An analysis of the steepest descent method to efficiently compute the three-dimensional acoustic single-layer operator in the high-frequency regime

Gasperini, D.; Beise, H.-P.; Schroeder, U.; Antoine, X.; Geuzaine, Christophe

doi:10.1093/imanum/drac038

Article (Scientific journals)

An analysis of the steepest descent method to efficiently compute the three-dimensional acoustic single-layer operator in the high-frequency regime

Gasperini, D.; Beise, H.-P.; Schroeder, U. et al.

2023 • In IMA Journal of Numerical Analysis, 43 (3), p. 1831 - 1854

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/324770

DOI
10.1093/imanum/drac038

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Keywords :

acoustic single-layer integral operator; high-frequency scattering; highly oscillatory integrals; steepest descent method; Acoustic single layers; Acoustic single-layer integral operator; Cauchy integral theorems; Frequency regimes; High frequency HF; High-frequency scattering; Highly oscillatory integrals; Integral operators; Steepest-descent method; Wave numbers; Mathematics (all); Computational Mathematics; Applied Mathematics

Abstract :

[en] Using the Cauchy integral theorem, we develop the application of the steepest descent method to efficiently compute the three-dimensional acoustic single-layer integral operator for large wave numbers. Explicit formulas for the splitting points are derived in the one-dimensional case to build suitable complex integration paths. The construction of admissible steepest descent paths is next investigated and some of their properties are stated. Based on these theoretical results, we derive the quadrature scheme of the oscillatory integrals first in dimension one and then extend the methodology to three-dimensional planar triangles. Numerical simulations are finally reported to illustrate the accuracy and efficiency of the proposed approach.

Disciplines :

Mathematics

Author, co-author :

Gasperini, D.; IEE S.A., Bissen, Luxembourg ; Université de Lorraine, CNRS, Inria, IECL, Nancy, France ; University of Liège, Liège, Belgium

Beise, H.-P.; FB Informatik, Hochschule Trier, Trier, Germany

Schroeder, U.; IEE S.A., Bissen, Luxembourg

Antoine, X.; Université de Lorraine, CNRS, Inria, IECL, Nancy, France

Geuzaine, Christophe ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Applied and Computational Electromagnetics (ACE) ; Institut Montefiore, Liège, Belgium

Language :

English

Title :

An analysis of the steepest descent method to efficiently compute the three-dimensional acoustic single-layer operator in the high-frequency regime

Publication date :

May 2023

Journal title :

IMA Journal of Numerical Analysis

ISSN :

0272-4979

eISSN :

1464-3642

Publisher :

Oxford University Press

Volume :

Issue :

Pages :

1831 - 1854

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://academic.oup.com/imajna/article-pdf/43/3/1831/50504186/drac038.pdf

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since 29 November 2024

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