Accelerating the convergence of Dynamic Iteration method with Restricted Additive Schwarz splitting for the solution of RLC circuits

TL;DR

This paper enhances the convergence speed of the dynamic iteration method for solving RLC circuit equations by integrating Restricted Additive Schwarz splitting with Aitken's acceleration, improving efficiency and robustness.

Contribution

It introduces a novel combination of Restricted Additive Schwarz splitting and Aitken's technique to accelerate convergence in dynamic iteration methods for RLC circuit simulations.

Findings

The method achieves faster convergence in linear RLC circuits.

It remains effective even with divergent splittings.

The approach extends to weakly nonlinear differential algebraic systems.

Abstract

The dynamic iteration method with a restricted additive Schwarz splitting is investigated to co-simulate linear differential algebraic equations system coming from RLC electrical circuit with linear components. We show the pure linear convergence or divergence of the method with respect to the linear operator belonging to the restricted additive Schwarz interface. It allows us to accelerate it toward the true solution with the Aitken's technique for accelerating convergence. This provides a dynamic iteration method less sensitive to the splitting. Numerical examples with convergent and divergent splitting show the efficiency of the proposed approach. We also test it on a linear RLC circuit combining different types of circuit modeling (Transient Stability model and Electro-Magnetic Transient model) with overlapping partitions. Finally, some results for a weakly nonlinear differential algebraic equations system are also provided.