Modeling and simulation of electro-quasistatic fields

We consider time-dependent electromagnetic fields with negligible propagation effect. These fields are called quasistatic. While the case with negligible displacement current (mainly inductive effects; magneto-quasistatics) is usually treated in classical theory, the case of fields free of eddy currents (mainly capacitive; electro-quasistatics) is still not too common. Yet, the electro-quasistatic model is applicable in many different constellations, especially for microelectronic devices, too. In this paper, we derive the electro-quasistatic (EQS) equations and deal with their discretization using the Finite Integration Technique. We treat the time-harmonic and the transient equations as well as anisotropic materials. For some application from high-voltage engineering we study Krylov-subspace methods with algebraic multigrid preconditioning. As special application, neuronal microelectrode arrays are chosen affording the coupling of the transient EQS equations with the Hodgkin-Huxley equations in order to simulate the so-called action potential of the nerves.