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Journal of Scientific Computing

Erschienen in:

01.06.2023

Quadrature by Two Expansions for Evaluating Helmholtz Layer Potentials

verfasst von: Jared Weed, Lingyun Ding, Jingfang Huang, Min Hyung Cho

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2023

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Abstract

In this paper, a Quadrature by Two Expansions (QB2X) numerical integration technique is developed for the single and double layer potentials of the Helmholtz equation in two dimensions. The QB2X method uses both local complex Taylor expansions and plane wave type expansions to achieve a resulting representation which is numerically accurate for all target points inside a leaf box in the fast multipole method (FMM) hierarchical tree structure. The QB2X method explicitly includes nonlinear dependency of the boundary geometry in the plane wave expansions, thereby providing for higher-order representations of both the boundary geometry and density functions in the integrand, with its convergence following standard FMM error analysis. Numerical results are presented to demonstrate the performance of the QB2X method for Helmholtz layer potentials using one expansion center for the entire FMM-leaf box for both flat and curved boundaries with various densities.

Vorheriger Artikel Flux Globalization Based Well-Balanced Central-Upwind Schemes for Hydrodynamic Equations with General Free Energy

Nächster Artikel Numerical Study of a Fast Two-Level Strang Splitting Method for Spatial Fractional Allen–Cahn Equations

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Titel: Quadrature by Two Expansions for Evaluating Helmholtz Layer Potentials
verfasst von: Jared Weed
Lingyun Ding
Jingfang Huang
Min Hyung Cho
Publikationsdatum: 01.06.2023
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2023
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-023-02222-5

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