Calculation of Inverse Square Root of RWG Gram Matrix Based on Chebyshev Polynomial Expansion

The boundary element method usually relies on surface integral equations (SIEs) for the analysis of electromagnetic scattering problems. However, using traditional discretizations for SIEs, the spectrum of boundary element matrices can not represent that of the corresponding surface integral operators, which introduces issues for methods utilizing the spectral properties. To solve this problem, one can use inverse square roots of Gram matrices for SIEs to disclose the spectrum of the surface integral operators. In this work, we designate an algorithm for the calculation of the inverse square root of the Gram matrix associated with the Rao-Wilton-Glisson discretization, which is based on the Chebyshev polynomial expansion of the inverse square root scalar function. Numerical results are provided to demonstrate the efficiency of the scheme.