Exact solution of surface-volume-surface electric field integral equation and analysis of its spectral properties
| dc.contributor.author | Goni, Md Osman | |
| dc.contributor.examiningcommittee | Wang, BingChen | |
| dc.contributor.examiningcommittee | Jeffrey, Ian | |
| dc.contributor.examiningcommittee | Bagci, Hakan (King Abdullah University of Science and Technology) | |
| dc.contributor.supervisor | Okhmatovski, Vladimir | |
| dc.contributor.supervisor | LoVetri, Joe | |
| dc.date.accessioned | 2023-09-06T15:45:35Z | |
| dc.date.available | 2023-09-06T15:45:35Z | |
| dc.date.issued | 2023-08-21 | |
| dc.date.submitted | 2023-08-21T17:08:28Z | en_US |
| dc.date.submitted | 2023-09-05T19:47:44Z | en_US |
| dc.degree.discipline | Electrical and Computer Engineering | en_US |
| dc.degree.level | Doctor of Philosophy (Ph.D.) | |
| dc.description.abstract | Exact solution of the Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) is presented for the problem of radiation in the vicinity of homogeneous dielectric sphere. The solution is obtained via Galerkin Method of Moments (MoM) utilizing rotational and irrotational complete sets of orthogonal vector spherical har- monics as basis and test functions according to the Helmholtz decomposition. In this work, two types of formulations derived from single-source integral equation rep- resentation namely, SVS-EFIE-J and SVS-EFIE-M have been analyzed and solved with the MoM discretization. Excitation in the form of radial and tangential electric dipole situated above the spherical scatterer and the electric field throughout the sphere evaluated via ana- lytic MoM solution of the SVS-EFIE is compared against the exact classical Mie series solution. The two are shown to agree to 12 digits of accuracy upon suffi- cient number of basis/test functions taken in the MoM solution and the Mie series expansion. The exact solution confirms and validates the rigorous nature of the SVS-EFIE formulation. It also reveals the spectral properties of its individual op- erators, their products and their linear combination, as well as the spectrum of the MoM impedance matrix. It is shown that upon choosing basis and test functions in Sobolev space H1/2(S) for SVS-EFIE-J and L2(S) for SVS-EFIE-M, while perform- div ing the testing in the spaces H−1/2(S) and L2(S), respectively, S being the surface of the sphere, the MoM impedance matrix features bounded condition number simi- lar with analogous exact MoM solution of the surface EFIE on perfectly electrically conducting (PEC) sphere and the solution involving MoM of the surface EFIE on perfectly magnetic conductor (PMC). The selection of the proper functional spaces makes proposed SVS-EFIE formulation free of oversampling breakdown. Moreover, both the spectrum of the continuous integral operators of this new magnetic current based SVS-EFIE-M and the spectrum of its MoM impedance matrix are bounded at low frequencies for simply connected smooth dielectric scatterers. | |
| dc.description.note | October 2023 | |
| dc.identifier.uri | http://hdl.handle.net/1993/37574 | |
| dc.language.iso | eng | |
| dc.rights | open access | en_US |
| dc.subject | surface integral equations, spherical harmonics, surface volume surface-EFIE-M formulation, low frequency breakdown, Method of Moments | |
| dc.title | Exact solution of surface-volume-surface electric field integral equation and analysis of its spectral properties | |
| dc.type | doctoral thesis | en_US |
| local.subject.manitoba | no |