In this paper, we construct numerical schemes for spectral collocation methods and spectral variational integrators which converge geometrically. We present a systematic comparison of how spectral collocation methods and Galerkin spectral variational integrators perform in terms of their ability to reproduce accurate trajectories in configuration and phase space, their ability to conserve momen...

Dolph-Chebychev arrays are known to exhibit the best compromise between sidelobe level and directivity. However, they place a constraint on the null locations. Any attempt to impose nulls or get them deeper will impact the directivity/sidelobe level trade-off. In this work, null placement in Dolph-Chebychev arrays through element position perturbation is carried out based on Taguchi method whil...

— The conservation and convergence properties o f spectral Fourier methods for the numerical approximation o f the Korteweg-de Vries équation are analyzed. It is proven thaï the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point ofview. This resuit provides a précise mathematica...

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...

We present a Python module named PyCheb, to solve the ordinary differential equations by using spectral collocation method. PyCheb incorporates discretization using Chebyshev points, barycentric interpolation and iterate methods. With this Python module, users can initialize the ODEsolver class by passing attributes, including the both sides of a given differential equation, boundary conditions...

A boundary variation method for the fast and accurate modeling of three-dimensional waveguide grating couplers is presented. The algorithm is verified by detailed comparisons with the results of a rigorous spectral collocation method, showing excellent agreement. Examples of the modeling of large waveguide grating couplers are given to illustrate the applicability and versatility of the method.

The increasing process variation and spatial correlation between process parameters makes capacitance extraction of interconnects an important yet challenging problem in modern VLSI designs. In this presentation, we will first introduce basic capacitance extraction flow follow by advance model considering process variation (E.g., orthogonal polynomial method). After that, approaches that solve ...

Instability of a viscous incompressible flow between two rotating concentric cylinders has been investigated numerically. The outer cylinder is stationary and the inner one rotates and moves axially simultaneously. D Chebychev tau method is used to solve eigenvalue problem governing the investigation of flow stability, In the Chebychev tau method, the eigen functions of governing equations are ...