Computing highly oscillatory physical optics integral on the polygonal domain by an efficient numerical steepest descent path method

Yu Mao Wu, Li Jun Jiang, Weng Cho Chew

Research output: Contribution to journalArticlepeer-review

Abstract

In this work, the computation of physical optics (PO) type integral with the integrand of quadratic phase and amplitude is studied. First, we apply the numerical steepest descent path (NSDP) method to calculate the highly oscillatory PO integral on the triangular patch. Then, we rigorously extend the proposed NSDP method to analyze the PO integral on polygonal domains. Furthermore, the contributions of critical points on polygonal domains, including the stationary phase point, resonance and vertex points, are comprehensively studied in terms of the NSDP method. Compared to the traditional high frequency asymptotic (HFA) method, when the wave frequency is not very high but in the high frequency regime, the NSDP method has improved the PO integral accuracy by one to two digits. Meanwhile, the computational cost by using the proposed NSDP method is independent of the wave frequency.

Original languageEnglish (US)
Pages (from-to)408-425
Number of pages18
JournalJournal of Computational Physics
Volume236
Issue number1
DOIs
StatePublished - Mar 1 2013

Keywords

  • Asymptotic approximation
  • Critical points
  • Highly oscillatory integral
  • Numerical steepest descent path
  • Physical optics
  • Polygonal domain

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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