Waveform relaxation for field/circuit coupled problems with cutsets of inductances and current sources

Abstract

Many electromagnetic problems can be simulated accurately by circuit models formulated for example in terms of the modified nodal analysis [1]. However, increasing frequencies, decreasing device sizes and more complex materials with highly nonlinear behavior, e.g. superconductors, force simulation engineers to account for more and more spatially resolved effects like wave propagation, eddy-currents, ferromagnetic saturation and hysteresis. Some of these effects can be sufficiently represented by order-reduced models that are embedded in the circuit description. However, in the general case, the coupling of electromagnetic field models and circuit equations is necessary and also well established, see for example the survey article [2].