2005-2006
UF MATHEMATICS COLLOQUIUM

Abstract. After a brief introduction to pseudospectral methods of solving initial value problems in PDE's, I will discuss two most efficient and accurate algorithms I recently developed for wave propagation in passive media. They are based on the Lanczos-Arnoldi process and the Faber polynomial approximation of analytic functions. Applications have included several real life problems in photonics, extraordinary light transmission, and modeling electromagnetic properties of nanostructured materials, which are now of significant interest in applied science and industry.

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