High-order Accurate Methods in Computational Electromagnetics

			  Jan S. Hesthaven   
		  Division of Applied Mathematics
		     Brown University, RI, USA
		     
As classic as Maxwell's equations are, their solution continues to challenge 
numerical analysts, computational scientists, and engineers alike. Typical 
roadblocks are very high geometric complexity, scale separation due to 
materials, and sheer size of a typical problem. On the other hand, accurate, 
efficient, and robust computational techniques may impact developments in
key technologies such as high-speed electronics, optical and/or wireless 
communication, and sensoring as well as numerous military applications, e.g., 
stealth coatings.

In this talk we discuss some of the typical obstacles in computational 
electromagnetics and argue that high-order accurate computational methods are 
well suited to address some of these issues. While mentioning several 
alternatives, we focus on the ongoing developments of high-order
discontinuous element/Galerkin methods on fully unstructured grids.

We shall first focus on problems posed in the time-domain, sketching a
convergence theory, and illustrating the efficiency and robustness
of the formulation through examples.

Recent results suggest, however, that similar formulations offer advantages 
for harmonic problems and eigenproblems also, allowing the use of a nodal
basis without suffering from spurious modes.

The efficacy and versatility of the complete three-dimensional scheme is
illustrated by solving electromagnetic benchmark problems as well as 
large scale geometrically complex problems.