Browsing by Author "Meyer, Frans J. C.(Frans Johannes Christiaan)"

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    The two-dimensional finite element/boundary element method in electromagnetics : formulation, applications, error estimates and mesh adaptive procedures
    (Stellenbosch : Stellenbosch University, 1994) Meyer, Frans J. C.(Frans Johannes Christiaan); Davidson, D. B.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
    ENGLISH ABSTRACT: The Finite Element/Boundary Element (FE/BE) method is a numerical method which has been used successfully in the past few years to solve general electromagnetic problems. This thesis presents a general investigation of the two-dimensional FE/BE method for electromagnetic applications. The Finite Element Method (FEM) is formulated for application to 2D electromagnetic problems. It is shown that the FEM can be coupled to the Boundary Element Method (BEM), with the BEM serving as a Neumann boundary condition, on a boundary enclosing the FEM region. The formulation of the FE/BE method, as a special case of the FEM, is thus also presented. The implementation of the FE/BE method is considered. This involves the calculation of the matrix elements of a number of matrices associated with the FE/BE method as well as the solution of the FE/BE method matrix equation system. A priori solution time and memory requirement estimates for specified accuracies of FE/BE method solutions are also investigated. The 2D FE/BE method is applied to a number of electromagnetic problems for which analytical solutions exist. This serves as validation of the formulation and implementation of the FE/BE method. The 2D FE/BE method is then used to obtain approximated radar-cross section results as well as time domain pulse response results for elongated aerofoil shaped objects. The radar-cross section results are compared to measured results. The 2D FE/BE method is further used to model the effect of a human being on a man-pack radio antenna and vice versa. Electromagnetic radiation from 2D horn antennas, calculated with the 2D FE/BE method, is also considered. A number of a posteriori error estimates and error indicators for FE/BE method solutions of electromagnetic problems are formulated and developed. These include local (in each finite element) and global Element Residual Method (ERM) error estimates. L2 -norm boundary field and boundary field derivative error estimates, a L2 -norm Neumann boundary condition error indicator and radar width and radiation intensity error indicators. The implementation of these error estimates and error indicators is considered and it is shown that these implementation procedures result in highly efficient error estimates with negligible computational times. The a posteriori error estimates and error indicators developed are applied to a number of FEM and FE/BE method solutions of electromagnetic problems. These includes static electric field problems and electromagnetic scattering and radiation problems. The results obtained are used to investigate the accuracy, reliability and applicability of the different error estimates and error indicators when applied to FE/BE method solutions of general electromagnetic problems. Adaptive finite element methods and adaptive FE/BE methods are also considered. Adaptive procedures developed are applied to static electric field problems as well as electromagnetic scattering and radiation problems. Rates of convergence obtained with the adaptive methods are investigated. Conclusions are drawn regarding the work presented in this dissertation as well as further research that needs to be done on this topic.