ME Seminar on "Fast Spectral frequency- and time-domain PDE solvers" - Oscar P. Bruno - Caltech


Monday, October 21, 2013 - 4:00pm to 5:00pm


ESB 1001


Oscar P. Bruno, Caltech -

Abstract: We present fast frequency- and time-domain spectrally accurate solvers for Partial Differential Equations that address some of the main difficulties associated with simulation of realistic engineering systems. Based on a novel Fourier-Continuation (FC) method for the resolution of the Gibbs phenomenon and fast high-order methods for evaluation of integral operators, these methodologies give rise to fast and highly accurate frequency- and time-domain solvers for PDEs on general three-dimensional spatial domains. Our fast integral algorithms can solve, with high-order accuracy, problems of electromagnetic and acoustic scattering for complex three-dimensional geometries; our FC-based differential solvers for time-dependent PDEs, in turn, give rise to essentially spectral time evolution, free of pollution or dispersion errors, for general PDEs. A variety of applications to linear and nonlinear PDE problems demonstrate the significant improvements the new algorithms provide over the accuracy and speed resulting from other approaches. 

Biosketch: Lic.  University of Buenos Aires, 1982; Ph.D., New York University (Courant Institute of Mathematical Sciences), 1989. Associate Professor, Caltech, 1995-98; Professor, 1998-. Executive Officer for Applied Mathematics, 1998-2000.

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