A bstract-A general method is presented for amalysis of wavegoide jonctions and diaphragms hy smnrning normal modes of propagation. giving solutions for the resulting scattered modes. Beeause interaction effeets of dominant and higher-order modes between discontkndtiea are allowed, tirdte-length obstructions can be stodied.Solutions are found without auy prior assumption about the total fields existing at the discontirndties and, as a reaott, the formrdation is applicable to a wide range of problems. The tecbrriqne proves to be simple and is ideally suited to computers, involving mainly the solution of sets of sirmdtaneous liiear equations. Thick and thin symmetrical bifurcations of a rectangrdar guide are studied. Forward-scattered mode amplitudes and iopnt admittances are calculated, the computed admittance of the thin bifurcation is compared with well-knowu results, and transverse field patterns on both sides of the junction are plotted, thus showing the accuracy of the matclh.The results of a tirrite-length bifurcation by a thick vane are presented for a range of lengths, the parameters of the equivalent T network being given in each case. For very short lengths, the problem corresponds to an inductive strip across the guide.

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Use of the Green function, for the solution of boundary-value problems, frequently results in singular integral equations. Algorithms arc presented for the accurate and efficient treatment of singular kernels frequently encountered in the boundary element method (BEM). They are based upon the use of appropriately weighted Gaussian quadrature formulae, together with numerical geometrical transformations of the region of integration. The use of high-order subdomain expansion functions, for interpolation over nonplanar elements, allows boundary curvature to be accommodated. In particular, thc handling of Green functions with logarithmic and r -' behaviour are detailed. Volume integrals, with r singularity, are outlined.Operations are performed on a simplex, thus resulting in generality and ease of automation. This scheme has been incorporated into boundary element method software and successfully applied to a variety of problems.

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