Analysis of volume integral equation formulations for scattering by high-contrast penetrable objects

Johannes Markkanen, Cai Cheng Lu, Xiande Cao, Pasi Ylä-Oijala

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


The volume integral equation method is applied in electromagnetic scattering from arbitrarily shaped three-dimensional inhomogeneous objects. The properties of the volume electric and magnetic field integral equations (VEFIE and VMFIE) are investigated. Numerical experiments show that if the Galerkin's method with the lowest mixed-order basis functions is used to discretize the equations the accuracy of the VMFIE can be significantly poorer than the accuracy of the VEFIE, in particular, for high-contrast objects at high frequencies. The accuracy of the VMFIE can be essentially improved with full first order (linear) basis functions. The linear basis functions are found to be useful also when a single volume integral equation is used to model a general scatterer where both permittivity and permeability differ from the background.

Original languageEnglish
Article number6163361
Pages (from-to)2367-2374
Number of pages8
JournalIEEE Transactions on Antennas and Propagation
Issue number5
StatePublished - 2012

Bibliographical note

Funding Information:
Manuscript received January 17, 2011; revised September 16, 2011; accepted November 19, 2011. Date of publication March 02, 2012; date of current version May 01, 2012. This work was supported by the Academy of Finland and the Graduate School in Electronics, Telecommunications and Automation, GETA. J. Markkanen and P. Ylä-Oijala are with the Department of Radio Science and Engineering, School of Electrical Engineering, Aalto University, Espoo 00076, Finland (e-mail: [email protected]). C. Lu and X. Cao are with Department of Electrical and Computer Engineering, University of Kentucky, Lexington, KY 40506 USA. Color versions of one or more of the figures in this paper are available online at Digital Object Identifier 10.1109/TAP.2012.2189704


  • Electromagnetic scattering
  • high-contrast dielectrics
  • volume integral equation methods

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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