Surface Integral Equation Methods for Electrostatics
Electrostatic polarizability of a sphere.
When a homogeneous dielectric objects is put into a homogeneous static electric field, it causes a perturbation to the total electric field distribution. The perturbation is concentrated in the neighbourhood of the objects and the main component of the perturbation is a dipolar field. This electrostatic dipolar field can be identified as arising from a point dipole. The ratio between the dipole moment and the amplitude of the incident field is called polarizability of the object.
In addition to time-harmonic dynamic field problems our group has also developed numerical methods for electrostatic problems. In collaboration with another research group from the RAD department, "Interaction of EM fields with matter" (prof. Sihvola) we have developed surface integral equation methods for the numerical calculation of the polarizability of objects whose shape does not allow an analytical solution. With the developed methods we have investigated polarizabilities of various canonical shapes (Platonic solids) such as a sphere, cube, tetrahedron as well as ad ellipsoid and hemi-sphere.
- Static polarizability of arbitrarily shaped 3D objects.
- High-order surface integral equation methods for static problems.
References
- A. Sihvola, P. Ylä-Oijala, S. Järvenpää and J. Avelin: Polarizabilities of Platonic solids, IEEE Transactions on Antennas and Propagation, 52(9), 2226-2233, 2004.
- A. Sihvola, J. Venermo and P. Ylä-Oijala: Dielectric response of matter with cubic, circular-cylinder, and spherical microstructure, Microwave and Optical Technology Letters, 41(4), 245-248, 2004.