  Waveform relaxation (WR) methods are based on partitioning large circuits
into sub-circuits which then are solved separately for multiple time steps in
so-called time windows, and an iteration is used to converge to the global
circuit solution in each time window. Classical WR converges quite slowly,
especially when long time windows are used. To overcome this issue, optimized
WR (OWR) was introduced which is based on optimized transmission conditions
that transfer information between the sub-circuits more efficiently than
classical WR. We study here for the first time the influence of overlapping
sub-circuits in both WR and OWR applied to RC circuits. We give a circuit
interpretation of the new transmission conditions in OWR and derive closed-form
asymptotic expressions for the circuit elements representing the optimization
parameter in OWR. Our analysis shows that the parameter is quite different in
the overlapping case, compared to the nonoverlapping one. We then show
numerically that our optimized choice performs well, also for cases not covered
by our analysis. This paper provides a general methodology to derive optimized
parameters and can be extended to other circuits or system of differential
equations or space-time PDEs.
