A quasilinear complexity algorithm for the numerical simulation of scattering from a two-dimensional radially symmetric potential

•A fast algorithm for the 2D variable coefficient Helmholtz equation in the radially symmetric case•Allows for the solution of problems which are hundreds of thousands of wavelengths in size on desktop computers•Lays the groundwork for algorithms for the more general case of nonradially symmetric co...

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Bibliographic Details
Published in:Journal of computational physics Vol. 410; p. 109401
Main Author: Bremer, James
Format: Journal Article
Language:English
Published: Cambridge Elsevier Inc 01.06.2020
Elsevier Science Ltd
Subjects:
Algorithms
Computational physics
Computer simulation
Fast algorithms
Helmholtz equation
Helmholtz equations
Mathematical analysis
Numerical solution of partial differential equations
Scattering
Scattering theory
Solvers
Wavelengths
Numerical solution of partial differential equations
Helmholtz equation
Fast algorithms
Scattering theory
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:•A fast algorithm for the 2D variable coefficient Helmholtz equation in the radially symmetric case•Allows for the solution of problems which are hundreds of thousands of wavelengths in size on desktop computers•Lays the groundwork for algorithms for the more general case of nonradially symmetric coefficients Standard solvers for the variable coefficient Helmholtz equation in two spatial dimensions have running times which grow at least quadratically with the wavenumber k. Here, we describe a solver which applies only when the scattering potential is radially symmetric but whose running time is O(klog⁡(k)) in typical cases. We also present the results of numerical experiments demonstrating the properties of our solver, the code for which is publicly available.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2020.109401