On the Various Applications of Stochastic Collocation in Computational Electromagnetics

  • Dragan PoljakEmail author
  • Silvestar Sesnic
  • Mario Cvetkovic
  • Anna Susnjara
  • Pierre Bonnet
  • Khalil El Khamlichi Drissi
  • Sebastien Lallechere
  • Françoise Paladian
Part of the PoliTO Springer Series book series (PTSS)


The application of deterministic-stochastic models in some areas of computational electromagnetics is presented. Namely, in certain problems there is an uncertainty in the input data set as some system properties are partly or entirely unknown. Thus, a simple stochastic collocation (SC) method is used to determine the relevant statistics about the given responses. The SC approach also provides the assessment of the related confidence intervals in the set of calculated numerical results. The expansion of statistical output in terms of mean and variance over a polynomial basis, via SC method, is shown to be robust and efficient approach providing a satisfactory convergence rate. The presented stochastic framework provides means for sensitivity analysis enabling a better insight into the relationship between the input parameters and the output of interest. This chapter provides certain computational examples from the previous work by the authors illustrating successful application of SC technique in the areas of: human exposure to electromagnetic fields, transcranial magnetic stimulation (TMS), transient analysis of buried wires and design of instrumental landing system (ILS).


Bioelectromagnetism Computational electromagnetics Deterministic modeling Engineering applications Sensitivity analysis Stochastic collocation Uncertainty quantification 


