Related papers: Boundary Element Solution of Electromagnetic Field…
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic…
A coupled BEM/FEM formulation for the transient interaction between an acoustic field and a piezoelectric scatterer is proposed. The scattered part of the acoustic wave is represented in terms of retarded layer potentials while the elastic…
We present a boundary element method to compute numerical approximations to the non-linear Molodensky problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. Our solution procedure…
We present a new finite element method, called $\phi$-FEM, to solve numerically elliptic partial differential equations with natural (Neumann or Robin) boundary conditions using simple computational grids, not fitted to the boundary of the…
This paper introduces a time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor. The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown…
In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
In this work, a recently developed novel solution of the famous "Sommerfeld Radiation Problem" is revisited. The solution is based on an analysis performed entirely in the spectral domain, through which a compact asymptotic formula…
The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…
The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric…
In this paper we develop a class of efficient Galerkin boundary element methods for the solution of two-dimensional exterior single-scattering problems. Our approach is based upon construction of Galerkin approximation spaces confined to…
We show how the central equality of scattering theory, the definition of the $\mathbb{T}$ operator, can be used to generate hierarchies of mean-field constraints that act as natural complements to the standard electromagnetic design problem…
We consider an inner problem for whispering gallery high-frequency asymptotic mode's scattering by a boundary inflection. The related boundary-value problem for a Schr\"{o}dinger equation on a half-line with a potential linear in both space…
Acoustic emission or scattering problems naturally involve uncertainties about the sound sources or boundary conditions. This article initiates the study of time domain boundary elements for such stochastic boundary problems for the…
Metasurfaces, consisting of large arrays of interacting subwavelength scatterers, pose significant challenges for general-purpose computational methods due to their large electric dimensions and multiscale nature. This paper introduces an…
The EMI (Extracellular-Membrane-Intracellular) model describes electrical activity in excitable tissue, where the extracellular and intracellular spaces and cellular membrane are explicitly represented. The model couples a system of partial…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…
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…
The construction of Ekman boundary layer solutions near the non-flat boundaries presents a complex challenge, with limited research on this issue. In Masmoudi's pioneering work [Comm. Pure Appl. Math. 53 (2000), 432--483], the Ekman…
We propose a new concept for determining the interior magnetic field vector components in neutron electric dipole moment experiments. If a closed three-dimensional boundary surface surrounding the fiducial volume of an experiment can be…