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Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2022

An analysis of the steepest descent method to efficiently compute the 3D acoustic single-layer operator in the high-frequency regime

Résumé

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 of 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.
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Dates et versions

hal-03209144 , version 1 (27-04-2021)

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David Gasperini, Hans-Peter Beise, Udo Schröeder, Xavier Antoine, Christophe Geuzaine. An analysis of the steepest descent method to efficiently compute the 3D acoustic single-layer operator in the high-frequency regime. IMA Journal of Numerical Analysis, 2022, ⟨10.1093/imanum/drac038⟩. ⟨hal-03209144⟩
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