Article Article
Hybrid Method of ACA and Interpolation-based Algorithms for Analysis of Eddy Current Nondestructive Evaluations

In this article, the hybridization of adaptive cross approximation (ACA) algorithm and interpolation-based separation of the kernel function is proposed to accelerate solving the matrix equations resulted in the boundary element method (BEM) for 3D arbitrary-shaped eddy current nondestructive evaluation problems. The hybrid method combines the advantages of both the ACA algorithm and the interpolation-based methods, and resolves the short-coming of pure ACA method, when modeling the planar eddy current nondestructive evaluation problems, that it cannot com-press the null entries the BEM generated when the testing and basis patches are co-planar. In the proposed method, the submatrices associated with the null entries are compressed by the interpolation-based method, while the others are compressed by the ACA algorithm. Several benchmarks are shown to demonstrate both the robustness and efficiency of the proposed fast and general solver.

DOI: https://doi.org/10.1080/09349847.2021.1991063

References

1.         H. Libby, Introduction to Electromagnetic Nondestructive Test Methods (Wiley-Inter-Science, New York, NY, 1971).

2.         R. Miorelli et al., IEEE Trans. Mag. 49, 2886–2892 (2013). DOI: 10.1109/TMAG.2012.2236102.

3.         T. Theodoulidis, N. Poulakis, and A. Dragogias, NDT&E Int. 43,13–19 (2009). DOI: 10.1016/j.ndteint.2009.08.005.

4.         T. Theodoulidis, NDT&E Int. 43, 591–598 (2010). DOI: 10.1016/j.ndteint.2010.06.003.

5.         M. Yang, dissertation, Iowa State University, 2010.

6.         R. Hamia, C. Christophe, and D. Christophe, NDT&E Int. 61,24–28 (2014). DOI: 10.1016/j.ndteint.2013.09.005.

7.         J. M. Song, C. C. Lu, and W. C. Chew, IEEE Trans. Antennas Propag. 45, 1488–1493 (1997). DOI: 10.1109/8.633855.

8.         J. M. Song and W. C. Chew, Micro. Optical Techn. Lett. 10,14–19 (1995). DOI: 10.1002/mop.4650100107.

9.         K. Z. Zhao, M. N. Vouvakis, and J. F. Lee, IEEE Trans. Electromag. Compat. 47, 763–773 (2005). DOI: 10.1109/TEMC.2005.857898.

10.       M. Bebendorf, Numer. Math. 86, 565–589 (2000). DOI: 10.1007/PL00005410.

11.       J. Smajic, Z. Andjelic, and M. Bebendorf, IEEE Trans. Mag. 43, 1269–1272 (2007). DOI: 10.1109/TMAG.2006.890971.

12.       S. Kurz, O. Rain, and S. Rjasanow, IEEE Trans. Mag. 38, 421–424 (2002). DOI: 10.1109/20.996112.

13.       Y. Bao, Z. W. Liu, and J. M. Song, J. Nondestructive Eval. 37,1–8 (2018). DOI: 10.1007/s10921-018-0521-1.

14.       Y. Bao et al., NDT&E Int. 104,1–9 (2019). DOI: 10.1016/j.ndteint.2019.03.005.

15.       Y. Bao, Z. W. Liu, and J. M. Song, Appl.Comput. Electromagn. Soc. J. 34,1262–1265 (2019).

16.       W. Hackbusch, Computing 62,89–108 (1999). DOI: 10.1007/s006070050015.

17.       W. Hackbusch and B. N. Khoromskij, Computing 64,21–47 (2000).

18.       L. Grasedyck and W. Hackbusch, Computing 70, 295–334 (2003). DOI: 10.1007/s00607-003-0019-1.

19.       J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, NY, 1941).

20.       Y. Bao and J. M. Song, Philosop. Trans. R. Soc. A 378,1–15 (2020).

21.       S. Bӧrm and L. Grasedyck, Numer. Math. 101, 221–249 (2005). DOI: 10.1007/s00211-005-0618-1.

22.       Y. Bao et al., NDT&E Int. 124, 1-13 (2021). DOI: 10.1016/j.ndteint.2021.102544.

23.       B. A. Auld and J. C. Moulder, J. Nondestructive Eval. 18,3–36 (1999). DOI: 10.1023/A:1021898520626.

24.       T. P. Theodoulidis and J. R. Bowler, Proc. R. Soc. 461, 3123–3139 (2005).

25.       C. V. Dodd and W. E. Deeds, J. Appl. Phys. 39,2829–2838 (1968). DOI: 10.1063/1.1656680.

26.       T. Wu and J. R. Bowler, IEEE Trans. Mag. 53,1–9 (2017).

27.       M. Y. Antimirov, A. A. Kolyshkin, and R. Vaillancourt, Mathematical Models for Eddy Current Testing (Les Publications CRM, 1997).

28.       H. A. Sabbagh and S. K. Burke, Review of Progress in Quantitative Nondestructive Evaluation (Brunswick, ME, 1992), pp. 217–224.

Metrics
Usage Shares
Total Views
70 Page Views
Total Shares
0 Tweets
70
0 PDF Downloads
0
0 Facebook Shares
Total Usage
70