Faculty members are actively working in the traditional and emerging areas of applied mathematics and scientific computing.
Current research activities in applied mathematics cover electromagnetic phenomena for nonlinear lasers, meta-materials, and fractional materials, uncertainty quantification and stochastics dynamics in biological and electrical power network, machine learning in data sciences and functional material studies, anomalous diffusion and fractional differential equations in biological and optical systems, electrostatic solvation and interactions in protein physics, free-surface fluid dynamics and foam rheology, 3-D vortex reconnection and magneto-hydrodynamics for plasma physics, dynamics systems and wave turbulence, density functional theory for electronic structures, kinetic theory for quantum transport and Bose-Einstein condensation, and transports in nano-manufacturing through interaction between electron and ion beams with solids, etc.
A wide selection of numerical methods and algorithm development, undertaken by faculty members to address problems in above mentioned areas, include deep neural network, polynomial chaos, high order and fast integral equation methods, absorbing boundary conditions, finite element and finite difference and discontinuous Galerkin methods, fast large scale eigensolver, multiphase flow interface modeling, and Monte Carlo methods, etc.