# Accurate, fast and stable solver for electromagnetic scattering of absorbing layer materials

Poster presentation at the 2016 Defence and Security Doctoral Symposium.

The boundary element method is an efficient and flexible tool for the modelling of scattering of electromagnetic waves by conducting and penetrable objects. It finds applications in the solution of forward and inverse problems in e.g. radar footprint determination, stealth technology, and imaging for diagnostics and security.

To model scattering by objects that are for almost perfectly conducting, the classic equations are augmented with a so called impedance boundary condition (IBC). The IBC specifies a relationship between the electric field and the magnetic field on the surface of the scatterer, or equivalently between the magnetic and electric currents. IBC applications are numerous: especially they are well suited to simulate metals coated by a dielectric/absorbing layer which is the base of stealth technologies.

In this contribution, an IBC enabled electric field integral equation will be introduced that can provide accurate results in linear time complexity at arbitrarily low frequency. The starting point of this work is the classic IBC formulation. Unfortunately, this suffers from low frequency and dense grid breakdowns. This means that the accuracy of the solution deteriorates and/or the computation time increases, when the frequency is low and/or when the number of unknown of the problem is high, because the iterative solvers used to solve the linear system require more iterations.

The new IBC-EFIE introduced in this work does not suffer from these problems and can deliver highly accurate solutions at arbitrary frequency in near linear computational complexity. The formulation is based on quasi Helmholtz decomposition techniques and multiplicative preconditioners and yields a system whose condition number is independent of both the frequency and the discretization density.