Fast Spectral Methods for PDEs with Integral Fractional Laplacian in Multiple Dimensions
Date/Time:28 Aug 2019 16:00Venue: S17 #05-11 SR5Speaker: Li-Lian Wang, Nanyang Technological UniversityFast Spectral Methods for PDEs with Integral Fractional Laplacian in Multiple DimensionsPDEs with fractional Laplacian have emerged as a powerful tool in modelling anomalous diffusion and nonlocal interactions, but their numerical solutions can be very difficult especially in multiple dimensions. Many nonlocal models are more physically motivated and naturally set in unbounded domains. In this talk, we shall present a superfast spectral-Galerkin method with two critical components (i) the Dunford-Taylor formulation of fractional Laplacian operator, and (ii) the use of Fourier-like bi-orthogonal mapped Chebyshev functions as basis functions. We shall also report some of our recent attempts for integral fractional Laplacian in bounded domains, which are deemed even more notoriously difficult for effective numerical discretisation. Along this line, we work with the formulation associated with the Fourier transformations, and derive a number of useful analytical formulas which are essential for the algorithm development.Add to calendar:
