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UID:a7701ff3d36916c620eb258f1d251b80
CATEGORIES:Applied and Computational Math Seminar
CREATED:20250130T185213
SUMMARY:Local Algorithms for Nonlocal Problems in Wave Theory
LOCATION:Hill 260
DESCRIPTION:<p>Although many mathematical models in wave theory lead to hyperbolic init
 ial-boundary value problems which are inherently local due to the finite do
 main-of-dependence of the solution at any point on past values, there are a
 lso examples where nonlocal operators, in particular space-time integral op
 erators, arise. A primary example is the radiation boundary condition neede
 d to truncate an unbounded domain to a finite one to enable numerical solut
 ions, as well as closely-related operators for unidirectional propagation. 
 In this work we show how to leverage results from rational function approxi
 mation theory to construct spectrally-convergent local algorithms for evalu
 ating such operators. For an important class of problems - systems equivale
 nt to the scalar wave equation, such as acoustics or Maxwell’s equations in
  homogeneous, isotropic media, we will explain the construction, analysis, 
 and implementation of our complete radiation boundary conditions, which are
  in a certain sense optimal. We will also discuss other applications of the
 se approximation methods, as well as the fundamental barriers to extending 
 the successful methods to other systems.</p>
CONTACT:Tom Hagstrom (Southern Methodist University)
DTSTAMP:20260827T141929
DTSTART;TZID=America/New_York:20250206T140000
DTEND;TZID=America/New_York:20250206T150000
SEQUENCE:0
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