Parallel Finite Element Assembly with High Order Whitney Elements on Curved Meshes

There is a growing consensus that state of the art finite element technology requires, and will continue to require too extensive computational resources to provide the necessary resolution for complex high-frequency electromagnetic compatibility (EMC) computations, even at the rate of computational power increase.

The complexity of such EMC problems has indeed been rapidly increasing for the last few years, with ever tighter constraints on accuracy due to more stringent regulations, more elaborate and interconnected systems leading to very complex geometrical configurations, and wider frequency spectra to simulate due to the increasing frequency of power controllers.

The requirement for high resolution naturally leads us to consider methods with a higher order of grid convergence than the classical (formal) 2nd order provided by most industrial grade codes. This indicates that higher-order discretization methods will replace at some point the finite element solvers of today, at least for part of their applications.

In this talk we will present our research efforts towards developing a new generation of electromagnetic finite element solvers making efficient use of new massively parallel and hybrid computing architectures to assemble high-order Whitney elements on high-order (curved) meshes.