Regularization of eddy-current formulations using discrete grad--div operators

Discrete formulations based on the consistent finite integration technique for magneto-quasi-static problems involve the solution of either singular or very ill-conditioned algebraic systems of equations. For these formulations a regularization based on an augmentation with discrete grad-div-operators is proposed, extending the ideas in Hahne and Weiland (1992) and Bossavit (2000). Possible effects on the spectra of the algebraic systems are discussed and confirmed in numerical experiments. Index Terms--Algorithms, eddy currents, finite integration technique (FIT), gauging, regularization.