A Robust Preconditioner for GMRES Method Applied to Finite Network Method
The aim of the autors is the calculation of induction and proximity effects of electric machines in an intermediate frequency range up to 100 kHz by the Finite Network Method (FNM). FNM excludes non-magnetic and non-conductive media (e. g. air) from the numerical calculation and fulfilles the asymptotic boundary conditions for the free space automatically. We present a short derivation of FNM for non-magnetic materials from Maxwells equations. Furthermore,we present the applicability of the GMRES method in the whole frequency range. In the low frequency limit f → 0 the impedance matrix reduces to its real part and can be used as preconditioner for GMRES. If the preconditioner is diagonally dominant preconditioning can be performed by Gauss-Seidel iterations. As an example we calculated the skin and proximity effect in two parallel copper wires with 200 to 500 degrees of freedom. Our problem allows the iterative calculation of the preconditioner by the Gauss-Seidel method. The preconditioner results in an acceleration of GMRES up to a factor 8 in addition with an early restart of the preconditioned GMRES. Despite the considerable portion of the imaginary part of the system matrix at higher frequencies the Gauss-Seidel preconditioner is applicable in the whole frequency range.
A.Farschtschi T.Richter
University of Technology Chemnitz,Germany
国际会议
Progress in Electromagnetics Research Symposium 2005(2005年电磁学研究新进展学术研讨会)(PIERS 2005)
杭州
英文
241-245
2005-08-22（万方平台首次上网日期，不代表论文的发表时间）