High Order and Efficient Numerical Methods for Simulating Electromagnetic Phenomena

New materials with special properties are necessary in the search for new clean energy sources and advanced medical devices. Electromagnetic phenomena play a key role in the design of new materials such as meta-materials and conducting materials. Meta-materials, assembled with blocks of meta-atoms of naturally available components, have provided a wide range of new possibilities to design man-made materials with special properties. Novel devices using meta-materials have been proposed including perfect lens and sub-diffraction-limited imaging for medical applications, light harvest in clear energy solar cells. In addition, understanding the conducting flow of a charged system is essential for studying confined nuclear thermal reactions for the exploration of new clean energy sources.

The computational simulation of electromagnetic phenomena is challenging, owing to the demand of highly accurate and efficient numerical methods that not only represent the correct physics in the magnetic induction equation but also resolve the multiple scattering and local field enhancements from random objects in meta-materials. To meet these requirements, the PIs will accomplish the following two tasks in this project: (1) to develop a highly efficient volume integral equation method for Maxwell equations for very accurate computation of multiple scatterings of large number of regular or random objects employed in the construction of meta-materials; (2) to devise a high order constrained transport finite element method for the magnetic induction equations in the magneto-hydrodynamics problem so the global divergence free condition on the magnetic field is preserved. The research findings will be disseminated through journal publications and software tool development.