Development of High-Order Conservative Numerical Methods for Electromagnetics in Metamaterials and Transport Flows in Environment

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The objective of the proposed program is to study, develop and analyze the conservative numerical methods for electromagnetics in metamaterials and transport flow problems in environment.******Modelling has been recently recognized as a crucial technique in electromagnetics. For their supernormal electromagnetic features, metamaterials play a very important role in many applications. Due to the long-time electromagnetic responses and the complicated scale structures, computations for electromagnetics in metamaterials are confronted with great challenges. Computing multi-component transport problems is of significant importance in the atmospheric environment and groundwater contamination modelling. The mathematical models describing the complex processes are the nonlinear partial differential equations, which are characterized by transport dominance, moving steep front or interface, turbulence, nonlinearity, multi-scales, enormous size of field scale and long time prediction. Solving these problems has been a driving force in developing efficient numerical methods and computational tools for large scale transport flows in environment and for electromagnetics in metamaterials, in which there are great interests in the development of high-order conservative numerical methods in three dimensions.******The program includes (1) Develop and analyze high-order energy conservative methods for electromagnetics in three dimensional metamaterials; (2) Develop and analyze high-order mass-preserving characteristic methods for aerosol transport problems in three dimensions; (3) Develop and analyze the mass conservative splitting domain decomposition method for multi-component aerosol transports in environment; (4) Development of controlling multicomponent pollution flows in porous media.