Experience using a preconditioned complex bi-conjugate gradient method with finite element Eddy current and electroheat problems

This paper describes practical user experience in applying the Preconditioned Complex Bi-Conjugate Gradient method to solve Finite Element simulations of eddy current and electrothermal problems. Attention is given to suitable preconditioning methods that provide good convergence with 2-dimensional TE and TM mode problems. It is shown that a preconditioning strategy that provides very rapid convergence in the case of TE mode problems can lead to a divergent solution when applied to TM mode problems. The reasons for the convergence failure are examined. The performance of the Complex Bi-Conjugate Gradient algorithm with real symmetric systems is also examined. It is shown that solution failure can occur and a simple strategy to rectify the failure is described.