A finite element wave-packet procedure is presented to solve problems of wave propagation in multiscale behavior. The proposed scheme combines the advantages of the finite element and spectral methods. The basic formulation is presented, and the capabilities of the procedure are demonstrated through the solution of some illustrative problems, including a problem that characterizes the mode-conv...

Recent work on octree-based finite-element systems has developed a multigrid solver for Poisson equations on meshes. While the idea of defining a regularly indexed function space has been successfully used in a number of applications, it has also been noted that the richness of the function space is limited because the function values can be coupled across locally disconnected regions. In this ...

Spectral and pseudo spectral methods for advection equations are investigated. A basic framework is given which allows the application of techniques used in finite element analysis to spectral methods with trigonometric polynomials. Error estimates for semidiscrete spectral and pseudo spectral as well as fully discrete explicit pseudo spectral methods are given. The approximation schemes are sh...

An analytical method for evaluating pole-residues in spectral method of moments (MoM) formulations is presented. Spectral integral formulations for periodic structures involve the inverse of the MoM matrix, which exhibits a periodic set of pole singularities, corresponding to the zeros of the matrix’s determinant. So far, these singularities have not been extracted and the corresponding pole-re...

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares; a finite element approximation is used on the first square and a spectral discretization is used on the second. Two kinds of matching conditions on the interface are presented and compared; in both cases, error estimates are proved.