國立東華大學應用數學系

專    題    演    講

主講人：Andreas Klöckner

講  題：Quadrature by Expansion: A New Method for the Evaluation of Layer Potentials

時  間：103 年 05月 19 日 (星期一)  18:00-19:30

地  點：理工一館 A211 教室

摘   要

Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior domains. The practical application of these methods, however, requires the accurate evaluation of boundary integrals with singular, weakly singular or nearly singular kernels. I will be presenting a new systematic, high-order approach that works for any singularity (including hypersingular kernels), based only on the assumption that the field induced by the integral operator is locally smooth when restricted to either the interior or the exterior. Discontinuities in the field across the boundary are permitted. The scheme, denoted QBX (quadrature by expansion), is easy to implement and compatible with fast hierarchical algorithms such as the fast multipole method. I will also present accuracy tests for a variety of integral operators in two dimensions on smooth and corner domains. with L. Greengard, A. Barnett, M. O'Neil)

講者簡介：

Andreas Klöckner是伊利諾大學 Urbana 分校電腦科學系，科學計算研究群的助理教授，他的研究包括 wave 模擬的 high-order 數值方法以及高效能大規模的平行處理的科學計算，為了支持他的研究 Dr. Klöckner 發展了許多科學計算用的 Python 軟體組件，包括PyOpenCL、PyCUDA、PuDB Python debugger。Andreas Klöckner 在布朗大學應用數學跟隨 Jan Hesthaven 取得博士學位，主要研究的是大尺度的有限元素模擬，之後到紐約大學擔任講師與加入 Leslie Greengard's 研究群，主要研究積分方程以及高速的演算法。

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