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03/31/03 Colloquium
DR. MI-SUN MIN
BROWN UNIVERSITY - PROVIDENCE, RI
BROWN UNIVERSITY - PROVIDENCE, RI
Spectral Methods for Discontinuous Problems
Abstract: When the standard Fourier methods are considered for discontinuous problems in periodic domain, the well-known phenomenon of the Gibbs oscillations deteriorate the accuracy of the spectral simulations. In this talk I will consider numerical techniques for resolving the Gibbs oscillations. Fourier-Padé rational approximations, multi-domain spectral methods and Gegenbauer reconstructions will be discussed for 2D incompressible Boussinesq convection flows, Maxwell's equations as an eigenproblem with discontinuous coefficients, and phantom image reconstruction. The successful mitigation or elimination of the oscillations near the singularity by those spectral methods will be demonstrated. Some convergence analysis using the minmax principle for the approximate solutions of the eigenproblem will be also provided.