Combining domain decomposition solution techniques with higher order hierarchical basis functions

Abstract

This paper considers the efficient numerical analysis of large and complex electromagnetic structures by using domain decomposition techniques such as the Numerical Green's Function (NGF) [1] and the Domain Green's Function Method (DGFM) [2] in connection with hierarchical higher order basis functions [3, 4]. Both the NGF and DGFM methods are applicable to problems that can be subdivided into distinct computational regions. Previously low order Rao-Wilton-Glisson (RWG) type basis functions [5] have been used to discretise each of the subdomains. In the current approach this has been extended to use hierarchical higher order basis functions that allow for larger and more complex geometries to be considered. The work presented in this article will discuss the formulation of the methods and the results of applying the solution techniques to various examples consisting of large and complex electromagnetic problems.