Iterative Schemes for Coupled Multiphysical Problems in Electrical Engineering

Abstract Multiphysical simulations become increasingly important for engineering applications due to the high accuracy of domain-specific modeling and numerical simulations; effects that were previously disregraded may become dominant. For this a monolithic approach, i.e., the solution of all subproblems in one system, is often cumbersome or even impossible because incompatible algorithms or software packages are involved. Thus simulation engineers need to “weakly”, i.e., each problem is tackled separately, couple subproblems in an stable and efficient way. For example for time-dependent problems where different time scales are present, waveform relaxation schemes are a promising approach that still allows for an efficient simulation of the problem. However, the independent treatment introduces splitting errors, which should be mitigated by iterative procedures that in turn can cause computational overhead. In this contributions we discuss theoretical and practical issues as the existence and uniqueness of solutions, accuracy, stability, convergence and numerical efficiency of the schemes. Advantages and disadvantages are addressed by examples from electrical engineering.