Professor Yingjie Liu
School of Mathematics
Georgia Institute of Technology
686 Cherry Street, Skiles Building
Atlanta, GA 30332-0160
E-mail: yingjie at math dot gatech dot edu
Advanced Numerical Methods for Partial Differential Equations
Simplified Physics behind a Powerful Forehand Loop in Table Tennis
Beautiful Okefenokee Swamp
My research interests have been on the numerical analysis, scientific computing, algorithm, partial differential equations and tangential suspension system. I have been working on:
Tangential Wheel Suspension System
Moving mesh finite element methods.
Conservative front tracking.
Back and forth error compensation and correction (BFECC) method with applications in level set interface computation, fluid simulations,
conveniently computing electromagnetic waves with complicated geometry
A smoke simulation by NVIDIA using BFECC
Central schemes and central discontinuous Galerkin methods on overlapping cells for conservation laws and associated differential equations.
Non-oscillatory hierarchical reconstruction (HR) for discontinuous Galerkin methods, central discontinuous Galerkin methods, central and finite volume schemes.
A common mistake in the implementation of HR.
Neural Networks with Local Converging Inputs (NNLCI,
) for solving differential equations in varying domains with orders of magnitude reduction in complexity and training costs. Predict a solution containing discontinuities, e.g., shocks, contacts and their interactions sharply and efficiently (see
predict electromagnetic waves scattered off complicated perfect electric conductors (with training and prediction in different domains)
predict supersonic flows in irregular domains with unstrucured grids (with training and prediction in different domains)
predict solutions of a PNP ion channel model (nonlinear elliptic systems in multi domains.)