Processing of complexly shaped multiply connected domains in finite element mesh generation

Large number of finite element models in modern materials science and engineering is defined on complexly shaped domains, quite often multiply connected. Generation of quality finite element meshes on such domains, especially in cases when the mesh must be 100% quadrilateral, is highly problematic. This paper describes mathematical fundamentals and practical implementation of a powerful method and algorithm allowing transformation of multiply connected domains of arbitrary geometrical complexity into a set of simple domains; the latter can then be processed by broadly available finite element mesh generators. The developed method was applied to a number of complex geometries, including those arising in analysis of parasitic inductances and capacitances in printed circuit boards. The quality of practical results produced by the method and its programming implementation provide evidence that the algorithm can be applied to other finite element models with various physical backgrounds.