Wave-ray algorithms for Helmholtz equations with variable wave numbers:\n a one-dimensional implementation of two-dimensional ideas

2013/12/10 by Ira Livshits, Livshits, Ira
Engineering · Physics and Astronomy · #65N55 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1312.2855

openalex publication_date 2013/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The subject of this paper is multigrid solvers for Helmholtz operators with\nlarge wave numbers. Algorithms presented here are variations of the wave-ray\nsolver which is modified to allow efficient solutions for operators with\nconstant, continuous, and discontinuous wave numbers. Both geometric and\nalgebraic frameworks are employed, all yielding efficient and scalable solvers\nat very little additional costs, compared to standard multigrid techniques. The\nalgorithms are implemented in one dimension, but with a clear extension to\nhigher dimensions.\n

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