A Seamless Reduced Basis Element Method for 2D Maxwell's Problem: An Introduction [chapter]

Yanlai Chen, Jan S. Hesthaven, Yvon Maday
2010 Lecture Notes in Computational Science and Engineering  
We present a reduced basis element method (RBEM) for the time-harmonic Maxwell's equation. The RBEM is a Reduced Basis Method (RBM) with parameters describing the geometry of the computational domain, coupled with a domain decomposition method. The basic idea is to first decompose the computational domain into a series of subdomains, each of which is deformed from some reference domain, and then to associate with each reference domain precomputed solutions to the same governing partial
more » ... ng partial differential equation, but with different choices of deformations. Finally one seeks the approximation on a new shape as a linear combination of the corresponding precomputed solutions on each subdomain. Unlike the work on RBEM for thermal fin and fluid flow problems, we do not need a mortar type method to "glue" the various local functions. This "gluing" is done "automatically" thanks to the use of a discontinuous Galerkin method. We present the rationale for the method together with numerical results showing exponential convergence for the simulation of a metallic pipe with both ends open. Some theoretical techniques for the a posteriori error estimate for RBEM are also discussed.
doi:10.1007/978-3-642-15337-2_11 fatcat:oyayfhisenh6lphkqhydlizefy