Dynamic simulation of electromechanical systems: from Maxwell's theory to common-rail diesel injection

This paper describes the state-of-the-art of dynamic simulation of electrom echanical systems. Electromechanical systems can be split into electromagne tic and mechanical subsystems, which are described by Maxwell's equations a nd by Newton's law, respectively. Since such systems contain moving parts, the concepts of Lorentz and Galilean relativity are briefly addressed. The laws of physics are formulated in terms of (partial) differential equations . Numerical methods ultimately aim at linear systems of equations, which ca n be solved efficiently on digital computers. The various discretization me thods for performing this task are discussed. Special emphasis is placed on domain decomposition as a framework for the coupling of different numerica l methods such as the finite element method and the boundary element method . The paper concludes with descriptions of some applications of industrial relevance: a high performance injection valve and an electromechanical rela y.