@article{f21706b0bad840eabcc1e5fe803f65f1, title = "CERTIFIED REDUCED BASIS METHOD FOR THE ELECTRIC FIELD INTEGRAL EQUATION", abstract = "[B. Fares et al., J. Comput. Phys., 230 (2011), pp. 5532-5555], a reduced basis method (RBM) for the electric field integral equation (EFIE) using 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. A central difficulty of the certified method is that the intrinsic solution space of the EFIE is Hdiv-1/2(Γ), inducing a relatively complicated norm. 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 an alternative norm and in this work use the H(div)-norm, which is computable and demonstrated to not degrade 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 then the certified RBM confirm the analysis.", keywords = "basis methods, integral equations, electromagnetics", author = "HESTHAVEN, {J. S.} and B. STAMM and S. ZHANG", year = "2012", doi = "10.1137/110848268", language = "English", volume = "34", pages = "A1777--A1799", journal = "SIAM Journal of Scientific Computing", issn = "1064-8275", publisher = "Society for Industrial and Applied Mathematics", number = "3", }