The use of projection methods for numerical solution of electromagnetic wave diffraction problems

The elaboration of direct Computational methods for efficient and fast modelling of problems of diffraction from locally inhomogeneous bodies is a topical problem in the development of modern numerical methods. Methods based on projection procedures are considered in this paper in the case Of linear operator equations. Projection methods applied to calculate the electromagnetic field distribution involve discrete models, which can be obtained when the radiation conditions at infinity are algorithmically taken into account. Note that these conditions are not local with any formulation. The radiation conditions are linear limitations coupling field values at aU points of the space, or these conditions are formulated via the Maxwell equations as linear relationships for the electromagnetic field components on any closed surface in a homogeneous space. The second peculiarity of electromagnetic diffraction problems is the fundamental energetic nonclosedness of a system. Energy comes from the exterior ofthe system, and most of it goes to infinity. Diffraction problems involve operator equations that are not sign-determined in any . functional space. Therefore, it becomes necessary to develop computational methods for solving linear nonself-conjugate boundary value problems. At the same time, diffraction problems are similar to elementary problems for well-known processes in the field theory. This allows one to hope that universal and efficient algorithms of solving diffraction problems can he developed.