.png){kind=icon}
.png){kind=icon}
Return
Numerical analysis of the high-frequency Helmholtz equation using semiclassical analysis
.png){kind=icon}
OA
AI
J
E
DOI：10.1017/S0962492925100275.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We consider the numerical solution of high-frequency scattering problems modelled by the Helmholtz equation with a bounded obstacle. Although the analysis of this problem dates back at least 50 years; over the past decade or so; tools and techniques from semiclassical analysis have provided a new perspective and been used to settle several long-standing open problems in this area. Semiclassical analysis works in phase space (i.e. position and frequency) and describes rigorously the extent to which solutions of high-frequency PDEs are dictated by the properties of the corresponding geometric optics rays.The goals of the article are (i) to give a introduction to semiclassical analysis aimed at non-experts and (ii) to showcase some of the numerical analysis results about finite element methods; boundary element methods and domain decomposition methods obtained using semiclassical techniques.
Keywords:
35J05
65N30
65N38
65N55
Journal
IF:
11.3
Papers:
89
Citations:
3.4K
Organization
Cited Papers