Integral Equation Methods

In electromagnetic integral equation methods the original boundary value problems for Maxwell's equations are reformulated as integral equations over the boundary interfaces of homogeneous domains. If the object is inhomogeneous, integral equations over the entire volume of the object has to be considered. Although the integral equations are in many cases flexible and efficient method for solving various electromagnetic problems, an additional numerical difficulty arises from the singular integral kernels.

The research group has developed a triangular patch model with RWG basis functions for both perfectly conducting and dielectric objects and also more complicated objects composed of both conducting and dielectric material. Special emphasis has been set on the efficient and accurate evaluation of singular integral kernels. Also the fast volume integral equation method with FFT has been studied. The developed methods have many applications e.g. in scattering problems, antenna design and in the analysis of waveguide discontinuities. The research group has had a special interest in developing methods for electromagnetic field computing in layered media. This topic has important applications e.g. in the analysis of microstrip antennas.

Research Topics

• Triangular patch model with RWG basis functions
• Analytical and numerical methods for computing singular kernels
• Composite dielectric and perfectly conducting objects
• Inhomogeneous scatterers (volume integral equation method with FFT)
• Electromagnetic field computing in layered media

Applications

• Scattering problems
• Microstrip computing
• Antenna design
• Waveguides and cavities
• Multipacting analysis in particle accelerators

Publications

• P. Ylä-Oijala and M. Taskinen: Application of Combined Field Integral Equation for Electromagnetic Scattering Problems, to be presented in XXVIIth URSI General Assembly, Maastricht, 2002.
  
  
• J. Sarvas: Using Fast Fourier Transform in the 3-D multilevel Fast Multipole Algorithm, to be presented in XXVIIth URSI General Assembly, Maastricht, 2002.
  
  
• P. Ylä-Oijala, M. Taskinen and J. Sarvas: A combined scattering matrix and boundary integral equation method for the analysis and field computation in 3D multi-port waveguide discontinuities, Electromagnetics, accepted for publication, 2002.
  
  
• P. Ylä-Oijala, M. Taskinen and J. Sarvas: Multilayered Media Green's Functions for MPIE with General Electric and Magnetic Sources by the Hertz Potential Approach, Progress in Electromagnetic Research, PIER 33, pp. 141-165, 2001.
  
  
• S. Järvenpää and P. Ylä-Oijala: Solution of Helmholtz equation in 3D by the volume integral equation method, Research Reports C40, Rolf Nevanlinna Institute, Helsinki, 2001.
  
  
• P. Ylä-Oijala and M. Taskinen: Efficient Use of Closed Form Green's Functions for the Electromagnetic Scattering by 3D Buried Objects, Proceedings of 2001 IEEE AP-S Symposium, Vol. 4, pp. 834-837, Boston, USA, 2001.
  
  
• J. Sarvas, P. Ylä-Oijala and M. Taskinen: Multilayered Media Green's Functions, Proceedings of 2001 USNC/URSI National Radio Science Meeting, pp. 137, Boston, USA, 2001.
  
  
• J. Sarvas: Performing interpolation and anterpolation entirely by fast Fourier transform in the 3-D multilevel fast multipole algorithm. Research Reports No. CCEM-13-00, Center for Computational Electromagnetics, University of Illinois, Urbana, USA, June 2000, pp. 1-23.
  
  
• J. Sarvas, M. Taskinen and S. Järvenpää: Computing the scattering matrix for a microstrip structure with coaxial ports. Proceedings of PIERS 2000 (Progress in Electromagnetics Research Symposium), Cambridge, MA, USA, 2000.
  
  
• P. Ylä-Oijala: Comparison of Boundary Integral Formulations for Electromagnetic Field Computation in Axisymmetric Resonators, Journal of Electromagnetic Waves and Applications, Vol. 14, pp. 767-793, 2000.
  
  
• M. Taskinen and P. Ylä-Oijala: 3D microstrip structures with surface integral equation in multilayered case, Electromagnetics 2000, The 10th National Electromagnetics Meeting, Nokia Research Center, Helsinki, Finland pp. 11-12, 2000.
  
  
• P. Ylä-Oijala and E. Somersalo: Computation of Electromagnetic Fields in Axisymmetric RF Structures with Boundary Integral Equations, Journal of Electromagnetic Waves and Applications, Vol. 13, pp. 445-489, 1999.
  
  
• P. Ylä-Oijala and J. Sarvas: Electromagnetic Field Computation in Axisymmetric RF Structures with BEM Applied to Multipacting Analysis, Proceedings of PIERS 98, p. 1027, Nantes France, 1998.
  
  
• J. Sarvas: Electromagnetic field computation in multiport microstrip structures. Proc. of Claremont Conference on diff. equations in biology and industry, June 1-4, Claremont, California, pp. 423-430, World Scientific pub. Co. New Jersey, 1996.
  
  
• J. Sarvas, M. Taskinen and S. Järvenpää: Computing the scattering matrix of a multiport and multilayer microstrip patch with the mixed potential integral equation method. PIERS 96 Conference, Innsbruck, 8-12 July, 1996.

Index | Research | Publications | Staff