This paper demonstrates the accuracy of the nonlinear frequency domainmethod in applications to unsteady flow calculations. The basis of themethod is a pseudospectral approach to recast a nonlinear unsteady systemof equations in the temporal domain into a stationary system in the frequency domain. The nonlinear frequency domain method, in principle, provides the rapid convergence of a spectral ...

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A Fourier-matching pseudospectral modal method [PSMM(f)] is developed for analyzing lamellar diffraction gratings or grating stacks. A Chebyshev pseudospectral method is first used to accurately calculate the eigenmodes of the grating layers, and then the Fourier coefficients are matched at the interfaces between the layers. Compared with an existing pseudospectral modal method based on point m...

Abstract. Let T : Ω → C be a matrix-valued function that is analytic on some simplyconnected domain Ω ⊂ C. A point λ ∈ Ω is an eigenvalue if the matrix T (λ) is singular. In this paper, we describe new localization results for nonlinear eigenvalue problems that generalize Gershgorin’s theorem, pseudospectral inclusion theorems, and the Bauer-Fike theorem. We use our results to analyze three non...

The Mindlin–Engelbrecht–Pastrone model is applied to simulating 1D wave propagation in microstructured solids. The model takes into account the nonlinearity in microand macroscale. Numerical solutions are found for the full system of equations (FSE) and the hierarchical equation (HE). The latter is derived from the FSE by making use of the slaving principle. Analysis of results demonstrates goo...

This paper extends an earlier work [Appl. Math. Comput. 140 (2003) 77] to differential-algebraic equations with constraint singularities. Numerical solution of these problems is considered by pseudospectral method with domain decomposition and by giving a condition under which the general linear form problem can easily be transformed to the index reduced form by a simple formulation. Furthermor...

This Addendum provides a revised set of figures containing converged numerical data for total scattering cross section (TSCS), replacing the figures in our recent publication [Opt. Lett. 29, 1393 (2004)]. Due to the use of an overly large time step, our original TSCS data exhibited a systematic, nonphysical diminution above 150 THz for all cases studied. We have determined that numerical conver...

in this paper, an advanced formulation of the spectral finite element method (sfem) is presented and applied in order to carry out site response analysis of 2d topographic structures subjected to vertically propagating incident in-plane waves in time-domain. the accuracy, efficiency and applicability of the formulation are demonstrated by solving some wave scattering examples. a numerical param...

Two different numerical methods for solving a non-self-adjoint evolution equation are compared in this paper. If the initial function lies in the domain of the operator, a recently proposed method that combines pseudospectral ideas and semigroup theory is shown to be considerably more accurate than a standard discretization method. One example is worked out in detail, but the methods used are o...