  1. 1.
    Xiu D (2009) Fast numerical methods for stochastic computations: a review. Commun Comput Phys 5(2–4):242–272MathSciNetzbMATHGoogle Scholar
  2. 2.
    Ahadi M, Roy S (2016) Sparse linear regression (SPLINER) approach for efficient multidimensional uncertainty quantifiation of high-speed circuits. IEEE Trans Comput Aided Des Integr Circuits Syst 35(10):1640–1652CrossRefGoogle Scholar
  3. 3.
    Manfredi P, Canavero F (2015) Efficient statistical simulation of microwave devices via stochastic testing-based circuit equivalents of nonlinear components. IEEE Trans Microw Theory Tech 63(5):1502–1511CrossRefGoogle Scholar
  4. 4.
    Chiaramello E, Parazzini M, Fiocchi S, Ravazzani P, Wiart J (2017) Assessment of fetal exposure to 4G LTE tablet in realistic scenarios: effect of position, gestational age, and frequency. IEEE J Electromagn RF Microw Med Biol 1(1):26–33CrossRefGoogle Scholar
  5. 5.
    Pinto Y, Wiart J (2017) Surrogate model based polynomial chaos of indoor exposure induced from WLAN source. In: URSI GASS, MontrealGoogle Scholar
  6. 6.
    Bai J, Zhang G, Wang D, Duffy AP, Wan L (2016) Performance comparison of the SGM and the SCM in EMC simulation. IEEE Trans Electromagn Compat 58(6):1739–1746CrossRefGoogle Scholar
  7. 7.
    Cheng X, Monebhurrun V (2017) Application of different methods to quantify uncertainty in specific absorption rate calculation using a CAD-based mobile phone model. IEEE Trans Electromagn Compat 59(1):14–23CrossRefGoogle Scholar
  8. 8.
    Drissaoui MA, Lanteri S, Leveque P, Mu F (2012) A stochastic collocation method combined with a reduced basis method to compute uncertainties in numerical dosimetry. IEEE Trans Magn 48(2):563–566CrossRefGoogle Scholar
  9. 9.
    Prasad A, Roy S (2015) Multidimensional variability analysis of complex power distribution networks via scalable stochastic collocation approach. IEEE Trans Compon Packag Manuf Technol 5(11):1656–1658CrossRefGoogle Scholar
  10. 10.
    Agarwal N, Aluru NR (2009) Stochastic analysis of electrostatic MEMS subjected to parameter variations. J Microelectromech Syst 18(6):1454–1468CrossRefGoogle Scholar
  11. 11.
    Zhang Z, Weng T, Daniel L (2017) Big-data tensor recovery for high-dimensional uncertainty quantification of process variations. IEEE Trans Compon Packag Manuf Technol 7(5):687–697CrossRefGoogle Scholar
  12. 12.
    Bai J, Zhang G, Duffy APAP, Wang L (2017) Dimension-reduced sparse grid strategy for a stochastic collocation method in EMC software. IEEE Trans Electromagn Compat 60(1):218–224CrossRefGoogle Scholar
  13. 13.
    Li P, Jiang LJ (2015) Uncertainty quantification for electromagnetic systems using ASGC and DGTD method. In: IEEE Trans Electromagn Compat 57(4):754–763CrossRefGoogle Scholar
  14. 14.
    Rossi M, Dierck M, Rogier H, Vande Ginste D (2014) A stochastic framework for the variability analysis of textile antennas. IEEE Trans Antennas Propag 62(12):6510–6514MathSciNetCrossRefGoogle Scholar
  15. 15.
    Inghelbrecht V, Verhaevert J, Van Hecke T (2016) Stochastic framework for evaluating the effect of displaced antenna elements on DOA estimation. IEEE Antennas Wirel Propag Lett 16:262–265CrossRefGoogle Scholar
  16. 16.
    Chauviere C, Hesthaven JS, Wilcox LC (2007) Efficient computation of RCS from scatterers of uncertain shapes. IEEE Trans Antennas Propag 55(5):1437–1448Google Scholar
  17. 17.
    Mathelin L, Hussaini MY (2003) A stochastic collocation algorithm for uncertainty analysis. NASA STI Report Series, Technical report, NASA/CR-2003-212153, NAS 1.26:212153, 2003Google Scholar
  18. 18.
    Babuuska I, Nobile F, Tempone R (2010) A stochastic collocation method for elliptic partial differential equations with random input data. Soc Ind Appl Math 52(2):317–355MathSciNetzbMATHGoogle Scholar
  19. 19.
    Lalléchère S, Bonnet P, El Baba I, Paladian F (2011) Unscented transform and stochastic collocation methods for stochastic electromagnetic compatibility. In: Computational electromagnetics international workshop (CEM), IzmirGoogle Scholar
  20. 20.
    Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S (2010) Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comput Phys Commun 181:259–270MathSciNetCrossRefGoogle Scholar
  21. 21.
    Sobol IM (1993) Sensitivity estimates for nonlinear mathematical models. Math. Model Comput Exp 1:407–414MathSciNetzbMATHGoogle Scholar
  22. 22.
    Sudret B (2008) Global sensitivity analysis using polynomial chaos expansion. Reliab Eng Syst Saf 93:964–979CrossRefGoogle Scholar
  23. 23.
    Tang G, Iaccarino G, Eldred MS (2010) Global sensitivity analysis for stochastic collocation. In: 51st AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Orlando, FloridaGoogle Scholar
  24. 24.
    Susnjara A, Cvetkovic M, Poljak D, Lallechere S, El Khamlichi Drissi K (2016) Stochastic sensitivity in thermal dosimetry for the homogeneous human brain model. In: BIOEM 2016, Ghent, BelgiumGoogle Scholar
  25. 25.
    Susnjara A, Cvetkovic M, Poljak D, Lallechere S, El Khamlichi Drissi K (2017) An efficient deterministic-stochastic model for the homogeneous human brain model dosimetry: ANOVA approaches for sensitivity analysis of model parameters. In: SPAS2017 international conference on stochastic processes and algebraic structures, Västerås, SwedenGoogle Scholar
  26. 26.
