Applied Math Seminar
Fall Quarter 2008
Friday November 7, 3:15p.m.Oscar Bruno
Applied and Computational Mathematics
California Institute of Technology
Accurate solution of highly oscillatory wave propagation and scattering problems
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.
Seminar website: http://math.stanford.edu/~applmath/