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 language | English (US) |
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Pages (from-to) | 408-425 |
Number of pages | 18 |
Journal | Journal of Computational Physics |
Volume | 236 |
Issue number | 1 |
DOIs | |
State | Published - Mar 1 2013 |
Externally published | Yes |
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)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics