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Name: Xinyu Liu
Office: MATH 709

Click here for my CV (last updated 4/15/17).

Research Interests

My research interests lie broadly in the fields of numerical analysis and scientific computing in general. More specifically, my research goal is to develop efficient spectral and high-order numerical methods for partial differential equations. Some of the research projects I've worked on, and continue to be interested in, are:

Fast structured spectral methods, including fast structured Galerkin methods, fast structured collocation methods and fast structured Jacobi transforms;
Efficient spectral sparse grid methods for high dimensional problems, with application in electronic Schrödinger equations;
Extended spectral methods for the problems with low regularity or corner singularities;
Two-level spectral methods for nonlinear elliptic equations with multiple solutions;
Fast spectral methods for the Boltzmann collision operator;
Rational spectral collocation methods for singularly perturbed problems with thin boundary layers.
Last updated March/29/17