Our research in Computational Electromagnetics

Computational electromagnetics (CEM) techniques have become increasingly important with the rapid advancements in technology in areas such as electromagnetic compatibility, antenna analysis, radar signature prediction, cellular phone-human body interaction, design of electrical and medical devices, target recognition and lightning strike simulation.

Electromagnetic phenomena are governed by the Maxwell equations, which can be expressed in either the frequency or the time domain.

Our own work is focused on the numerical approximation of Maxwell’s equations using finite-element technology. The computational solution of problems in electromagnetism presents considerable challenges at both low and high frequencies. 

In low frequency problems there are considerable challenges in resolving the thin skin depth, a problem akin to the boundary layer in fluids. In high frequency electromagnetic problems the numerical simulation of electromagnetic wave propagation problems, involving realistic industrial geometries and wave frequencies, poses a significant computational challenge. In order to address these problems, various sophisticated numerical techniques are currently being investigated.

Research areas

Low Order Methods

Low Order MethodsTime domain electromagnetic problems have been simulated at Swansea using low order nodal finite elements. Research council and industrial funding has been used to achieve improved efficiency by employing a hybrid finite element/finite difference time domain algorithm.

Current research is aimed at achieving further efficiency improvement by means of an unstructured mesh implementation of the finite difference time domain technique. This co-volume approach is very efficient provided that appropriate meshes can be generated for the problem of interest.

hp-Finite Elements

hp-Finite ElementsPractical engineering problems have geometries with sharp corners and edges and involve objects that have material interfaces. Electromagnetic fields can exhibit strong singularities at these locations and our work in hp-finite elements is devoted to accurately capturing the fields for such problems. To achieve this, the hp-version of the finite element method includes both local refinement of the finite element grid combined with non-uniform polynomial degrees and offers the possibility of achieving exponentially fast rates of convergence, as apposed to the slower algebraic rates of convergence, usually experienced by conventional finite element techniques. Royal Society funded collaborative work with groups of mathematicians has involved the development of special types of hp-finite elements that allow us to correctly describe the vectoral nature of the electromagnetic fields on complex geometries and achieve rapid solutions.

Discontinuous Galerkin

Discontinuous GalerkinThe excessive memory and computing time required by traditional low-order methods is evident when dealing with electrically large radar targets or when high fidelity simulations are mandatory, for instance in electromagnetic compatibility applications. In these situations, the use of high-order discontinuous Galerkin (DG) methods is an attractive alternative because it is able to reduce significantly both the memory usage and the computing time, opening the door to the simulation of more challenging problems. Current research is focused on the application of this technique to challenging electromagnetic scattering problems using hybrid meshes and to computational photonics, where high fidelity simulations with microwave and optical frequencies are required.

Coupled Electro-Mechanical-Fluid Problems

Industry is increasingly interested in the use of "new smart materials" that have special properties under combined mechanical-electromagnetic loading. To understand the complex behaviour of these materials we are developing computational tools for modelling the possibly large non-linear deformations and complex electromagnetic fields. To understand the behaviour of conducting fluids we are developed computational tools that involve solving coupled sets of Navier-Stokes and Maxwell's equations using mathematical insights to correctly describe the behaviour of this multi-field, multi-physics problem.

In collaborative work with the College of Science at Swansea University we are applying our computational approaches to the simulation of the behaviour of sediment layers in glacial deposits to better understand the mechanisms contributing to the deprecation of these massive ice masses.

Research areas

NURBS Enhanced Finite Element Method

NURBS Enhanced Finite Element Method NURBS Enhanced Finite Element Method (NEFEM)

The benefits of high-order finite element methods are usually found when using very coarse meshes and very high-order approximations, but in many occasions the geometric complexity requires to increase the mesh resolution to avoid missing important physic phenomena. A new technique called NURBS-Enhanced Finite Element Method (NEFEM) has been developed in collaboration with UPC, Barcelona. This technique allows meshing the domain with no dependency on the geometric complexity, ensuring that the proper physics are captured and reducing the computational cost compared to other high order finite element techniques. Current research is focused on increasing, even more, the efficiency of this technique, aiming for the industrialisation of high-order technology.

Computational Photonics

Computational photonicsThe design and analysis of many optical and photonic devices requires the use of numerical simulation. Current research is aimed at producing an efficient high-order time domain solver that is capable of simulating problems over a wide range of frequencies, including optical and photonic frequencies. The solver is able to accurately represent the geometry of optical and photonic devices and the high-order approach allows a substantial reduction in the dispersion and dissipation errors that are inherent in the traditional low-order solvers that are used in many commercial packages.

Staff

The following staff are involved in Computational Electromagnetics research at Swansea University:

Dr Ruben Sevilla 

 

Computational electromagnetics