Related papers: Variational Methods For Phononic Calculations
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by a novel variational method, where the velocity profile is assumed to be monotonic and analytic. Unstable eigenvalues of the Rayleigh…
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…
In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…
Turbulence driven by gyrokinetic instabilities is largely responsible for transport in magnetic fusion devices. To estimate this turbulent transport, integrated modeling codes often use mixing length estimates in conjunction with reduced…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
In contrast to the traditional elastodynamic equations, a more comprehensive formulation of one dimensional (1D) elastodynamic equations is given for inhomogeneous media by using the coordinate transformation method. These modified…
We present a family of Virtual Element Methods for three-dimensional linear elasticity problems based on the Hellinger-Reissner variational principle. A convergence and stability analysis is developed. Moreover, using the hybridization…
We address the numerical simulation of periodic solids (phononic crystals) within the framework of couple stress elasticity. The additional terms in the elastic potential energy lead to dispersive behavior in shear waves, even in the…
Variational quantum algorithms offer a promising framework for solving eigenvalue problems on near-term quantum hardware, yet their applicability beyond electronic structure calculations remains relatively unexplored. In this work, we…
The vertical modes of linearized equations of motion are widely used by the oceanographic community in numerous theoretical and observational contexts. However, the standard approach for solving the generalized eigenvalue problem using…
Wave propagation problems are notoriously difficult to solve. Time-harmonic problems are especially challenging in mid and high frequency regimes. The main reason is the oscillatory nature of solutions, meaning that the number of degrees of…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…
We derive the invariant imbedding equations for plane electromagnetic waves propagating in stratified magnetic media, where both dielectric and magnetic permeabilities vary in one spatial direction in an arbitrary manner. These equations…
We present example applications of an approach to first-principles calculations of vibrational properties of materials implemented within the Exabyte.io platform. We deploy models based on the Density Functional Perturbation Theory to…
This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a…
In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…
Mathematical modeling of resonant waves propagating in 2D periodic infinite lattices is conducted. Rectangular-cell, triangular-cell and hexagonal-cell lattices are considered. Eigenvalues (here eigenfrequencies) of steady-state problems…
We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing…
The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and…