# Low-frequency multilevel fast multipole algorithm using an approximate diagonalization of the Green's function

2014-08-23
We present an approximate diagonalization of the Green's function to implement a stable multilevel fast multipole algorithm (MLFMA) for low-frequency problems. The diagonalization is based on scaled spherical functions, leading to stable computations of translation operators at all distances and for all frequencies. Similar to the conventional diagonalization, shift operators are expressed in terms of complex exponentials, while radiated and incoming fields are expanded in terms of scaled plane waves. Even though its accuracy is limited, the low-frequency MLFMA developed by using the proposed diagonalization technique provides stable matrix-vector multiplications for arbitrarily low frequencies, while it can easily be implemented via minor modifications on the existing codes.

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 Stabilization of the Fast Multipole Method for Low Frequencies Using Multiple-Precision Arithmetic Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2014-08-23) We stabilize a conventional implementation of the fast multipole method (FMM) for low frequencies using multiple-precision arithmetic (MPA). We show that using MPA is a direct remedy for low-frequency breakdowns of the standard diagonalization, which is prone to numerical errors at short distances with respect to wavelength. By increasing the precision, rounding errors are suppressed until a desired level of accuracy is obtained with plane-wave expansions. As opposed to other approaches in the literature, u...
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Citation Formats
Ö. S. Ergül, “Low-frequency multilevel fast multipole algorithm using an approximate diagonalization of the Green’s function,” 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41548.