Anderson acceleration for electromagnetic nonlinear problems

Abstract

Purpose

The purpose of this paper is to implement the Anderson acceleration for different formulations of eletromagnetic nonlinear problems and analyze the method efficiency and strategies to obtain a fast convergence.

Design/methodology/approach

The paper is structured as follows: the general class of fixed point nonlinear problems is shown at first, highlighting the requirements for convergence. The acceleration method is then shown with the associated pseudo-code. Finally, the algorithm is tested on different formulations (finite element, finite element/boundary element) and material properties (nonlinear iron, hysteresis models for laminates). The results in terms of convergence and iterations required are compared to the non-accelerated case.

Findings

The Anderson acceleration provides accelerations up to 75 per cent in the test cases that have been analyzed. For the hysteresis test case, a restart technique is proven to be helpful in analogy to the restarted GMRES technique.

Originality/value

The acceleration that has been suggested in this paper is rarely adopted for the electromagnetic case (it is normally adopted in the electronic simulation case). The procedure is general and works with different magneto-quasi static formulations as shown in the paper. The obtained accelerations allow to reduce the number of iterations required up to 75 per cent in the benchmark cases. The method is also a good candidate in the hysteresis case, where normally the fixed point schemes are preferred to the Newton ones.

Citation

Filippini, M., Alotto, P. and Giust, A. (2019), "Anderson acceleration for electromagnetic nonlinear problems", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 38 No. 5, pp. 1493-1506. https://doi.org/10.1108/COMPEL-11-2018-0483