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We analyze the convergence of piecewise collocation methods for computing periodic solutions of general retarded functional differential equations under the abstract framework recently developed in [S. Maset, Numer. Math. (2016)…

Numerical Analysis · Mathematics 2020-12-02 Alessia Andò , Dimitri Breda

Consider the problem of scattering of electromagnetic waves by a doubly periodic structure. The medium above the structure is assumed to be inhomogeneous characterized completely by an index of refraction. Below the structure is a perfect…

Analysis of PDEs · Mathematics 2013-05-07 Jiaqing Yang , Bo Zhang

This manuscript presents an efficient boundary integral equation technique for solving two-dimensional Helmholtz problems defined in the half-plane bounded by an infinite, periodic curve with Neumann boundary conditions and an aperiodic…

Numerical Analysis · Mathematics 2025-11-07 Riley Fisher , Fruzsina Agocs , Adrianna Gillman

Two boundary value problems for the Helmholtz equation in a semi-infinite strip are considered. The main feature of these problems is that, in addition to the function and its normal derivative on the boundary, the functionals of the…

Analysis of PDEs · Mathematics 2016-04-26 Y. A. Antipov

We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…

Analysis of PDEs · Mathematics 2019-12-13 Jean-François Babadjian , Vito Crismale

In this paper we consider high-frequency acoustic transmission problems with jumping coefficients modelled by Helmholtz equations. The solution then is highly oscillatory and, in addition, may be localized in a very small vicinity of…

Numerical Analysis · Mathematics 2025-03-03 Silvia Falletta , Stefan Sauter

Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…

Numerical Analysis · Mathematics 2023-01-25 Fredrik Fryklund , Sara Pålsson , Anna-Karin Tornberg

Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…

Numerical Analysis · Mathematics 2024-02-21 Elwin van 't Wout

Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…

Mathematical Physics · Physics 2012-10-18 M. P. Ramirez T. , C. M. A. Robles G. , R. A. Hernandez-Becerril

Consider the electromagnetic scattering of a time-harmonic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper is concerned with the numerical solutions of the transverse…

Numerical Analysis · Mathematics 2021-04-07 Yanli Chen , Peijun Li , Xiaokai Yuan

The purpose of this work is to introduce and analyze a numerical scheme to efficiently solve boundary value problems involving the spectral fractional Laplacian. The approach is based on a reformulation of the problem posed on a…

Numerical Analysis · Mathematics 2018-08-17 Dominik Meidner , Johannes Pfefferer , Klemens Schürholz , Boris Vexler

This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…

Numerical Analysis · Mathematics 2023-01-25 Heping Dong , Peijun Li

In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…

Analysis of PDEs · Mathematics 2018-02-06 Mokhtar Kirane , Batirkhan K. Turmetov , Berikbol T. Torebek

In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…

Numerical Analysis · Mathematics 2022-09-14 Heping Dong , Jun Lai , Peijun Li

Over the last ten years, results from [Melenk-Sauter, 2010], [Melenk-Sauter, 2011], [Esterhazy-Melenk, 2012], and [Melenk-Parsania-Sauter, 2013] decomposing high-frequency Helmholtz solutions into "low"- and "high"-frequency components have…

Analysis of PDEs · Mathematics 2022-08-02 Jeffrey Galkowski , David Lafontaine , Euan A. Spence , Jared Wunsch

The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…

Numerical Analysis · Mathematics 2025-10-02 Lefu Cai , Zhixin Liu , Minghui Song , Xianchao Wang

We consider the Helmholtz equation defined in unbounded domains, external to 2D bounded ones, endowed with a Dirichlet condition on the boundary and the Sommerfeld radiation condition at infinity. To solve it, we reduce the infinite region,…

Numerical Analysis · Mathematics 2021-07-13 Luca Desiderio , Silvia Falletta , Matteo Ferrari , Letizia Scuderi

We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…

Numerical Analysis · Mathematics 2025-09-26 Tristan Goodwill , Shidong Jiang , Manas Rachh , Kosuke Sugita

We analyze electromagnetic scattering of TM polarized waves from a diffraction grating consisting of a periodic, anisotropic, and possibly negative-index dielectric material. Such scattering problems are important for the modelization of,…

Analysis of PDEs · Mathematics 2015-06-03 Armin Lechleiter , Dinh-Liem Nguyen

We use inverted finite elements method for approximating solutions of second order elliptic equations with non-constant coefficients varying to infinity in the exterior of a 2D bounded obstacle, when a Neumann boundary condition is…

Numerical Analysis · Mathematics 2025-01-24 R Belbaki , S K Bhowmik , T Z Boulmezaoud , N Kerdid , S Mziou