Error Control of MLFMA within a Multiple-Precision Arithmetic Framework

Date

2018-07-13

Author

Kalfa, Mert
ERTÜRK, VAKUR BEHÇET
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

188
views

0
downloads

We present a new error control scheme that provides the truncation numbers as well as the required digits of machine precision for the multilevel fast multipole algorithm (MLFMA). The proposed method is valid for all frequencies, whereas the previous studies on error control are valid only for high-frequency problems. When combined with a multiple-precision arithmetic framework, the proposed method can be used to solve low-frequency problems that would otherwise experience overflow issues. Numerical results in the form of optimal truncation numbers and machine precisions for a variety of box sizes and desired relative error thresholds are presented and compared with the results available in the literature.

Subject Keywords

Algorithm

URI

https://hdl.handle.net/11511/52778

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Error control in MLFMA with multiple-precision arithmetic Kalfa, Mert; Ergül, Özgür Salih; Ertürk, Vakur B. (null; 2018-04-13) We present a new error control method that provides the truncation numbers as well as the required digits of machine precision for the translation operator of the multilevel fast multipole algorithm (MLFMA). The proposed method is valid for all frequencies, whereas the previous studies on error control are valid only for high-frequency problems (i.e., electrically large translation distances). When combined with a multiple-precision implementation of MLFMA, the proposed method can be used to solve low-frequ...
Efficient and Accurate Electromagnetic Optimizations Based on Approximate Forms of the Multilevel Fast Multipole Algorithm Onol, Can; Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2016-01-01) We present electromagnetic optimizations by heuristic algorithms supported by approximate forms of the multilevel fast multipole algorithm (MLFMA). Optimizations of complex structures, such as antennas, are performed by considering each trial as an electromagnetic problem that can be analyzed via MLFMA and its approximate forms. A dynamic accuracy control is utilized in order to increase the efficiency of optimizations. Specifically, in the proposed scheme, the accuracy is used as a parameter of the optimiz...
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...
Rigorous Solutions of Large-Scale Scattering Problems Discretized with Hundreds of Millions of Unknowns Guerel, L.; Ergül, Özgür Salih (2009-09-18) We present fast and accurate solutions of large-scale scattering problems using a parallel implementation of the multilevel fast multipole algorithm (MLFMA). By employing a hierarchical partitioning strategy, MLFMA can be parallelized efficiently on distributed-memory architectures. This way, it becomes possible to solve very large problems discretized with hundreds of millions of unknowns. Effectiveness of the developed simulation environment is demonstrated on various scattering problems involving canonic...
Shape Optimizations of Metallic Sheets Using a Multigrid Approach Altinoklu, Askin; Karaova, Gokhan; Ergül, Özgür Salih (2017-09-27) We present a novel multigrid approach for the shape optimizations of corrugated metallic sheets by using genetic algorithms (GAs) and the multilevel fast multipole algorithm (MLFMA). The overall mechanism is obtained by an efficient integration of GAs and MLFMA, while the optimizations are improved by applying multiple grids at different layers. We show that the multigrid approach provides more effective optimizations than the conventional no-grid optimizations that employ the discretization nodes directly....

Citation Formats

M. Kalfa, V. B. ERTÜRK, and Ö. S. Ergül, “Error Control of MLFMA within a Multiple-Precision Arithmetic Framework,” 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52778.