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RESEARCH INTERESTS
My research interests center around the development of both deterministic
and stochastic mathematical models for simulating complicated biological
and chemical transport processes in porous media, and the use of these models
in water resources management and environmental engineering.
I have presented a series of new concepts and methods for solving both
forward and inverse problems in groundwater modeling, such as the multiple
cell balance method (MCB), the management equivalent identifiability,
the adjoint state method for stochastic partial differential equations,
a stepwise regression method for solving the generalized inverse problem,
and more recently, the finite cell method (FCM), the theory of model structure
reduction, and the algorithms for finding sufficient and robust designs.
My current research comprises (1) Developing an effective and accurate
numerical method, the finite cell method, for simulating complicated biological
and chemical reaction- transport processes in porous media; (2) Presenting
a new methodology for determining the complexity of model structure of
distributed parameter systems; (3) Designing cost-effective field experiments
and observation networks for model calibration and environmental monitoring.
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