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An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the perfectly matched layer (PML) technique. The well-posedness and exponential convergence of the solution are established for the truncated PML problem by developing an equivalent transparent boundary condition. Second, an a posteriori error estimate is deduced for the discrete problem and is used to determine the finite elements for refinements and to determine the PML parameters. Numerical experiments are included to demonstrate the competitive behavior of the proposed adaptive method.

This paper describes a finite element approach to a hybrid-mode analysis of isolated and coupled microwave transmission lines. Both the first and higher-order ordinary elements, as well as singular and infinite elements, are used to solve for the eigenvalues and eigenvectors of the modes propagating along the line. Once the field distribution in the cross section of the line is known the characteristic impedance of the dominant mode propagating along the line can readily be obtained. A perturbational approach is developed for estimating the losses due to conductor and dielectric dissipation and computing the attenuation constant for each mode. Lines treatable by this method may contain an arbitrary number arbitrarily shaped conductors, including a system of conductors either placed above a single ground plane or between two parallel ground planes, and inhomogeneous dielectric regions that can be approximated locally by a number of homogeneous subregions. The results obtained using the finite element procedure have been compared for various types of microwave transmission lines and have been found to agree well with available data. (Author)

The primary aim of this study is to develop a finite element model for elastic scattering by axisymmetric bodies submerged in a heterogeneous ocean acoustic waveguide.