The Journal of Korean Institute of Electromagnetic Engineering and Science (한국전자파학회논문지)

The Korean Institute of Electromagnetic Engineering and Science (한국전자파학회)
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Computational Complexity of BiCGstab(l) in Multi-Level Fast Multipole Method(MLFMM) and Efficient Choice of l

MLFMM(Multi-Level Fast Multipole Method) 방법에 적용된 BiCGstab(l)반복법의 l값에 따른 연산량 분석 및 효율적인 l값

  • Lee, Hyunsoo (Department of Electronic Engineering, Inha University) ;
  • Rim, Jae-Won (Department of Electronic Engineering, Inha University) ;
  • Koh, Il-Suek (Department of Electronic Engineering, Inha University) ;
  • Seo, Seung-Mo (Agency for Defense Development)
  • Received : 2017.12.06
  • Accepted : 2018.02.12
  • Published : 2018.03.31
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Abstract

The method of moments(MoM) is one of the most popular integral-equation-based full-wave simulation methods, and the multi-level fast multipole method(MLFMM) algorithm can be used for its efficient calculation. When calculating the surface current on the large scatterer in the MoM or MLFMM, iterative methods for the final matrix inversion are used. Among them, BiCGstab(l) has been widely adopted due to its good convergence rate. The number of iterations can be reduced when l becomes larger, but the number of operations per iteration is increased. Herein, we analyze the computational complexity of BiCGstab(l) in the MLFMM method and propose an optimum choice of l.

MoM은 대표적인 적분방정식기반 full-wave simulation 방법이며, 이는 MLFMM 방법을 적용하여 효율적으로 계산될 수 있다. MoM 또는 MLFMM 방법에서 대규모 산란체 표면전류를 계산하는 과정에는 주로 반복법들이 사용된다. 이 가운데 BiCGstab(l)은 l값이 증가할수록 반복횟수는 줄어들지만, 반복당 수행되는 연산횟수가 증가하는 특징이 있다. 본 논문에서는 MLFMM 방법에 적용된 BiCGstab(l) 반복법의 l값에 따른 수렴속도와 연산량을 분석한 후, 효율적인 l값을 제안한다.

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References

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