Work

Approximations of the Helmholtz equation with variable wave number in one dimension

Year: 2024

Type: article

Abstract: This work is devoted to the numerical solution of the Helmholtz equation with variable wave number and including a point source in appropriately truncated infinite domains. Motivated by a two‐dimensional model, we formulate a simplified one‐dimensional model. We study its well posedness via wave number explicit stability estimates and prove convergence of the finite element approximations. As a proof of concept, we present the outcome of some numerical experiments for various wave number configurations. Our experiments indicate that the introduction of the artificial boundary near the source and the associated boundary condition lead to an efficient model that accurately captures the wave propagation features.

Source: Studies in Applied Mathematics

DOI: 10.1111/sapm.12756

Authors: Dimitrios A. Mitsoudis, Michael Plexousakis, George N. Makrakis, Charalambos Makridakis

Institutions: University of West Attica, FORTH Institute of Applied and Computational Mathematics, University of Crete, University of Sussex

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,330

OpenAlex ID: W4401785532

FWCI:

Cites: 35

Cited by:

Related to: 10