2018年南京农业大学理学院数学学术交流系列报告(一)
--- 微分方程保结构算法及应用
时间:2018 年 3 月 7 日(星期三)下午 3:00 –6:00
地点:理学院教四楼B211
名师Qin Sheng 教授(美国Baylor大学)学术报告
A pact Scheme for Subwavelength Applications: Is it Numerically Stable?
Abstract:Rapid advances in nanophotonics constantly demand highly effective, efficient, and yet reliable PDE solvers. This is primarily due to broadband radiation absorptions of the metamaterial models which can be tailored from infrared to visible spectrums which have important applications in not only engineering but also biological pathways. Focusing features of the oscillatory waves through subwavelength gaps have been extremely difficult to calculate and simulate.
For the simplicity, let us consider a radially symmetric field in transverse directions in this conversation. Thus, standard polar coordinates can thus be employed. To eliminate the transformation singularity occurred, we deploy a transverse domain position which enables a multiscaled environmental setting that allows multi-feature wave approximations. We then consider a pact method for a paraxial Helmholtz equation modeling nanobeams focusing through subwavelength holes. pound numerical method is straightforward, simple-to-use. However, we can show that such a highly pact scheme shies away from the stability in the conventional von Neumann sense.
But, can this multiscale algorithm still be vibrating in model
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