Finite Elements in Electromagnetics - Subtleties in Discretisation

Paul Ledger

Dec. 18, 2007, 3:30 p.m. HF 136

Electromagnetic problems are governed by Maxwell’s equations. Applications are wide ranging and include radar, medical imaging, land mine detection and electromagnetic compatibility problems to name a few. In electromagnetic problems, one is typically faced with trying to determine the electromagnetic fields inside or surrounding geometrically complex objects made up of a variety of different materials. This in turn leads to singularities at material interfaces and sharp corners.

A firm mathematical foundation is key to the accurate modelling of electromagnetic problems by the finite element method. Subtle differences in the finite element discretisation already emerge when considering electrostatic and magnetostatic problems and care must be exercised to use the correct type of approximation. This talk will discuss the special types of finite elements that are required to accurately solve problems in electromagnetics. Particular attention will be given to the hp version of the finite element method which combines both h (mesh) refinement and p (polynomial) enrichment. Recent work relating to efficient preconditioning and fast solvers will be presented as well as a series of possible applications.