The objective of the proposed research is to study high order numerical methods for shock calculations and for computational electromagnetics. High order methods can resolve complicated physical problems with a relatively coarse mesh, hence reducing computational cost for such problems. However, high order methods for shock calculations and for computational electromagnetics involve many theoretical and practical issues which must be investigated. The proposed work involves the development, analysis, and applications of high order finite difference, finite element and spectral methods in the applications areas of computational fluid dynamics and computational electromagnetics. Two emphasized aspects of the proposed effort are complex geometries and efficient parallel implementations. In particular, the proposal contains the following components: high order methods for shock wave calculations, including finite difference ENO and WENO schemes, finite element discontinuous Galerkin methods, spectral methods, and high order methods in computational electromagnetics, including spectral methods, spectral multidomain methods, and absorbing layers. It is expected that the proposed effort will improve the state of art in high order methods for discontinuous problems and long time integrations, especially in complex geometry.