    Susnjara A, Cvetkovic M, Poljak D, Lallechere S, El Khamlichi Drissi K (2017) Stochastic thermal dosimetry for homogeneous human brain model. In: Uncertainty modelling for engineering applicaions, Turin, ItalyGoogle Scholar
  27. 27.
    Cvetkovic M, Susnjara A, Poljak D, Lallechere L, El Khamlichi Drissi K (2016) Stochastic collocation method applied to transcranial magnetic stimulation analysis. In: BIOEM 2016, Ghent, BelgiumGoogle Scholar
  28. 28.
    Cvetkovic M, Susnjara A, Poljak D, Lallechere S, El Khamlichi Drissi K (2017) Stochastic dosimetry for transcranial magnetic stimulation analysis. In: Uncertainty modelling for engineering applications, Turin, ItalyGoogle Scholar
  29. 29.
    Cvetkovic M, Poljak D, Hirata A (2016) The electromagnetic-thermal dosimetry for the homogeneous human brain model. Eng Anal Boundary Elem 63:61–73MathSciNetCrossRefGoogle Scholar
  30. 30.
    Wiart J (2016) Radio-frequency human exposure assessment: from deterministic to stochastic methods. WileyGoogle Scholar
  31. 31.
    Susnjara A, Cvetkovic M, Dodig H, Poljak D (2018) Numerical analysis of a three-compartment head model subjected to variation of input parameters. In: BIOEM 2018, Portoroz, SloveniaGoogle Scholar
  32. 32.
    Cvetkovic M, Poljak D, Haueisen J (2015) Analysis of transcranial magnetic stimulation based on the surface integral equation formulation. IEEE Trans Biomed Eng 62(6):1535–1545CrossRefGoogle Scholar
  33. 33.
    Cvetkovic M, Poljak D, Rogic Vidakovic M, Dogas Z (2016) Transcranial magnetic stimulation induced fields in different brain models. J Electromag Waves Appl 30(14):1820–1835CrossRefGoogle Scholar
  34. 34.
    Weise K, Di Rienzo L, Brauer H, Haueisen J (2015) Uncertainty analysis in transcranial magnetic stimulation using nonintrusive polynomial chaos expansion. IEEE Trans Magnet 51(7):1–8CrossRefGoogle Scholar
  35. 35.
    Gomez L, Yucel A, Hernandez-Garcia L, Taylor S, Michielssen E (2015) Uncertainty quantification in transcranial magnetic stimulation via high-dimensional model representation. IEEE Trans Biomed Eng 62(1):31–372CrossRefGoogle Scholar
  36. 36.
    Fyre RE, Rotenberg A, Ousley M, Pascual-Leon A (2008) Transcranial magnetic simulation in child neurology: current and future directions. J Child Neurol 23(1):79–96CrossRefGoogle Scholar
  37. 37.
    Grcev LD, Dawalibi F (1990) An electromagnetic model for transients in grounding systems. IEEE Trans Power Deliv 5(4):1773–1781CrossRefGoogle Scholar
  38. 38.
    Visacro S (2007) A comprehensive approach to the grounding response to lighting currents. IEEE Trans Power Deliv 22(1):381–386CrossRefGoogle Scholar
  39. 39.
    Jurisic B, Xemard A, Uglesic I, Paladian F, Lallechere S, Bonnet P (2016) Evaluation of transmitted over-voltages through a power transformer taking into account uncertainties on lightning paramters. In: 33rd international conference on lightning protection, Estoril, PortugalGoogle Scholar
  40. 40.
    Sesnic S, Susnjara A, Lallechere S, Poljak D, El Khamlichi Drissi K, Bonnet P, Paladian F (2017) Advanced analysis of the transient impedance of the horizontal grounding electrode: from statistics to sensitivity indices. In: 32nd URSI GASS, Montreal, CanadaGoogle Scholar
  41. 41.
    Lallechere S, Bonnet P, El Khamlichi Drissi K, Paladian F, Sesnic S, Susnjara A, Poljak D (2017) Statistical transient impedance of horizontal grounding systems: application to sensitivity analysis with ANOVA approaches. In: SpliTECH 2017, Split, CroatiaGoogle Scholar
  42. 42.
    Poljak D, Sesnic S, Cvetkovic M, Susnjara A, Dodig H, Lallechere S, El Kamlichi Drissi K (2018) Stochastic collocation applications in computational electromagnetics. Math Probl Eng 2018:13, Article ID 1917439. Scholar
  43. 43.
    Sesnic S, Poljak D, Tkachenko SV (2013) Analytical modeling of a transient current flowing along the horizontal grounding electrode. IEEE Trans Electromagn Compat 55(6):1132–1139CrossRefGoogle Scholar
  44. 44.
    Sesnic S, Lallechere S, Poljak D, Bonnet P, El Khamlichi Drissi K (2016) A stochastic analysis of the transient current induced along the thin wire scatterer buried in a lossy medium. Int J Antennas Propag 2016:12Google Scholar
  45. 45.
    Marcum F (1995) Design of an image radiation monitor for ILS glide slope in the presence of snow. Ohio UniversityGoogle Scholar
  46. 46.
    Susnjara A, Doric V, Lallechere S, Poljak D, Birkic M, Bonnet P, Paladian F (2017) Sensitivity analysis of the main lobe direction for glide slope antenna due to snow cover on runway. In: Uncertainty modelling in engineering applications, Turin, ItalyGoogle Scholar
  47. 47.
    Bradford JH et al (2009) Complex dielectric measurements from ground-penetrating radar data to estimate snow liquid water content in the pendular regime. Water Resour Res 45:12Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Dragan Poljak
    • 1
    Email author
  • Silvestar Sesnic
    • 1
  • Mario Cvetkovic
    • 1
  • Anna Susnjara
    • 1
  • Pierre Bonnet
    • 2
  • Khalil El Khamlichi Drissi
    • 2
  • Sebastien Lallechere
    • 2
  • Françoise Paladian
    • 2
  1. 1.FESB, University of SplitSplitCroatia
  2. 2.CNRS, Sigma Clermont, Institut Pascal Clermont-Ferrand, Université Clermont AuvergneClermont-FerrandFrance

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