Use of the boundary element method for pulsed power electromagnetic field designs

The boundary element method (BEM) is a numerical technique for solving boundary integral equations. In this technique, electromagnetic phenomena are mathematically described by Maxwell´s equations in integral form. Enforcing the boundary conditions along the material interfaces allows one to obtain a set of boundary integral equations with the unknowns as the equivalent sources or field variables along the interface. One may then separate the boundaries into boundary elements, represent the unknowns on elements, and obtain a system of linear equations. All field variables at any point in space may be obtained by performing integrations associated with the equivalent sources or fields on the boundaries. The BEM is a valuable technique in the electromagnetic field modelling carried out by many engineers during the design phase of their work. The BEM has found wide application in fields as diverse as medical, power, defence, research and education engineering design, from the modelling of components (motors, insulators, bushings, lasers etc... .) to complete systems, with many pulsed power laboratories and high voltage industries utilising it in various electromagnetic research and development programmes. As electromagnetic field simulation enters the mainstream of computer-aided engineering, the boundary element method is emerging as an efficient alternative to FEM. This paper describes the boundary element technique in detail and includes a comparison with electromagnetic analysis using the finite element method.