Electromagnetic Materials and Boundary Conditions
Electric current on a cube with the DB boundary condition.
One of the basic problems in computational electromagnetism is to solve the scattered fields for given the incident fields, scatterer and boundary conditions. Boundary conditions restrict the behaviour of the electric and magnetic fields at the boundary and they affect the solution in the region of interest, while the region behind the boundary does not affect to the solution at all. To obtain a unique solution, the boundary value problem should be well-posed, in other words, the boundary conditions must have a proper form.
Conventionally electromagnetic boundary conditions apply to the tangential components of the fields, for example, perfect electric or magnetic conductors (PEC and PMC) require vanishing of the tangential components of the electric or magnetic fields, respectively, at the boundary. An extension of these conventional boundary conditions is the perfect electromagnetic conductor (PEMC) condition requiring that a linear combination of the tangential electric and magnetic fields vanishes on the surface.
In collaboration with another research group from the RAD department, "Interaction of EM fields with matter" (prof. Sihvola, prof. Lindell) we have developed surface integral equation methods for scattering by 3D arbitrarily shaped objects with non-conventional boundary conditions given in terms of the normal components of the fields and their normal components.
- Numerical methods for DB, D'B', PEMC and other extreme EM boundary conditions.
- Material realizations.
References
- J. Markkanen, P. Ylä-Oijala and A. Sihvola: Computation of scattering by DB objects with surface integral equation method, IEEE Transactions on Antennas and Propagation, Vol. 59, No. 1, pp. 154-161, Jan. 2011.
- S. P. Kiminki, J. Markkanen and P. Ylä-Oijala: Integral equation solution for the D'B' boundary condition, IEEE Antennas and Wireless Propagation Letters, 9, 526-529, 2010.
- P. Ylä-Oijala, S. P. Kiminki, J. Markkanen, H. Wallen, A. Sihvola, I. V. Lindell and S. Järvenpää: Numerical methods for scattering problems expressed in terms of normal field components and their normal derivatives, URSI Commission B 2010 International Symposium on Electromagnetic Theory, Aug. 2010, Berlin, Germany.
- A. Sihvola, P. Ylä-Oijala and I. V. Lindell: Scattering by PEMC (perfect electromagnetic conductor) spheres using surface integral equation approach, Applied Computational Electromagnetics Society (ACES) Journal, 22(2), 236-249, 2007.