Abstract
A multi-grid method is one of the most powerful linear solvers for finite element electromagnetic field analysis. However, as the discretized model has recently been enlarged, a solution process for a linear system arising on the coarsest level tends to be problematic in a complete multi-grid solution process. Whereas a linear system on the coarsest level is generally solved by a direct solver, we solve it here by means of an iterative solver to reduce the memory requirements. Since a conventional preconditioning technique is not effective for such a linear system, we introduce preconditioning techniques based on Arnold, Falk, and Winther’s and on Hiptmair’s smoothers. Numerical tests show that the newly installed preconditioning technique greatly improves the convergence rate.
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Communicated by C.Oosterlee.
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Iwashita, T., Yosui, K., Mori, M. et al. Preconditioned iterative solver on the coarsest level of a multi-grid method for high frequency time harmonic electromagnetic field analyses. Comput. Visual Sci. 11, 123–128 (2008). https://doi.org/10.1007/s00791-007-0063-z
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DOI: https://doi.org/10.1007/s00791-007-0063-z