In this paper we prove that simply discarding conductors beyond a certain spacing during BEM capacitance extraction will result in a lower bound on the self-capacitance calculations and an upper bound on the mutual capacitance calculations that lie within that spacing. We prove that a potential-shift and truncate scheme can yield bounds opposite to those for the truncate only case; namely, an upper bound on the self capacitance and a lower bound on the mutual capacitance that lies within the chosen spacing. The ease with which the upper and lower bounds are calculated is shown, and their utility for selection of an optimal window size is described. A metal shell is also presented here that results in bounds similar to those of shift--truncate. We further propose a new potential--shift function that yields increased approximation accuracy compared to shift--truncate in many cases. 1 Introduction Boundary element methods (BEM) have been used extensively for parasitic capacitance extract..
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