High Order Methods for Shock Calculations and Computational Electromagnetics

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The objective of the proposed research is to study high order numericalmethods for shock calculations and for computational electromagnetics.High order methods can resolve complicated physical problems with arelatively coarse mesh, hence reducing computational cost for suchproblems. However, high order methods for shock calculations and forcomputational electromagnetics involve many theoretical and practicalissues which must be investigated. The proposed work involves thedevelopment, analysis, and applications of high order finite difference,finite element and spectral methods in the applications areas ofcomputational fluid dynamics and computational electromagnetics.Two emphasized aspects of the proposed effort are complex geometriesand 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 computationalelectromagnetics, including spectral methods, spectral multidomainmethods, 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.