Efficient finite element electromagnetic analysis of antennas and microwave devices : the FE-BI-FMM formulation and a posteriori error estimation for p adaptive analysis

[摘要] ENGLISH ABSTRACT:This document presents a Galerkin FE formulation for the full-wave, frequency domain,electromagnetic analysis of three dimensional structures relevant to microwave engineering,together with the investigation of two techniques to enhance the formulation's computationalefficiency. The first technique considered is the fast multi pole method (FMM) and the secondtechnique is adaptive refinement of the discretization, based on a posteriori error estimation.Thus, the motivation for the work presented in this document is to increase the computationalefficiency of the FE formulation considered.The FE formulation considered is widely used within the microwave engineering, finite elementcommunity. Tetrahedral, rectilinear, curl-conforming, mixed- and full order, hierarchicalvector elements are used. The formulation is extended to incorporate a cavity backedaperture employing the appropriate half-space Green function within a BI boundary condition,which represents a specific member of a large class of hybrid FE-BI formulations. Theformulation is also extended to model coaxial ports via a Neumann boundary condition, usinga priori knowledge of the dominant modal fields. Results are presented in support of theformulation and its extensions, including novel results on the coupling between microstrippatch antennas on a perforated substrate.The FMM is investigated first, with the purpose of optimizing the non-local BI componentof the cavity FE-BI formulation, in light of its coupling with the differential equation based,sparse FEM. The FMM results in a partly sparse factorization of the BI contribution tothe system matrix. Error control schemes for the FMM are thoroughly reviewed and anadditional, novel scheme is empirically devised.The second technique investigated, which is more directly related to the FEM and larger inscope, is the use of a posteriori error estimation, in order to optimize the FE discretizationthrough adaptive refinement. A overview of available a posteriori error estimation techniquesin the general FE literature is given as well as a survey of available techniques that arespecifically tailored to Maxwell's equations. Two known approaches within the appliedmathematics literature are adapted to the FE formulation at hand, resulting in two novel,residual based error estimation procedures for this FE formulation - one explicit in natureand the other implicit. The two error estimators are then used to drive a single p adaptiveanalysis cycle of the FE formulation, experimentally demonstrating their effectiveness. Aquasi-static condition is introduced and successfully used to enhance the adaptive algorithm'seffectiveness, independently of the error estimation procedure employed. The novel errorestimation schemes and adaptive results represent the main research contributions of thisstudy.

[发布机构] Stellenbosch University