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Speaker: Professor Yuan Liu (Wichita State University)
We introduce a class of adaptive multiresolution discontinuous Galerkin methods for several time dependent PDEs including reaction-diffusion equations, wave equations and Schrodinger equations. The main ingredients of the sparse grid discontinuous Galerkin methods include L2 orthonormal Alpert’s multiwavelets and the interpolatory multiwavelets. By exploring the inherent mesh hierarchy and the nested polynomial approximation spaces, multiresolution analysis is able to accelerate the computation, and adjust the computational grid adaptively. Sparse tensor product is further introduced to decrease the computational cost in multi-dimensional space.