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A highly efficient and accurate higher order large-domain finite-element technique is presented for three-dimensional (3-D) analysis of N-port waveguide structures with arbitrary metallic and dielectric discontinuities on standard PCs. The technique implements hierarchical polynomial vector basis functions of arbitrarily high field-approximation orders on Lagrange-type curved hexahedral finite elements of arbitrary geometrical orders. Preprocessing is carried out by a semiautomatic higher order meshing procedure developed for waveguide discontinuity problems. The computational domain is truncated by coupling the 3-D finite-element method (FEM) with a two-dimensional (2-D) modal expansion technique across the waveguide ports. In cases where analytical solutions are not available, modal forms at the ports are obtained by a higher order 2-D FEM eigenvalue analysis technique. The examples demonstrate very effective higher order hexahedral meshes constructed from a very small number of large curved finite elements (large domains). When compared to the existing higher order (but small domain) finite-element solutions, the presented models require approximately 1/5 of the number of unknowns for the same (or higher) accuracy of the results.