Convergence improvement of the conjugate gradient iterative method for finite element simulations

Abstract

The slow convergence of the incomplete Cholesky preconditioned conjugate gradient (CG) method, applied to solve the system representing a magnetostatic finite element model, is caused by the presence of a few little eigenvalues in the spectrum of the system matrix. The corresponding eigenvectors reflect large relative differences in permeability. A significant convergence improvement is achieved by supplying vectors that span approximately the partial eigenspace formed by the slowly converging eigenmodes, to a deflated version of the CG algorithm. The numerical experiments show that even roughly determined eigenvectors already bring a significant convergence improvement. The deflating technique is embedded in the simulation procedure for a permanent magnet DC machine.

Citation

De Gersem, H. and Hameyer, K. (2001), "Convergence improvement of the conjugate gradient iterative method for finite element simulations", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 20 No. 1, pp. 90-97. https://doi.org/10.1108/03321640110359778