Related papers: Improvement of accuracy of the spectral element me…
When numerically solving partial differential equations (PDEs), the first step is often to discretize the geometry using a mesh and to solve a corresponding discretization of the PDE. Standard finite and spectral element methods require…
In this work, we numerically study the higher-ordered/extended Boussinesq system describing the propagation of water-waves over flat topography. A reformulation of the same order of precision that avoids the calculation of high order…
Currently, mass matrices are computed by means of sufficiently accurate numerical integration schemes. Two-point and nine-point (Gauss) quadrature remain frequently used. We derive an exact, easy to implement integration rule for six-node…
Acoustic wave propagation in a fluid with a random assortment of identical cylindrical scatterers is considered. While the leading order correction to the effective wavenumber of the coherent wave is well established at dilute areal density…
We present a new class of efficient and robust discontinuous spectral-element methods of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular and tetrahedral unstructured grids. Such discretizations…
The INTEGRAL/SPI, X-gamma-ray spectrometer (20 keV - 8 MeV) is an instrument for which recovering source intensity variations is not straightforward and can constitute a difficulty for data analysis. In most cases, determining the source…
The paper presents an approach for the identification of elasto-static parameters of a robotic manipulator using the virtual experiments in a CAD environment. It is based on the numerical processing of the data extracted from the finite…
A version of the projection method for solving the scattering problem for acoustic and electromagnetic waves is proposed and shown to be more efficient numerically than the earlier ones because the corresponding matrix is not…
End-to-end optimization, which simultaneously optimizes optics and algorithms, has emerged as a powerful data-driven method for computational imaging system design. This method achieves joint optimization through backpropagation by…
The complex interplay of elastic and inelastic scattering amenable to different levels of approximation constitutes the major challenge for the computation and hence interpretation of TEM-based spectroscopical methods. The two major…
Previous studies of the response of the Moon to gravitational waves have been carried out using analytical or semi-analytical models assuming ideal lunar structures. Such models are advantageous for their high-speed calculation but fail to…
We propose a short-memory operator splitting scheme for solving the constant-Q wave equation, where the fractional stress-strain relation contains multiple Caputo fractional derivatives with order much smaller than 1. The key is to exploit…
In this paper, we propose and analyse a numerical method to solve 2D Dirichlet time-harmonic elastic wave equations. The procedure is based on the decoupling of the elastic vector field into scalar Pressure ($P$-) and Shear ($S$-) waves via…
The coherent propagation of elastic waves in a solid filled with a random distribution of pinned dislocation segments is studied to all orders in perturbation theory. It is shown that, within the independent scattering approximation, the…
We introduce a \textit{non-modal} analysis technique that characterizes the diffusion properties of spectral element methods for linear convection-diffusion systems. While strictly speaking only valid for linear problems, the analysis is…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant…
Staggered grid finite difference scheme is widely used for the first order elastic wave equation, which constitutes the basis for least-squares reverse time migration and full waveform inversion. It is of great importance to improve the…
We present a novel approach for the numerical solution of problems of elastic scattering by open arcs in two dimensions. Our methodology relies on the composition of weighted versions of the classical operators associated with Dirichlet and…
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…