Related papers: Numerical solution of the wave propagation problem…
A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…
We propose a novel formulation for parametric finite element methods to simulate surface diffusion of closed curves, which is also called as the curve diffusion. Several high-order temporal discretizations are proposed based on this new…
Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…
This article investigates the velocity dispersion and the spurious reflection of the viscoelastic wave that occur in the numerical integration of the viscoelastic wave equation. For this purpose, the classic finite element of two nodes,…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
Optical properties of hybrid plasmonic waveguides and of low-Q cavities, formed by waveguides of finite length are investigated numerically. These structures are of interest as building-blocks of plasmon lasers. We use a time-harmonic…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…
We have developed a computational method to describe the nonlinear light propagation of an intense and ultrashort pulse at oblique incidence on a flat surface. In the method, coupled equations of macroscopic light propagation and…
Towards identifying the number of minimal surfaces sharing the same boundary from the geometry of the boundary, we propose a numerical scheme with high speed and high accuracy. Our numerical scheme is based on the method of fundamental…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…
Due to the nonlocal feature of fractional differential operators, the numerical solution to fractional partial differential equations usually requires expensive memory and computation costs. This paper develops a fast scheme for fractional…
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
We report a special phenomenon: trailing waves. They are generated by the propagation of elastic waves in plates at large frequency-thickness (fd) product. Unlike lamb waves and bulk waves, trailing waves are a list of non-dispersive pulses…
This study is concern with the numerical solution of the initial boundary value problem (IBVP) for the semilinear scale-invariant wave equation with damping and mass and power non-linearity. Numerical results of the aforementioned IBVP is…
The approximation properties of a quadratic iso-parametric finite element method for a typical cavitation problem in nonlinear elasticity are analyzed. More precisely, (1) the finite element interpolation errors are established in terms of…
When a pulsed, few-cycle electromagnetic wave is focused by optics with f-number smaller than two, the frequency components it contains are focused to different regions of space, building up a complex electromagnetic field structure.…
Light transmission through circular subwavelength apertures in metallic films with surrounding nanostructures is investigated numerically. Numerical results are obtained with a frequency-domain finite-element method. Convergence of the…
We consider time-harmonic scalar transmission problems between dielectric and dispersive materials with generalized Lorentz frequency laws. For certain frequency ranges such equations involve a sign-change in their principle part. Due to…