An algebraic multilevel preconditioner for field-circuit coupled problems
Quasi-stationary magnetic field formulations are often coupled with lumped parameter models for the driving electrical systems. The finite element discretization of the coupled problem results in solving large linear systems with a coefficient matrix bordered by dense coupling blocks. The presence of these blocks prevents the straightforward application of black box algebraic multigrid solvers. The authors propose a modified multigrid cycle that takes the coupling blocks into account. Furthermore the authors use block preconditioning and algebraic multigrid shemes as a preconditioner for the conjugate gradient method for complex symmetric systems. Numerical results are presented for a 45kW induction machine, using the the block Jacobi and the generalized algebraic multigrid (AMG) scheme accelerated by the conjugate gradient method. The number of iterations required by both schemes is mesh-width independent, and the generalized AMG scheme is better than the block Jacobi scheme. In terms of performance (CPU time) the generalized AMG scheme is superior to the block Jacobi scheme and becomes more significant with increasing mesh size.
scientific article; zbMATH DE number 2091464