Error Analysis of MLFMA With Closed-Form Expressions

被引：2

作者：

Kalfa, Mert ^{[1
,2
]}

Erturk, Vakur B. ^{[1
]}

Ergul, Ozgur ^{[3
]}

机构：

[1] Bilkent Univ, Dept Elect & Elect Engn, TR-06800 Ankara, Turkey

[2] Huawei Turkey Res & Dev Ctr, TR-34768 Istanbul, Turkey

[3] Middle East Tech Univ, Dept Elect & Elect Engn, TR-06800 Ankara, Turkey

来源：

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION | 2021年 / 69卷 / 10期

关键词：

Error correction; Closed-form solutions; Antennas; Frequency control; Green's function methods; Finite wordlength effects; Complexity theory; Error analysis; low-frequency breakdown; multilevel fast multipole algorithm (MLFMA); multiple-precision arithmetic; ELECTROMAGNETIC SCATTERING; MULTIPOLE;

D O I：

10.1109/TAP.2021.3070086

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

The current state-of-the-art error control of the 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.

引用

页码：6618 / 6623

页数：6

共 12 条

[1]

Abramowitz M., 1964, HDB MATH FUNCTIONS F, V55

[2]

Chew W. C., 2001, Fast and Efficient Algorithms in Computational Electromagnetics

[3]

Coifman R., 1993, IEEE Antennas and Propagation Magazine, V35, P7, DOI 10.1109/74.250128

[4] EFFICIENT SOLUTIONS OF METAMATERIAL PROBLEMS USING A LOW-FREQUENCY MULTILEVEL FAST MULTIPOLE ALGORITHM [J].

Erguel, Oe ;

Gurel, L. .

PROGRESS IN ELECTROMAGNETICS RESEARCH-PIER, 2010, 108 :81-99

[5] Accelerating fast multipole methods for the Helmholtz equation at low frequencies [J].

Greengard, L ;

Huang, JF ;

Rokhlin, V ;

Wandzura, S .

IEEE COMPUTATIONAL SCIENCE & ENGINEERING, 1998, 5 (03) :32-38

[6] Error control of the translation operator in 3D MLFMA [J].

Hastriter, ML ;

Ohnuki, S ;

Chew, WC .

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, 2003, 37 (03) :184-188

[7]

IEEE Standard for Floating-Point Arithmetic, 2019, 7542019 IEEE

[8] Error Control of Multiple-Precision MLFMA [J].

Kalfa, Mert ;

Ergul, Ozgur ;

Erturk, Vakur B. .

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 2018, 66 (10) :5651-5656

[9] Error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem [J].

Koc, S ;

Song, JM ;

Chew, WC .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, 36 (03) :906-921

[10] Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects [J].

Song, JM ;

Lu, CC ;

Chew, WC .

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 1997, 45 (10) :1488-1493

← 1 2 →