Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics

摘要: The problem of error estimation in the numerical solution integral equations that arise electromagnetics is addressed. direct method (Green's theorem or field approach) and indirect (layer ansatz source lead to well-known both first kind [electric (EFIE)] second [magnetic (MFIE)]. These are analyzed systematically terms mapping properties operators. It shown how assumption quantities have finite energy leads naturally describing appropriate Sobolev spaces. function spaces demystified through simple examples which also used demonstrate importance knowing space given data lives should be sought. further moments (or Galerkin method) formulated these residual can estimate actual condition number all impedance matrices result from discretizing equations, including bounded when elements computed appropriately. Finally, consequences carrying out computations square integrable functions, a particularly friendly space, explained.