Boundary Element Method for 3D Problems of Electromagnetism

Numerical algorithms of the boundary problems described by Laplace, Poisson, Helmholtz and Maxwell equations based on the integral representations are described. Combinations of single-layer, double-layer and volume potentials are used to represent the solution. Analytical technique of singularity extraction is used to obtain precision and stable numerical solutions for a potential and its high-order derivatives. The numerous examples of test problems and applications to the precision problems of electron optics, accelerator physics and plasma-beam interaction are demonstrated. The original algorithms can be used for the problems of analysis, optimization and synthesis of physical electronic devices. Decomposition algorithms to solve complex three-dimensional problems are presented. Keywords - Boundary Element Method; integral representation; single-layer potential; double-layer potential; numerical approximation; singularity.