Prof. Nicodemus Abungu Odero

Citation:

Odero AN. HYBRID METHOD OF MOMENTS (MOM)/FINITE ELEMENT METHOD (FEM) FORMULATION FOR PROBLEMS OF TRANSMISSION THROUGH NON-BACKED AND WAVEGUIDE-BACKED CAVITIES OF ARBITRARY SHAPE IN THICK CONDUCTING SCREENS . Benard KD, ed. Juja: JKUAT; 2007.

Thesis Type:

Abstract:

Concerted efforts have been made towards developing more elaborate techniques for solving aperture coupling problems. The majority of these techniques, however, deal with apertures of regular shapes and, in each case, only a particular problem has been solved. It is only with the development of numerical methods, such as the Method of Moments and Finite Element Method that it has become possible to treat irregularly shaped apertures.

However, each of the above methods has its own advantages and disadvantages when applied to different problems. The Method of Moments is an integral equation method which handles unbounded problems very effectively but becomes computationally intensive when material and structural inhomogeneities exist. In contrast, the true power of the finite element method is revealed in three-dimensional volume formulations in the presence of material and structural inhomogeneities. The method requires less computer time and storage because of its sparse and banded matrix. The matrix filling time is also negligible when simple basis functions are used. For complex basis functions, the matrix filling time can be significant.

A suitably implemented hybrid method takes advantage of the strengths of the individual methods constituting it while avoiding their weaknesses. This research therefore, as one of its objectives, has developed a hybrid method that combines the method of moments and the finite element method (MOM/FEM). The analysis is based upon the "generalized network formulation" for aperture problems. The cavity region is subdivided into tetrahedral elements resulting in triangular elements on the surfaces of the apertures.

In this work, a hybrid MOM/FEM solution procedure for the general problem of apertures of arbitrary shapes in thick conducting screens and waveguide walls has been developed and used in the analysis of a variety of representative problems. Appropriate modeling of the aperture/cavity has been carried out using tetrahedral and triangular elements. Suitably defined sets of basis functions have been integrated into the formulation which is capable of accurately evaluating fields of apertures of arbitrary shape. The problem has been formulated by invoking the equivalence principles and utilizing boundary conditions on the apertures/cavity to derive equations which have then been transformed into matrices that are then solved numerically by simulation on a digital computer. The finite element method, employing reliable vector formulation, has been employed in the computation of the interior admittance matrix. Here, edge elements or tetrahedra in which the degrees of freedom are assigned to the edges rather than the nodes are utilized. This resulted in the avoidance of nonphysical or spurious modes, a difficulty that arises when node-based elements are used. Based on the preceding formulation, extensive computation of various parameters for apertures/cavities of various shapes has been done and results presented. The two main classes of problems treated in this study comprise apertures of arbitrary shape in thick conducting screens and waveguide-backed apertures.