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This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularized BEM approach that requires the use of electric measurements only. The regularization…

Medical Physics · Physics 2017-03-08 Rajendra Mitharwal , Francesco P. Andriulli

We consider a class of potential problems on a periodic half-space for the modelling of electrified oil films, which are used in the development of novel switchable liquid optical devices (diffraction gratings). A boundary integral…

Numerical Analysis · Mathematics 2015-02-03 David J. Chappell

Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary…

Numerical Analysis · Mathematics 2020-10-29 Stefan Kurz , Dirk Pauly , Dirk Praetorius , Sergey Repin , Daniel Sebastian

A symmetric boundary integral formulation for the transient scattering of acoustic waves off homogeneous and isotropic elastic obstacles is analyzed. Both the acoustic scattered field and the elastodynamic excited field are represented…

Numerical Analysis · Mathematics 2025-08-19 Tonatiuh Sánchez-Vizuet

The phase-integral method (PIM) is an asymptotic method of the geometrical optics or semi-classical type for solving approximately, but in many cases very accurately, a wide class of differential equations in physics. Unlike the related…

Mathematical Physics · Physics 2010-01-05 S. Yngve , B. Thidé

We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this…

Numerical Analysis · Mathematics 2021-08-04 Xiaodong Wei , Benjamin Marussig , Pablo Antolin , Annalisa Buffa

Nonlocal models and their associated theories have been extensively investigated in recent years. Among these, nonlocal versions of the classical Laplace operator have attracted the most attention, while higher-order nonlocal operators have…

Analysis of PDEs · Mathematics 2025-05-13 Weiye Gan , Tangjun Wang , Qiang Du , Zuoqiang Shi

We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical…

Numerical Analysis · Mathematics 2018-04-04 Eduardo Corona , Shravan Veerapaneni

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational…

Numerical Analysis · Mathematics 2023-07-19 Nabil M. Atallah , Claudio Canuto , Guglielmo Scovazzi

The availability of a reliable bound on an integral involving the square of the modulus of a form factor on the unitarity cut allows one to constrain the form factor at points inside the analyticity domain and its shape parameters, and also…

High Energy Physics - Phenomenology · Physics 2012-07-25 B. Ananthanarayan , Irinel Caprini

The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence…

Numerical Analysis · Mathematics 2021-03-23 Fleurianne Bertrand , Daniele Boffi , Gonzalo G. de Diego

We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…

Numerical Analysis · Mathematics 2024-04-29 Alexandre L. Madureira , Marcus Sarkis

This paper presents an axisymmetric Galerkin boundary element method (BEM) for modeling eddy-current interactions between excitation coils and conductive objects. The formulation derives boundary integral equations from the Stratton-Chu…

Numerical Analysis · Mathematics 2026-01-28 Yao Luo

A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…

Numerical Analysis · Mathematics 2024-11-20 Shidong Jiang , Hai Zhu

This paper introduces the scaled boundary cubature (SBC) scheme for accurate and efficient integration of functions over polygons and two-dimensional regions bounded by parametric curves. Over two-dimensional domains, the SBC method reduces…

Numerical Analysis · Mathematics 2021-11-09 Eric B. Chin , N. Sukumar

In this paper, the Immersed Boundary Method (IBM) proposed by Pinelli is implemented for finite volume approximations of incompressible Navier-Stokes equations solutions in the open source toolbox OpenFOAM version 2.2. Solid obstacles are…

Fluid Dynamics · Physics 2016-09-15 E. Constant , C. Li , J. Favier , M. Meldi , P. Meliga , E. Serre

In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…

Numerical Analysis · Mathematics 2025-10-02 Mohamed Mostafa

The correct treatment of boundary conditions is a key step in the development of the SPH method. The SPH community has to face several challenges in this regard - in particular, a primordial aspect for any boundary formulation is to ensure…

Fluid Dynamics · Physics 2025-01-15 J Calderon-Sanchez , JL Cercos-Pita , D Duque

Two-dimensional Stokes flow through a periodic channel is considered. The channel walls need only be Lipschitz continuous, in other words they are allowed to have corners. Boundary integral methods are an attractive tool for numerically…

Numerical Analysis · Mathematics 2020-05-11 Lukas Bystricky , Sara Pålsson , Anna-Karin Tornberg

Since their advent nearly a decade ago, physics-informed neural networks (PINNs) have been studied extensively as a novel technique for solving forward and inverse problems in physics and engineering. The neural network discretization of…

Numerical Analysis · Mathematics 2025-12-18 Conor Rowan , Kai Hampleman , Kurt Maute , Alireza Doostan