Some remarks on Maxwell solvers for computational electromagnetics

Summary form only given. To model electromagnetic wave interactions on the complicated structures in microwave remote-sensing, devices used in the microwave and optical wave regions, and material sciences, we need to process ultra wideband signals on such structures. So far we have two types of Maxwell solvers. One type incudes techniques, such as the finite element method, the generalized multipoles method, and the boundary element method, for solving boundary value problems about the second order partial differential equation called the Helmholtz equation. The other is a direct Maxwell, for example, the finite difference time domain method in which Maxwell´s equations, denoted by a set of first order coupled partial differential equations, can be solved. The author discusses the development of efficient and stable numerical algorithms for use as Maxwell solvers.