Robust and Efficient Numerical Methods for Electromagnetic Wave Propagation in Complex Media

University Of Nevada Las Vegas, Las Vegas NV

Investigators

Abstract

This project will develop novel mathematical modeling and robust computational methods for simulating wave propagation in complex media such as metamaterials and graphene. This interdisciplinary research has direct applications in nanotechnology and materials through the advancement of discovery and understanding of new phenomena in nanooptics and stealth technology brought by metamaterials and graphene. Graphene can be used to generate picosecond laser pulses because of its wide absorption range, fast decay, and high stability properties. Graphene can be used in sensors to concurrently sense mass, gas, tension, diseases, and explosives; graphene can be used in low-cost display screens of mobile devices, lithium-ion batteries with fast recharge capacity, hydrogen storage for fuel cell-powered cars, and low-cost fuel cells and water desalination, etc. All of these applications benefit from accurate and efficient numerical algorithms for solving the associated mathematical models by reducing the cost of physical experiments. This project will provide support for one PhD student per year. The focus of this project is to develop and analyze robust and efficient finite element methods for solving electromagnetic wave propagation problems in complex media. Theoretical analysis and practical algorithms will be developed with the following objectives: (1) Further explore some perfectly matched layer (PML) models recently developed for metamaterials, develop and analyze time-domain finite element methods using both edge elements and discontinuous Galerkin methods for solving them; (2) Explore graphene models and efficient FEM algorithms to simulate wave propagation in graphene; (3) Develop robust and efficient a posteriori error estimators for time-dependent Maxwell’s equations in metamaterial and graphene, explore possible superconvergence points for high-order triangular and tetrahedral edge elements; (4) Develop, and analyze efficient numerical methods for Maxwell's equations with random inputs with applications for random metamaterials. The developed algorithms and codes in the project will lead to a better understanding of metamaterials and graphene, and their physical effects, so that researchers can design and use them in applications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.