Cutting multiply connected domains

The calculation of electromagnetic fields in three dimensions using discrete finite element methods and potential formulations requires that the topological connectivity of sub-domains of the total problem space be known. There may also be a need to define cutting surfaces such that the sub-domains are simply connected or in order that integral relationships can be imposed on the solutions, methods of determining the cutting surfaces for multiply connected sub-domains are developed in this paper, based on the discrete finite element model of the system. The algorithms are completely general and have an operation count of order n, where n is the number of discrete elements in the sub-domain.