My primary research interests are in computational mathematics and scientific computing, with an emphasis on the development, analysis, and implementation of numerical methods for solving partial differential equations (PDEs) and graph problems arising from different applications in science and engineering. Contemporary scientific computing is different from the traditional theory and laboratory experiment in science and engineering. It obtains understanding of many real-world phenomena through the analysis of mathematical models implemented on computers. Due to the complex nature of the mathematical models, numerical simulations are oftentimes the only possible way for scientific discovery. A main focus of my research is on adaptive, parallel, and multilevel methods for solving discretized systems of coupled PDEs and graph problems, such as multiphase flow in porous media, complex fluid, magnetohydrodynamics, and fluid-structure interaction.
More specifically, some of my research topics are:
•theoretical and algorithmic development of fast solvers based on (geometric and algebraic) multigrid methods,
•parallelization of efficient solvers on multicore platform such as graphics processing unit (GPUs) and multicore CPUs,
•applications of adaptive, parallel and multilevel solvers in practical problems such as reservoir simulations, magnetohydrodynamics, and fluid-structure iteration.