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

Date

2014-08-23

Author

Ergül, Özgür Salih

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

170
views

0
downloads

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.

Subject Keywords

MLFMA

URI

https://hdl.handle.net/11511/41548

DOI

https://doi.org/10.1109/ursigass.2014.6929224

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

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...
Using multiple-precision arithmetic to prevent low-frequency breakdowns in the diagonalization of the green's function Ergül, Özgür Salih (2014-08-28) 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 broadb...
Broadband MLFMA based on an approximate diagonalization of the three-dimensional Green's function Ergül, Özgür Salih (2015-09-11) We present an approximate diagonalization of the three-dimensional Green's function for straightforward broadband implementations of the multilevel fast multipole algorithm. The diagonalization is based on the use of scaled spherical functions and plane waves, leading to approximate but stable expansions for arbitrarily short distances with respect to wavelength. Despite its limited accuracy, the approximate diagonalization is easy to insert into existing MLFMA implementations for converting them into broad...
Broadband Multilevel Fast Multipole Algorithm For Large-Scale Problems With Nonuniform Discretizations Ergül, Özgür Salih; Takrimi, Manouchehr; Erturk, Vakur B. (2016-08-18) We present a broadband implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of multiscale problems involving highly nonuniform discretizations. Incomplete tree structures, which are based on population-based clustering with flexible leaf-level boxes at different levels, are used to handle extremely varying triangulation sizes on the same structures. Superior efficiency and accuracy of the developed implementation, in comparison to the standard and broadband MLFMA...
Benchmark Solutions of Large Problems for Evaluating Accuracy and Efficiency of Electromagnetics Solvers Gurel, Levent; Ergül, Özgür Salih (2011-07-08) We present a set of benchmark problems involving conducting spheres and their solutions using a parallel implementation of the multilevel fast multipole algorithm (MLFMA). Accuracy of the implementation is tested by comparing the computational results with analytical Mie-series solutions. Reference solutions are made available on an interactive website to evaluate and compare the accuracy and efficiency of fast solvers. We also demonstrate the capabilities of our solver on real-life problems involving compl...

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.