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Radiation boundary conditions for waves: extensions and open problems
时间  Datetime
2019-08-15 09:30 — 10:30 
地点  Venue
630
报告人  Speaker
Thomas Hagstrom
单位  Affiliation
Southern Methodist University
邀请人  Host
Zhenli Xu
报告摘要  Abstract

The radiation of energy to the far eld is a central feature of wave physics. As such ecient, conver-
gent domain truncation algorithms are a necessary component of any wave simulation software. For
the scalar wave equation and equivalent systems such as Maxwell's equations in a uniform dielectric
medium, Complete Radiation Boundary Conditions (CRBC), which are optimized local radiation
boundary condition sequences, provide a satisfactory solution: spectral convergence, rapid parame-
ter selection based on sharp a priori error estimates, and e ective corner/edge closures. Issues that
arise in extending the method to more general problems include the treatment of so-called reverse
modes, waves whose group and phase velocities are misaligned relative to the normal direction at
the radiation boundary, as well as problems with inhomogeneities and nonlinearities. Here we will
explore a number of ideas for constructing reliable and ecient domain truncation algorithms in
these more dicult settings:
 Modi cations of the CRBC recursions to handle reverse modes - this approach is successful
for problems with single wave families;
 Rigorous a priori error analysis and optimization of ad hoc damping/stretching layers;
 Application of kernel compression/reduced order modeling to nonlocal formulations.
Speci c applications to dispersive models of electromagnetic waves, the elastic wave equation, as
well as waves in inhomogeneous media will be given.