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The aim of this paper is to extend the method of improving cloaking structures in the conductivity to scattering problems. We construct very effective near-cloaking structures for the scattering problem at a fixed frequency. These new…

Analysis of PDEs · Mathematics 2015-05-30 Habib Ammari , Hyeonbae Kang , Hyundae Lee , Mikyoung Lim

We describe an accelerated direct solver for the integral equations which model acoustic scattering from curved surfaces. Surfaces are specified via a collection of smooth parameterizations given on triangles, a setting which generalizes…

Numerical Analysis · Mathematics 2013-09-02 James Bremer , Adrianna Gillman , Per-Gunnar Martinsson

We develop a method for computing the scattering of flexural waves off of a periodic wall or a periodic line of scatterers. These waves model the fluctuations of thin plates with periodic clamped, supported, or free edges. We use the…

Numerical Analysis · Mathematics 2026-03-04 Fruzsina Agocs , Tristan Goodwill , Jeremy G. Hoskins , Peter Nekrasov

We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for time-harmonic scattering problems of Helmholtz type with high wavenumber $\kappa$. On a coarse mesh of width $H$, the proposed method identifies local…

Numerical Analysis · Mathematics 2024-08-05 Philip Freese , Moritz Hauck , Daniel Peterseim

This work is about a new two-level solver for Helmholtz equations discretized by finite elements. The method is inspired by two-grid methods for finite-difference Helmholtz problems as well as by previous work on two-level…

Numerical Analysis · Mathematics 2025-09-23 Christiaan C. Stolk

We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in $\mathbb{R}^d$, $d=2,3$, using near field measurements of the scattered wave on an open set of the boundary above the…

Analysis of PDEs · Mathematics 2024-12-20 Alexander Konschin , Armin Lechleiter

This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…

Numerical Analysis · Mathematics 2020-02-25 Trung Truong , Dinh-Liem Nguyen , Michael Klibanov

In this paper, an efficient solver for the Helmholtz equation using a noval approximation space is developed. The ingradients of the method include the approximation space recently proposed, a discontinuous Galerkin scheme extensively used,…

Numerical Analysis · Mathematics 2025-12-11 Shuhai Zhao

A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld…

Mathematical Physics · Physics 2021-12-21 A. V. Shanin , A. I. Korolkov

This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…

Analysis of PDEs · Mathematics 2018-12-03 Heping Dong , Jun Lai , Peijun Li

We present a new numerical scheme to solve the Helmholtz equation in a wave-guide. We consider a medium that is bounded in the $x_2$-direction, unbounded in the $x_1$-direction and $\varepsilon$-periodic for large $|x_1|$, allowing…

Numerical Analysis · Mathematics 2017-08-23 Tomáš Dohnal , Ben Schweizer

We present a fast iterative solver for scattering problems in 2D, where a penetrable object with compact support is considered. By representing the scattered field as a volume potential in terms of the Green's function, we arrive at the…

Numerical Analysis · Mathematics 2023-03-28 Vaishnavi Gujjula , Sivaram Ambikasaran

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

This paper introduces a class of approximate transparent boundary conditions for the solution of Helmholtz-type resonance and scattering problems on unbounded domains. The computational domain is assumed to be a polygon. A detailed…

Numerical Analysis · Mathematics 2010-04-08 Lothar Nannen , Achim Schädle

We present a fast solver for the 3D high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media. The solver is based on the method of polarized traces, coupled with distributed linear algebra libraries and…

Numerical Analysis · Mathematics 2018-01-29 Leonardo Zepeda-Núñez , Adrien Scheuer , Russell J. Hewett , Laurent Demanet

The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…

Numerical Analysis · Mathematics 2022-03-15 Anne-Sophie Bonnet-Ben Dhia , Simon N. Chandler-Wilde , Sonia Fliss

We establish soliton-like asymptotics for finite energy solutions to the Schr\"odinger equation coupled to a nonrelativistic classical particle. Any solution with initial state close to the solitary manifold, converges to a sum of traveling…

Analysis of PDEs · Mathematics 2009-11-11 Alexander Komech , Elena Kopylova

This paper focuses on the well-posedness (or lack thereof) of three-dimensional time-harmonic wave propagation problems modeled by the Helmholtz equation. It is well-known that if the problem is set in bounded domain with Dirichlet boundary…

Analysis of PDEs · Mathematics 2025-05-16 T. Chaumont-Frelet

This paper gives a note on an application of the enclosure method to an inverse obstacle scattering problem governed by the Helmholtz equation in two dimensions. It is shown that one can uniquely determine the convex hull of an unknown…

Analysis of PDEs · Mathematics 2011-09-21 Masaru Ikehata

We consider time domain acoustic scattering from a penetrable medium with a variable sound speed. This problem can be reduced to solving a time domain volume Lippmann-Schwinger integral equation. Using convolution quadrature in time and…

Numerical Analysis · Mathematics 2014-07-30 Armin Lechleiter , Peter Monk