Fast multipole method for Helmholtz equation in layered media

Abstract: The fast multipole method (FMM) has been a revolutionary development in modern computational algorithms for many-body problems, which reduces the complexity of long-range interactions among N particles from O(N^2) to O(N) or O(N log N). In this talk we generalize the FMM for Helmholtz equation to handle the layered media. Our approach starts from the 2-D case. The multipole expansion (ME) and the multipole-to-local translation (M2L) are introduced in the frequency domain together with theoretical analysis showing their exponential convergence using the Cagniard--de Hoop transform. The analysis further suggests the FMM framework for layered media should use polarized sources for the far-field separation. Finally we apply the FMM to the 3-D layered problem and discuss the numerical result. This is a joint work with Bo Wang and Wei Cai.

general mathematics

Audience: researchers in the topic

Comments: Meeting ID: 970 1588 0121 Passcode: 835247

---

Global Seminar on Mathematical Modeling and Applications

Series comments: Description: Occasional seminar on mathematical modeling and related topics

In light of the worldwide cancellations of meetings workshops and conferences many of us are forced to switch to online mode of communication. Thus following the example of many other initiatives we decided to organize a Global Seminar on Mathematical Modeling and Applications.

Zoom links will appear on the seminar website 15 minutes before talks begin so that we may convene a little earlier, get acquainted and/or catch-up.

Additionally here you can subscribe to the mailing list.

---