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Research:

Numerical partial differential equations and integral equations, computational linear algebra, scientific computing (scalable solvers and applications), multigrid methods, uncertainty quantification, and coarse-graining techniques.

Professor Lee’s research focuses on the mathematical modeling, numerical algorithmic development, and scientific computing of large-scale industrial and laboratory applications. His current research interests include efficient methods for the Boltzmann transport equation (neutron/photon transport), Maxwell equations (fusion), equations of elasticity (structural designs), general coupled systems of elliptic partial differential equations (scalable algorithms), and large systems of algebraic-differential equations (electric power grid networks and synchronous models). Central to his research is the development of schemes that give optimal computational efficiency on serial and large-scale parallel computer platforms. Thus, an essential component of his research is computational linear algebra, particularly scalable multigrid and multilevel methods. His current collaborations include mathematicians, physicists, and electrical engineers at the Lawrence Livermore, Pacific Northwest, and ERCOT. His research has appeared in SIAM J. Scientific Computing, SIAM J. Numerical Analysis, Numerical Linear Algebra with Applications, Mathematics of Computation, and Electronic Transactions of Numerical Analysis.