Parallel Communication Mechanisms in Solving Integral Equations for Electromagnetic Scattering Based on the Method of Moments

  • Lan SongEmail author
  • Dennis K. Peters
  • Weimin Huang
  • Zhiwei Liu
  • Lixia Lei
  • Tangliu Wen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11334)


In this paper, a parallel solution of impedance filling was studied to improve the efficiency for the method of moments (MOM) in solving the integral equation for electromagnetic scattering. Based on the formalization method, the correctness verification method of the parallel communication protocol was proposed to avoid the abnormal situation such as deadlock caused by unsynchronized MPI message delivery. Finally, a numerical example is given to verify the accuracy of the parallel algorithm in a multi-core cluster environment, and the parallel efficiency and computational capability are also tested. From the experiment data, it can be seen that the results of the parallel-based integral equation match well with the results of the Mie analytical solution. The parallel algorithm proposed in this paper is evaluated in terms of the acceleration ratio and parallel efficiency. The experimental results demonstrate the reliability and effectiveness of the method.


Formal verification Parallel communication Electromagnetic scattering Petri net 



This work is supported in part by the project of science and technology department of Jiangxi province (No. 20161BBH80039, 20171BAB202013), the National Natural Science Foundation (No. 61462041, 61763014, 61762049),Jiangxi University humanities and social science (No. JC1507).


  1. 1.
    Harrington, R.: Origin and development of the method of moments for field computation. IEEE Antennas Propag. Mag. 32(3), 31–36 (1990)CrossRefGoogle Scholar
  2. 2.
    Mur, G.: Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations. IEEE Trans. Electromagn. Compat. EMC-23(4), 377–382 (1981)Google Scholar
  3. 3.
    Oskooi, A.F., Roundy, D., Ibanescu, M., Bermel, P., Joannopoulos, J.D., Johnson, S.G.: MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method. Comput. Phys. Commun. 181(3), 687–702 (2010)CrossRefGoogle Scholar
  4. 4.
    Surana, K.S., Reddy, J.N.: The Finite Element Method for Boundary Value Problems: Mathematics and Computations. CRC Press, USA (2016)CrossRefGoogle Scholar
  5. 5.
    Zhan, Y.: CAD modeling method in numerical simulation of electromagnetic fields. Master thesis. Xian: Xidian University (2008)Google Scholar
  6. 6.
    Sumithra, P., Thiripurasundari, D.: Review on computational electromagnetics. Adavanced Electromagn. 6(1), 42–55 (2017)CrossRefGoogle Scholar
  7. 7.
    Guo, H., Hu, J., Nie, Z.P.: An MPI-OpenMP hybrid parallel H-LU direct solver for electromagnetic integral equations. Int. J. Antennas Propag. 2015, 1–10 (2015)Google Scholar
  8. 8.
    Kaporin, I., Milyukova, O.: MPI + OpenMP parallel implementation of explicitly preconditioned conjugate gradient method, pp. 1–27. Preprints of the Keldysh Institute of Applied Mathematics (2018)Google Scholar
  9. 9.
    Wu, Z.: Introduction to Petri net, pp. 10–30. China Machine Press, Beijing (2006)Google Scholar
  10. 10.
    Yuan, J.: Petri Net Modeling and Intelligent Analysis, pp. 39–122. National Defence Industry Press, Beijing (2011)Google Scholar
  11. 11.
    Holzmann, G.J.: The spin model checker: primer and reference manual, pp. 95–123. Addison-Wesley, New Jersey (2003)Google Scholar
  12. 12.
    Wiscombe, W.J.: Improved Mie scattering algorithms. Appl. Opt. 19(9), 1505–1509 (1980)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Lan Song
    • 1
    • 2
    • 3
    Email author
  • Dennis K. Peters
    • 3
  • Weimin Huang
    • 3
  • Zhiwei Liu
    • 2
  • Lixia Lei
    • 2
  • Tangliu Wen
    • 1
  1. 1.School of Computer, State Key Laboratory of Software EngineeringWuhan UniversityWuhanChina
  2. 2.School of Information EngineeringEast China Jiaotong UniversityNanchangChina
  3. 3.Electrical and Computer Engineering, Faculty of Engineering and Applied ScienceMemorial UniversitySt. John’sCanada

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