An analysis of the steepest descent method to efficiently compute the three-dimensional acoustic single-layer operator in the high-frequency regime
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| Název: | An analysis of the steepest descent method to efficiently compute the three-dimensional acoustic single-layer operator in the high-frequency regime |
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| Autoři: | Gasperini, D., Beise, H.-P., Schroeder, U., Antoine, X., Geuzaine, Christophe |
| Zdroj: | IMA Journal of Numerical Analysis. 43:1831-1854 |
| Informace o vydavateli: | Oxford University Press (OUP), 2022. |
| Rok vydání: | 2022 |
| Témata: | Acoustic single layers, Integral operators, Applied Mathematics, Physique, chimie, mathématiques & sciences de la terre, steepest descent method, high-frequency scattering, 01 natural sciences, High frequency HF, Computational Mathematics, Mathématiques, Physical, chemical, mathematical & earth Sciences, Steepest-descent method, Frequency regimes, High-frequency scattering, Cauchy integral theorems, Wave numbers, Highly oscillatory integrals, Mathematics (all), highly oscillatory integrals, 0101 mathematics, acoustic single-layer integral operator, Mathematics, Acoustic single-layer integral operator |
| Popis: | 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. |
| Druh dokumentu: | Article |
| Jazyk: | English |
| ISSN: | 1464-3642 0272-4979 |
| DOI: | 10.1093/imanum/drac038 |
| Přístupová URL adresa: | https://hdl.handle.net/2268/324770 https://doi.org/10.1093/imanum/drac038 |
| Rights: | OUP Standard Publication Reuse |
| Přístupové číslo: | edsair.doi.dedup.....27d6ec05d78f6660691ec8fae01d6439 |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | 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. |
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| ISSN: | 14643642 02724979 |
| DOI: | 10.1093/imanum/drac038 |