Related papers: Local Multiple Traces Formulation for Electromagne…
We consider the three-dimensional time-harmonic electromagnetic (EM) wave scattering transmission problem involving heterogeneous scatterers. The fields are approximated using the local multiple traces formulation (MTF), originally…
This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\"uller equation to composite structures through the global multi-trace…
We stabilize the full Arthur-Selberg trace formula for the metaplectic covering of symplectic groups over a number field. This provides a decomposition of the invariant trace formula for metaplectic groups, which encodes information about…
The free metaplectic transformation (FMT) has gained much popularity in recent times because of its various application in signal processing, paraxial optical systems, digital algorithms, optical encryption and so on. However, the FMT is…
This paper aims to address two issues of integral equations for the scattering of time-harmonic electromagnetic waves by a perfect electric conductor with Lipschitz continuous boundary: ill-conditioned {boundary element Galerkin matrices}…
The subject of fractional calculus has witnessed rapid development over past few decades. In particular the area of fractional differential equations has received considerable attention. Several theoretical results have been obtained and…
We develop a stability theory for contractive local IFSs on compact metric spaces. Unlike the classical global setting, local systems may exhibit a richer symbolic and geometric structure, including code spaces that are not of finite type…
The Electric Field Integral Equation (EFIE) is a well-established tool to solve electromagnetic scattering problems. However, the development of efficient and easy to implement preconditioners remains an active research area. In recent…
We consider an initial-boundary value problem for the $n$-dimensional wave equation with the variable sound speed, $n\geq 1$. We construct three-level implicit in time and compact in space (three-point in each space direction) 4th order…
In this paper we prove a stable determination of the coefficients of the time-harmonic Maxwell equations from local boundary data. The argument --due to Isakov-- requires some restrictions on the domain.
We deal with an inverse elastic scattering problem for the shape determination of a rigid scatterer in the time-harmonic regime. We prove a local stability estimate of log log type for the identification of a scatterer by a single far-field…
Local time-stepping methods permit to overcome the severe stability constraint on explicit methods caused by local mesh refinement without sacrificing explicitness. In \cite{DiazGrote09}, a leapfrog based explicit local time-stepping…
Multitrace formulations (MTFs) are based on a decomposition of the problem domain into subdomains, and thus domain decomposition solvers are of interest. The fully rigorous mathematical MTF can however be daunting for the non-specialist. We…
This paper introduces a new boundary element formulation for transient electromagnetic scattering by homogeneous dielectric objects based on the time-domain PMCHWT equation. To address dense-mesh breakdown, a multiplicative Calderon…
In this paper, we consider a problem for finding the locations of electromagnetic inhomogeneities completely embedded in homogeneous two layered medium. For this purpose, we present a filter function operated at several frequencies and…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
The PMCHWT integral equation enables the modelling of scattering of time-harmonic fields by penetrable, piecewise homogeneous, systems. They have been generalised to include the modelling of composite systems that may contain junctions,…
This is the first of a series of papers devoted to the stabilization of the twisted trace formula. It is just an introduction. We present the local theory of twisted endoscopy, following the fundamental works of Kottwitz-Shelstad, Labesse…
This paper considers the phenomenon of distinct regional frequencies recently observed in some power systems. First, a reduced-order mathematical model describing this behaviour is developed. Then, techniques to solve the model are…
The domain integral equation method with its FFT-based matrix-vector products is a viable alternative to local methods in free-space scattering problems. However, it often suffers from the extremely slow convergence of iterative methods,…