Integral Equations and Method of Moments

Course Description

Formulation of physical problems via integral equations. Different formulations of integral equations (EFIE, MFIE, CFIE) in electromagnetic applications. Method of Moments (MoM). Applications to wire and microstrip antennas and wave scattering problems. Fast multipole method (FMM), algorithm analysis and applications.

Learning Outcomes

  1. select appropriate numerical method for analysis of antennas or EM scatterers
  2. describe basic concepts related to integral equations and moment method
  3. estimate the limitations of the moment method
  4. estimate numerical difficulties related to implementation of moment method
  5. apply commercial full-wave simulator based on moment method in analysis of engineering problems
  6. develop a program for analyzing simple EM problems using finite-difference method
  7. develop a method of moments based code using numerical libraries
  8. implement fast multipole method

Forms of Teaching

Lectures

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Exercises

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Independent assignments

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Week by Week Schedule

  1. Integral equations in electromagnetics; Method of Moments: formulation of the method
  2. Method of Moments: selection of basis and test functions; efficient calculation of the moment method matrix elements
  3. Dyadic Green's functions
  4. Electric, magnetic and combined field integral equations; mixed-potential integral equation; singularities and non-uniqueness of solution
  5. Method of Moments: efficient calculation of the moment method matrix elements
  6. Method of Moments: analysis of periodic structures
  7. Mode matching method
  8. Midterm exam
  9. Applications: analysis of the wire antennas
  10. Applications: two-dimensional scattering analysis
  11. Applications: analysis of microstrip antennas
  12. Applications: analysis of antenna arrays
  13. The fast multiple method; matrix elements of the fast multiple method; one-level and multi-level fast multipole algorithms
  14. The fast multiple method; matrix elements of the fast multiple method; one-level and multi-level fast multipole algorithms
  15. Final exam

Study Programmes

University graduate
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Data Science (profile)
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Electrical Power Engineering (profile)
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Electric Machines, Drives and Automation (profile)
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Electronic and Computer Engineering (profile)
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Information and Communication Engineering (profile)
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Literature

W. C. Gibson (2014.), The Method of Moments in Electromagnetics, Chapman and Hall/CRC
A. F. Peterson, S. L. Ray and R. Mittra (1998.), Computational Methods in Electromagnetics, IEEE press
C.M. Butler, D.R. Wilton and A.W. Glisson (1982.), Numerical Methods in Electromagnetics, Lecture Notes
R.F. Harrington (1993.), Field computation by Moment Method, IEEE Press
J. L.Volakis and K. Sertel (2012.), Integral Equation Methods for Electromagnetics, SciTech Publishing

For students

General

ID 222561
  Summer semester
5 ECTS
L3 English Level
L1 e-Learning
45 Lectures
13 Laboratory exercises

Grading System

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