Explicit time integration techniques for electro- and magneto-quasistatic field simulations

Transient electro-quasistatic (EQS) and magneto-quasistatic (MQS) field problems are discretized in space and integrated in time using explicit schemes, e.g. the explicit Euler or the Runge-Kutta-Chebychev method. These methods avoid iterative linearization strategies, as e.g. the Newton-Raphson method, required within implicit time integration schemes. The inversion of the mass matrix in EQS and MQS problems and the evaluation of a pseudo-inverse in the Schur complement reformulation of MQS problems, require to repeatedly solve algebraic systems of equations with constant matrix and varying right-hand sides. The resulting formulations benefit from using multiple right-hand side techniques for computing improved start vectors for the iterative solver.