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Using multiple-precision arithmetic to prevent low-frequency breakdowns in the diagonalization of the green's function

2014-08-28
Ergül, Özgür Salih
Karaosmanoʇlu, B.
Multiple-precision arithmetic (MPA) is used to prevent low-frequency breakdowns in the diagonalization of the Green's function that is required to implement the multilevel fast multipole algorithm (MLFMA). The breakdown problem is considered at a numerical level, where rounding errors are reduced by increasing the precision as much as required. Using MPA seems to provide a direct solution to low-frequency breakdowns of the standard diagonalization, which may lead to straightforward implementations of broadband MLFMA.