Related papers: Finite Element Approximation and Analysis of Visco…
Space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analyzed. This model includes waves with finite speed, as well as…
We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle $ \Omega \subset \mathbb{R}^3 $. From the Stratton-Chu integral representation, we derive a new representation formula when constant…
The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or bounded kernels in the diffusion term. The presented…
The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives…
We consider the scattering of in-plane waves that interact with an edge of a structured {penetrable (inertial)} line defect contained in a triangular lattice, composed of periodically placed masses interconnected by massless elastic rods.…
The variational multiscale (VMS) formulation formally segregates the evolution of the coarse-scales from the fine-scales. VMS modeling requires the approximation of the impact of the fine scales in terms of the coarse scales. In linear…
We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations to represent large-scale sea-ice dynamics. However, the…
This paper presents a new method to approximate the time-dependent convection-diffusion equations using conforming finite element methods, ensuring that the discrete solution respects the physical bounds imposed by the differential…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
Travelling solitary waves in the one-dimensional discrete nonlinear Schr\"{o}dinger equation (DNLSE) with saturable onsite nonlinearity are studied. A variational approximation (VA) for the solitary waves is derived in an analytical form.…
Consider the scattering of a time-harmonic elastic plane wave by a bi-periodic rigid surface. The displacement of elastic wave motion is modeled by the three-dimensional Navier equation in an open domain above the surface. Based on the…
We study an inverse problem for the viscoacoustic wave equation, an integro-differential model describing wave propagation in viscoacoustic media with memory in the leading order term. The medium is characterized by a spatially varying…
The scalar wave equation is solved using higher order immersed finite elements. We demonstrate that higher order convergence can be obtained. Small cuts with the background mesh are stabilized by adding penalty terms to the weak…
Existing methods rarely capture the temporal evolution of solution norms in vector nonlinear DDEs with variable delays and coefficients, often leading to overly conservative boundedness and stability criteria. We develop a framework that…
We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…
In this paper we propose a new mixed virtual element formulation for the numerical approximation of viscoelasticity equations with weakly imposed stress symmetry. The governing equations use the Zener model and are expressed in terms of the…
The paper is concerned with comparative analysis of differential and integral formulations for boundary value problems in nonlocal elasticity. For the sake of simplicity, the focus is on an antiplane problem for a half-space for an…
In this work, we introduce a new space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable, and a modified Hilbert transformation is used. For this…
This paper presents a boundary element formulation for the solution of the Mild-Slope equation in wave propagation problems with variable water depth in one direction. Based on the Green's function approximation proposed by Belibassakis…
We present a numerical approach to efficiently calculate spin-wave dispersions and spatial mode profiles in magnetic waveguides of arbitrarily shaped cross section with any non-collinear equilibrium magnetization which is translationally…