In recent years, spectral methods have become increasingly popular among computational scientists and engineers because of their superior accuracy and efficiency, if implemented properly.
In this talk, we shall present some fast spectral-Galerkin algorithms developed in the last few years. Their computational complexities are comparable to those of finite difference and finite element algorithms, yet they provide much more accurate results while using a significantly smaller number of unknowns. We shall also present recent numerical results using these fast spectral-Galerkin algorithms for various scientific and engineering applications.
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