This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems. Our model equation is a phase-field model of infiltration, but the proposed discretization can be directly extended to similar equations arising in thin film flows. The sharpness and structure of the wetting front preclude the use of the standard Chebysh...

Pseudo-spectral method is one of the most accurate techniques for simulating turbulent flows. Fast Fourier transform (FFT) is an integral part of this method. In this paper, we present a new procedure to compute FFT in which we save operations during interprocess communications by avoiding transpose of the array. As a result, our transpose-free FFT is 15% to 20% faster than FFTW.

In this paper, a two-step regularization method is used to solve an ill-posed spherical pseudo-differential equation in the presence of noisy data. For the first step of regularization we approximate the data by means of a spherical polynomial that minimizes a functional with a penalty term consisting of the squared norm in a Sobolev space. The second step is a regularized collocation method. A...

The von-K arm an non-linear, dynamic, partial differential system over rectangular domains is solved by the Chebyshev-collocation method in space and the implicit Newmark-b time marching scheme in time. In the Newmark-b scheme, a non-linear fixed point iteration algorithm is employed. We monitor both temporal and spatial discretization errors based on derived analytical solutions, demonstrating...

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 ...

We present the OptiBounce algorithm, a new and fast method for finding bounce action cosmological phase transitions. This is done by direct solution of “reduced” minimisation problem proposed Coleman, Glaser, Martin. Using formula action, our avoids rescaling step used in other algorithms based on this formulation. The path represented using pseudo-spectral Gauss-Legendre collocation scheme lea...