# Acceleration of an Iterative Method for the Evaluation of High-Frequency Multiple Scattering Effects

@article{Boubendir2017AccelerationOA, title={Acceleration of an Iterative Method for the Evaluation of High-Frequency Multiple Scattering Effects}, author={Yassine Boubendir and Fatih Ecevit and Fernando Reitich}, journal={SIAM J. Sci. Comput.}, year={2017}, volume={39} }

High frequency integral equation methodologies display the capability of reproducing single-scattering returns in frequency-independent computational times and employ a Neumann series formulation to handle multiple-scattering effects. This requires the solution of an enormously large number of single-scattering problems to attain a reasonable numerical accuracy in geometrically challenging configurations. Here we propose a novel and effective Krylov subspace method suitable for the use of high…

## 7 Citations

Coupling modes in high-frequency multiple scattering problems: the case of two circles

- Mathematics, Computer ScienceArXiv
- 2017

A Taylor approximation is computed of the limiting phase of the wave pattern of two circular scatterers, independently of the incident wave and with a computational complexity independent of the wavenumber.

Galerkin Boundary Element Methods for High-Frequency Multiple-Scattering Problems

- Computer Science, MathematicsJ. Sci. Comput.
- 2020

High-frequency multiple-scattering problems in the exterior of two-dimensional smooth scatterers consisting of finitely many compact, disjoint, and strictly convex obstacles are considered and Galerkin boundary element methods are proposed to deal with this problem.

On the eigenmodes of periodic orbits for multiple scattering problems in 2D

- PhysicsInternational Journal of Mechanical Sciences
- 2019

Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency…

A Galerkin BEM for high-frequency scattering problems based on frequency dependent changes of variables

- Mathematics
- 2016

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…

A high-frequency boundary element method for scattering by a class of multiple obstacles

- Mathematics, Computer Science
- 2020

It is shown that the number of degrees of freedom required in the HNA space to maintain a given accuracy needs to grow only logarithmically with respect to the frequency, as opposed to the (at least) linear growth required by standard polynomial-based schemes.

Acceleration of Born Series by Change of Variables

- MathematicsIEEE Transactions on Antennas and Propagation
- 2021

In this work, we propose a method to enhance the convergence of the Born series. The Born series is widely used in scattering theory, but its convergence is only guaranteed under certain restrictive…

A sharp relative-error bound for the Helmholtz h-FEM at high frequency

- Computer Science, MathematicsNumerische Mathematik
- 2022

A key ingredient in the proofs is a result describing the oscillatory behaviour of the solution of the plane-wave scattering problem, which is proved using semiclassical defect measures and is sufficient for the relative error of the FEM solution in 2 or 3 dimensions to be controllably small.

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