Convergence acceleration of heterogeneous domain decomposition method for EMT-TS electrical network DAE system

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 convergence acceleration technique. 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 ElectroMagnetic Transient model) with and without overlapping partitions. Finally, some results for a weakly nonlinear differential algebraic equations system are also provided.

Héléna Shourick, Damien Tromeur-Dervout, Laurent Chédot

Published in Journal of Computational and Applied Mathematics