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Applied Mathematics Colloquium
Friday, March 6, 11:30 am
Cullimore Lecture Hall II
New
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Accurate solution of highly
oscillatory wave propagation and scattering problems
Oscar Bruno
Applied & Computational Mathematics
California Institute of Technology
Pasadena, CA
Abstract
The numerical solution of highly oscillatory wave-propagation and scattering
problems presents a variety of significant challenges:
these problems require high discretization densities and often give rise to poorly
conditioned numerics; realistic engineering
configurations, further, usually
require consideration of geometries of great complexity and large extent. In
this talk we will consider a
number of methodologies that were
introduced recently to address these difficulties. We will thus discuss
algorithms that can solve, with
high-order accuracy, problems of
scattering for complex three-dimensional geometries---including, possibly,
singular elements
such as wires, corners, edges and
open screens. In particular, we will describe solutions achieved for two
realistic three-dimensional
problems of very high
frequency---surface scattering and atmospheric GPS propagation---which previous
three-dimensional solvers could not
address adequately. We will also describe a new class of
high-order surface representation methods which, starting from point clouds or
CAD data, can produce
high-order-accurate surface parametrizations of complex
engineering surfaces, as required by high-order solvers. In
all cases these algorithms exhibit
high-order convergence, they run on low memories and reduced operation counts,
and they can produce
solutions with a high degree of accuracy.