Colloquium: Oscar Bruno

Speaker: Oscar Bruno, California Institute of Technology

Title: Fourier Continuation, resolution of the Gibbs phenomenon, and application to numerical analysis and computation.

Abstract: Fourier expansions possess excellent properties of approximation of smooth and periodic functions--which make them ideal elements for simulation of periodic systems. This talk presents a new approach which extends use of rapidly convergent Fourier series to general problems in computational science. We will demonstrate these ideas with results of recent applications to numerical solution of linear and non-linear Partial Differential Equations in complex three dimensional geometries, including general solution of PDEs in the time domain such as the fluid-dynamics and elastic wave equations (where virtual dispersionlessness is demonstrated) and, using integral equation methods and related fast highly-accurate algorithms, solution of Laplace eigenvalue problems and problems of acoustics and electromagnetism at high frequencies.

Faculty host: Junshan Lin