演講通知-Prof. Qin Sheng 2023/9/15(五)Title: A Study of Asymptotic Stability of a Dual-Scale Compact Computational Method for the Solutions of Highly Oscillatory Helmholtz Equations
Speaker: Prof. Qin Sheng (Baylor University, USA)
Lecture time: 9/15 Fri. 7:30 pm
Lecture venue: Room 414, Information Science Building
Abstract:
In this discussion, we will focus at laser beams with radially symmetric fields in transverse directions. Standard polar coordinates can thus be deployed. To eliminate the transformation singularity occurred, we formulate a transverse domain decomposition which enables a multiscale environmental configuration that allows multi-feature wave approximations. We then consider a compact strategy for a highly oscillatory paraxial equation modeling nanobeams focusing through subwavelength holes. Such a highly accurate algorithm, however, shies away from the stability in connection to conventional von Neumann sense. Our investigation continues to a novel new concept called asymptotical stability. Highly oscillatory migration waves for applications will be explored. Physical concerns are once again placed before traditional mathematical arguments. Intensive auxiliary expansions and analysis will be carried out. It will be proven that, while appropriate constraints are reinforced, the asymptotical stability of the novel multiscale compact method remains affective. Computer experiments with realistic validations will be given to illustrate our conclusions. Our dual-scale procedures are remarkably vibrating for various laser e-optics applications that were outlined by Bose and Einstein a century ago.
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