Related papers: A recursive approach for the finite element comput…
Assembling stiffness matrices represents a significant cost in many finite element computations. We address the question of optimizing the evaluation of these matrices. By finding redundant computations, we are able to significantly reduce…
Linear electromagnetic wave scattering systems can be characterized by an impedance matrix that relates the voltages and currents at the ports of the system. When the system size becomes greater than the wavelength of the fields involved,…
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also…
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…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
This article takes the form of a tutorial on the use of a particular class of mixed finite element methods, which can be thought of as the finite element extension of the C-grid staggered finite difference method. The class is often…
We begin by addressing the time-domain full-waveform inversion using the adjoint method. Next, we derive the scaled boundary semi-weak form of the scalar wave equation in heterogeneous media through the Galerkin method. Unlike conventional…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
An adaptive moving mesh finite element method is proposed for the numerical solution of the regularized long wave (RLW) equation. A moving mesh strategy based on the so-called moving mesh PDE is used to adaptively move the mesh to improve…
Microstructured materials, such as architected metamaterials and phononic crystals, exhibit complex wave propagation phenomena due to their internal structure. While full-scale numerical simulations can capture these effects, they are…
Time-harmonic solutions to the wave equation can be computed in the frequency or in the time domain. In the frequency domain, one solves a discretized Helmholtz equation, while in the time domain, the periodic solutions to a discretized…
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…
In this paper, we develop an accurate and efficient framework for computing subwavelength guided modes in high-contrast periodic media with line defects, based on a tight-binding approximation. The physical problem is formulated as an…
Truss structures at macro-scale are common in a number of engineering applications and are now being increasingly used at the micro-scale to construct metamaterials. In analyzing the properties of a given truss structure, it is often…
The finite element method is one of the widely employed numerical techniques in electrical engineering for the study of electric and magnetic fields. When applied to the moving conductor problems, the finite element method is known to have…
A numerical implementation of the transition state theory (TST) is presented which can be used to calculate the attempt frequency $f_{0}$ of arbitrary shaped magnetic nanostructures. The micromagnetic equations are discretized using the…
A general-purpose computational homogenization framework is proposed for the nonlinear dynamic analysis of membranes exhibiting complex microscale and/or mesoscale heterogeneity characterized by in-plane periodicity that cannot be…
A discrete-module-finite element (DMFE) based hydroelasticity method has been proposed and well developed. Firstly, a freely floating flexible structure is discretized into several macro-submodules in two horizontal directions to perform a…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
We calculate the net energy per unit time exchanged between two sets of modes in a generic system governed by a three-wave kinetic equation. Our calculation is based on the property of detailed energy conservation of the triadic resonant…