2024-03-28T13:43:59Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/387192022-11-17T02:08:08Zhdl_2115_20053hdl_2115_145Convergence of preconditioned conjugate gradient method applied to driven microwave problems1000090212737Igarashi, H.Honma, T.open access© 2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.condition numberconjugate gradient (CG) methodelectromagnetic wavesfinite-element methodpreconditioning427Driven microwave problems can be solved with the finite-element method formulated in terms of the electric field, as well as the vector and scalar potentials. It is known that the latter gives faster convergence of the preconditioned conjugate gradient method than the former. This can be understood from the following facts: namely, the preconditioned finite-element matrix of the former method can contain small negative eigenvalues which make the matrix condition worse. On the other hand, in the latter, such eigenvalues are shown to be composed of zeros and normalized ones.IEEE2003-05engjournal articleVoRhttp://hdl.handle.net/2115/38719https://doi.org/10.1109/TMAG.2003.8101680018-9464AA00667933IEEE Transactions on Magnetics39317051708https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/38719/1/igarashi03.pdfapplication/pdf157.45 KB2003-05