Certified Reduced Basis Method for the Electric Field Integral Equation

In [5], a reduced basis method (RBM) for the electric field integral equation (EFIE) based on the boundary element method (BEM) is developed, based on a simplified a posteriori error estimator for the Greedy-based snapshot selection. In this paper, we extend this work and propose a certified RBM for the EFIE based on a mathematically rigorous a posteriori estimator. The main difficulty of the certified method is that the intrinsic solution space of the EFIE is H − 1 2 div (Γ), with a norm that is not computable in practice. Since the measured error consists of the difference between the reduced basis solution and the boundary element solution, which is a member of the discrete boundary element space, we clarify that the intrinsic norm can be replaced by alternative norms, in this work the H(div)-norm, that are computable without degrading the quality of the error estimator. A successive constraint method (SCM) for complex matrices is discussed in detail and numerical tests for the SCM and certified RBM are performed to confirm the analysis.