Radiation condition for the 3-dimensional Helmholtz equation on the boundary of a bounded domain

2022/02/11 by Vladimir V. Gorin, Gorin, Vladimir V.
Mathematics · #31C20 #65-02 #65N99 #76M25 #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Plasma Physics (physics.plasm-ph)

paper · pdf · doi:10.48550/arxiv.2202.05489

openalex publication_date 2022/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the formulation of the problem of scattering of monochromatic waves and the numerical simulation of the solution to the Helmholtz equation, there is a computational inconvenience: the calculation is performed on a finite grid of discretization nodes of the finite scattering region, while the radiation conditions for the scattered wave are formulated at the infinitely distant boundary. Overcoming this inconvenience leads to a new type of boundary condition: a nonlocal boundary condition (or condition of the 4th kind).

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