of the electric field integral equation on a Lipschitz polyhedral surface $\Gamma$. We study the Galerkin boundary element discretisations based on the lowest-order Raviart-Thomas surface elements on…

Numerical Analysis · Mathematics 2015-04-13 Alex Bespalov , Serge Nicaise

We derive a short wave length approximation of a boundary integral operator for two-dimensional isotropic and homogeneous elastic bodies of arbitrary shape. Trace formulae for elastodynamics can be deduced in this way from first principles…

Chaotic Dynamics · Physics 2015-06-26 Gregor Tanner , Niels Sondergaard

This paper is concerned with the boundary integral equation method for solving the exterior Neumann boundary value problem of dynamic poroelasticity in two dimensions. The main contribution of this work consists of two aspescts: the…

Computational Physics · Physics 2020-08-18 Lu Zhang , Liwei Xu , Tao Yin

An efficient and easy-to-implement method is proposed to regularize integral equations in the 3D boundary element method (BEM). The method takes advantage of an assumed three-noded triangle discretization of the boundary surfaces. The…

Classical Physics · Physics 2009-01-26 Patrick Dangla , Jean-François Semblat , H. Xiao , Nicolas Delépine

The Calder\'on formulas (i.e., the combination of single-layer and hyper-singular boundary integral operators) have been widely utilized in the process of constructing valid boundary integral equation systems which could possess highly…

Analysis of PDEs · Mathematics 2021-08-26 Liwei Xu , Tao Yin

We present a boundary integral method, and an accompanying boundary element discretization, for solving boundary-value problems for the Laplace-Beltrami operator on the surface of the unit sphere $\S$ in $\mathbb{R}^3$. We consider a closed…

Analysis of PDEs · Mathematics 2011-11-30 Simon Gemmrich , Nilima Nigam , Olaf Steinbach

This paper presents novel methodologies for the numerical simulation of scattering of elastic waves by both closed and open surfaces in three-dimensional space. The proposed approach utilizes new integral formulations as well as an…

Computational Physics · Physics 2020-04-22 Oscar P. Bruno , Tao Yin

Isogeometric approach applied to Boundary Element Methods is an emerging research area. In this context, the aim of the present contribution is that of investigating, from a numerical point of view, the Symmetric Galerkin Boundary Element…

Numerical Analysis · Mathematics 2022-04-07 A. Aimi , M. Diligenti , M. L. Sampoli , A. Sestini

Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment.…

Classical Physics · Physics 2016-11-24 Matti Stenroos

In this paper we study Steklov eigenvalues for the Lam\'e operator which arise in the theory of linear elasticity. In this eigenproblem the spectral parameter appears in a Robin boundary condition, linking the traction and the displacement.…

Analysis of PDEs · Mathematics 2021-04-14 Sebastián Domínguez

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

Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations.…

Computational Physics · Physics 2016-08-24 Ross Adelman , Nail A. Gumerov , Ramani Duraiswami

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

We present a boundary integral formulation of the Helmholtz equation with visco-thermal boundary conditions, in two dimensions. Such boundary conditions allow for the accurate simulation of viscous and thermal losses in the vicinity of the…

Numerical Analysis · Mathematics 2026-01-27 Jacob Linden , Travis Askham , Jeremy Hoskins