Numerical comparison of spectral properties of volume-integral-equation formulations

•Spectral properties of volume-integral-equation formulations are investigated.•The discrete spectrum is shown to depend on the discretization procedure.•The discrete potential formulation produces the theoretically predicted spectrum.•Preconditioning strategies based on the spectral properties are discussed.

We study and compare spectral properties of various volume-integral-equation formulations. The equations are written for the electric flux, current, field, and potentials, and discretized with basis functions spanning the appropriate function spaces. Each formulation leads to eigenvalue distributions of different kind due to the effects of discretization procedure, namely, the choice of basis and testing functions. The discrete spectrum of the potential formulation reproduces the theoretically predicted spectrum almost exactly while the spectra of other formulations deviate from the ideal one. It is shown that the potential formulation has the spectral properties desired from the preconditioning perspective.