Error Analysis of MLFMA with Closed-Form Expressions

Date

2021-01-01

Author

Kalfa, Mert
Erturk, Vakur B.
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

153
views

0
downloads

The current state-of-the-art error control of Multilevel Fast Multipole Algorithm (MLFMA) is valid for any given error threshold at any frequency, but it requires a multiple-precision arithmetic framework to be implemented. In this work, we use asymptotic approximations and curve-fitting techniques to derive accurate closed-form expressions for the error control of MLFMA that can be implemented in common fixed-precision computers. Moreover, using the proposed closed-form expressions in conjunction with the state-of-the-art scheme, we report novel design curves for MLFMA that can be used to determine achievable error limits, as well as the minimum box sizes that can be solved with a given desired error threshold for a wide range of machine precision levels.

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85103911763&origin=inward
https://hdl.handle.net/11511/90916

Journal

IEEE Transactions on Antennas and Propagation

DOI

https://doi.org/10.1109/tap.2021.3070086

Collections

Department of Electrical and Electronics Engineering, Article

Suggestions

OpenMETU
Core

Error Control of Multiple-Precision MLFMA Kalfa, Mert; Ergül, Özgür Salih; Erturk, Vakur B. (Institute of Electrical and Electronics Engineers (IEEE), 2018-10) We introduce and demonstrate a new error control scheme for the computation of far-zone interactions in the multilevel fast multipole algorithm when implemented within a multiple-precision arithmetic framework. The proposed scheme provides the optimum truncation numbers as well as the machine precisions given the desired relative error thresholds and the box sizes for the translation operator at all frequencies. In other words, unlike the previous error control schemes which are valid only for high-frequenc...
Error Control of MLFMA within a Multiple-Precision Arithmetic Framework Kalfa, Mert; ERTÜRK, VAKUR BEHÇET; Ergül, Özgür Salih (2018-07-13) 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...
Concurrency control in distributed databases through time intervals and short-term locks Halıcı, Uğur (Institute of Electrical and Electronics Engineers (IEEE), 1989) A method for concurrency control in distributed database management systems that increases the level of concurrent execution of transactions, called ordering by serialization numbers (OSN), is proposed. The OSN method works in the certifier model and uses time-interval techniques in conjunction with short-term locks to provide serializability and prevent deadlocks. The scheduler is distributed, and the standard transaction execution policy is assumed, that is, the read and write operations are issued contin...
Statistical analysis of block ciphers and hash functions Sulak, Fatih; Doğanaksoy, Ali; Department of Cryptography (2011) One of the most basic properties expected from block ciphers and hash functions is passing statistical randomness testing, as they are supposed to behave like random mappings. Previously, testing of AES candidate block ciphers was done by using the statistical tests defined in the NIST Test Suite. As some of the tests in this suite require long sequences, data sets are formed by concatenating the outputs of the algorithms obtained from various input types. However, the nature of block cipher and hash functi...
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...

Citation Formats

M. Kalfa, V. B. Erturk, and Ö. S. Ergül, “Error Analysis of MLFMA with Closed-Form Expressions,” IEEE Transactions on Antennas and Propagation, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85103911763&origin=inward.