New trends in frequency-domain volume integral equations

Volume integral equations (VIEs) are powerful numerical techniques to analyze and simulate electromagnetic properties of structures involving inhomogeneous and anisotropic materials. A number of different VIE formulations exist, and generally speaking, finding the most optimal formulation for a given problem is not straightforward. This requires careful investigation of mapping and spectral properties of operators and selection of finite -element spaces used to convert continuous equations to discrete matrix equations. In this chapter, we review the most commonly used VIE formulations and discuss recent advances in theoretical considerations and numerical discretization techniques. We investigate accuracy, conditioning, and stability of formulations and introduce some recent applications of VIE -based methods.