Computational Electromagnetics

The Electromagnetics Group has built a long tradition and world-wide reputation in the area of numerical solutions to electromagnetic field problems. Our research interests include full-wave solving methods, such as the method of moments (MoM), the fast multipole method (FMM), the finite element method (FEM), and the finite-difference time-domain (FDTD) method. Furthermore, there is expertise in stochastic modelling and uncertainty quantification, polynomial chaos, etc. On the one hand, the numerical methods developed by the EM Group are commercialized through links with the industry. On the other hand, practical problems are solved on demand of various Flemish and international companies. Our full-wave algorithms were applied to model practical problems concerning antenna design, radio wave propagation, electromagnetic aware design for the solution of signal integrity and power integrity problems (SI/PI) in electronic circuits and electromagnetic compatible (EMC) design.

The method of moments is one of the most popular full-wave solvers used in research and industrial applications. Computationally, it is less demanding than FDTD and FEM. However, the corresponding dense matrix equations that have to be solved become ill-conditioned in a lot of practically relevant situations. The Electromagnetics Group, being one of the pioneers in the field of MoM, puts a lot of effort to solve this problem. For this reason, an in-house 3D MoM-solver was developed. Our research focuses on the creation of a preconditioner that solves the current ill-conditioning. This research also extends to hybrid MoM-FEM algorithms, for which purpose the in-house solver Hybrid was made.

In order to speed up MoM-computations, the fast multipole method is used, in order to simulate ever larger and more complex electromagnetic field problems. This research builds on a long tradition of the application of integral equations in the EM Group to compute electromagnetic fields. Active research activities deal with the development of fast multipole and fast Fourier transform methods as well as parallellisation of these methods in GRID computing environments. Applications range from waveguide problems, scattering problems,material design, passive optical components to electromagnetic compatibility problems. Research on fast multipole methods and time-domain integral equation techniques is done in close collaboration with Prof. Eric Michielssen from the University of Michigan in Ann Arbor.

Open FMM is a free collection of our electromagnetic software for scattering at very large objects. It currently consists of a fast two-dimensional TM solver Nero2d. In the near future, a full wave solver aimed at simulating photonic crystals will be added. Work on a full wave three-dimensional solver is currently in progress. We aim for solvers that are capable to handle extremely large problems. The Nero2d solver, makes use of a parallel variant of the Multilevel Fast Multipole Algorithm (MLFMA).

The finite-difference time-domain (FDTD) method is one of the prevalent numerical techniques to model electromagnetic wave propagation directly in the time domain. Therefore, it benefits from broadband information after a single run as well as the ability to treat complex media with non-linear behaviour. The FDTD method typically uses a large number of unknowns due to its volume discretisation, which is fortunately balanced by its simple arithmetic and massive parallellisability. Despite its intuitive nature, a lot of research is done to improve the performance and accuracy of FDTD solvers by developing subgridding techniques, hybrid implicit-explicit methods, model order reduction techniques, collocated discretisation, ...

The Electromagnetics Group also has a wide interest in uncertainty quantification, sensitivity analysis and stochastic modelling of S-parameters and other electrical properties of devices. A lot of research has been done on the application of polynomial chaos expansion with the Stochastic Galerkin Method and the Stochastic Collocation Method for the parametric quantification of uncertainty. There is also a growing interest in borrowing elements from machine learning and statistics to model stochastic variability.

Projects:

• New Modelling Tools for High-Speed Connectors
• BESTCOM: BElgian network on STochastic modelling, analysis, design and optimization of COMmunication systems

Antennas and Propagation: Wearable antenna systems and body-centric communication

Electromagnetic Compatibility and Signal/Power Integrity