Boundary Element Method for 3D Problems of Electromagnetism
Abstract - 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.