My research is interdisciplinary in science and engineering, ranging from numerical methods (finite difference, finite element, finite volume, stability, convergence) for solving partial differential equations including fractional order PDEs to numerical heat transfer, micro/nano heat transfer and thermal deformation, bio-heat transfer, quantum physics, computational fluid dynamics, image processing, and numerical simulations for studying the bio-effect of electromagnetic waves, hydrogen-metal reactions for hydrogen storage, DNA sequencing, and micro-fabrications such as X-ray lithography, laser chemical vapor deposition, and melt crystallization.