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Research Focus:

Numerical methods for partial differential equations and integral equations; mathematical modeling of structural biology; fast algorithms for N-body problems.

Professor Geng's research focuses on modeling problems in structural and systems biology using differential equations and integral equations, and solving these problems numerically with fast algorithms and high performance computing. Particularly, Professor Geng is interested in numerically solving interface problems described by PDEs and integral equations. These problems appear when adjacent layers with different physical, chemical and biological properties are present. As far as the numerical algorithms are concerned, Professor Geng is interested in 1) matched interface and boundary (MIB) methods (high order, finite difference mesh-based algorithms used in solving elliptic PDEs with discontinuities and singularities); and 2) boundary integral methods combined with treecode (a fast algorithm for evaluating interactions of N-body problems) to achieve high accuracy and efficiency. Recently Professor Geng has been working on the extension of these numerical algorithms to electrodynamics and fluid mechanics for the structural biology study at the molecular level. Professor Geng collaborates with mathematicians, computer scientists, and biologists at the Michigan State University, University of Michigan, University of Alabama, Pacific Northwest National Laboratory, and other institutions. His work has appeared in journals such as Journal of Computational Physics, Journal of Computational Chemistry, Computer Physics Communications, and Journal of Chemical Physics.