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The Darwin field model addresses an approximation to Maxwell's equationswhere radiation effects are neglected. It allows to describe generalquasistatic electromagnetic field phenomena including inductive, resistive andcapacitive effects. A Darwin formulation based on the Darwin-Amp\`ere equationand the implicitly included Darwin-continuity equation yields a non-symmetricand ill-conditioned algebraic systems of equations received from applying ageometric spatial discretization scheme and the implicit backwarddifferentiation time integration method. A two-step solution scheme ispresented where the underlying block-Gauss-Seidel method is shown to change theinitially chosen gauge condition and the resulting scheme only requires tosolve a weakly coupled electro-quasistatic and a magneto-quasistatic discretefield formulation consecutively in each time step. Results of numerical testproblems validate the chosen approach.

A Darwin Time Domain Scheme for the Simulation of Transient Quasistatic Electromagnetic Fields Including Resistive, Capacitive and Inductive Effects