报告人：Hongkai Zhao教授

        University of California, Irvine, USA

报告题目：Learning adaptive basis for ray-based finite element method for the high-frequency Helmholtz equation

报告时间：2016年12月15日16:30

报告地点：海韵数理楼661

联系人：邱建贤教授

报告摘要：

We present a ray-based finite element method (ray-FEM) by learning basis adaptive to the underlying high-frequency Helmholtz equation in smooth media. Based on the geometric optics ansatz of the wave field, we learn local dominant ray directions by probing the medium using low-frequency waves with the same source. Once local ray directions are extracted, they are incorporated into the finite element basis to solve the high-frequency Helmholtz equation. This process can be continued to further improve approximations for both local ray directions and the high frequency wave field iteratively. The method requires a fixed number of grid points per wavelength to represent the wave field and achieves an asymptotic convergence without the pollution effect.

A fast solver is developed for the resulting linear system with an empirical linear complexity up to a poly-logarithmic factor..

报告人简介：

Hongkai Zhao是美国加州大学欧文分校数学系主任，教授。2007年获得冯康科学计算奖。他主要从事计算与应用数学方面的研究。

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