Modelling external energy sources in massive conductor circuits using the Aψ formulation with a `re-modified´ vector potential

The authors present a scheme based on the Aψ representation that can be used to deal with current or voltage forced transient or quasi-steady state situations. The new Aψ scheme with the remodified vector potential has been shown to give equivalent results to the AVψ scheme for a simple problem in which the current direction does not change. The authors show, however, that for a more complicated problem which involves a sharp turn for the current path, the AVψ scheme can lead to inconsistent results. This is believed to be due to the constraints of Δ×A=0 and A×n&capped; being imposed on the vector potential (without these constraints the matrix tends to be very ill conditioned). The new Aψ scheme, however, does converge as the mesh is refined