Related papers: 2D numerical simulation of lunar response to gravi…
Forming the Moon by a high-angular momentum impact may explain the Earth-Moon isotopic similarities, however, the post-impact angular momentum needs to be reduced by a factor of 2 or more to the current value (1 L_EM) after the Moon forms.…
The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults,…
The existing predictions of the energy density of gravitational waves produced during preheating mostly rely on computer simulations in which the matter field inhomogeneities essentially behave classically. In this article we follow instead…
The novel idea of weak Galerkin (WG) finite element methods is on the use of weak functions and their weak derivatives defined as distributions. Weak functions and weak derivatives can be approximated by polynomials with various degrees.…
Electromagnetic methods recently proposed for detecting gravitational waves modify the Michelson phase shift analysis (historically employed for special relativity). We suggest that a frequency modulation analysis is more suited to general…
This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary condition. An approximation of this problem combining the finite element and mass redistribution methods is proposed. The mass redistribution…
We report on a systematic study of the dynamics of gravitational waves in full 3D numerical relativity. We find that there exists an interesting regime in the parameter space of the wave configurations: a near-linear regime in which the…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
It is described, explicitly, how a popular, commercially-available software package for solving partial-differential-equations (PDEs), as based on the finite-element method (FEM), can be configured to calculate the frequencies and fields of…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
We address the problem of estimating realistic, spatially varying reflectance for complex planetary surfaces such as the lunar regolith, which is critical for high-fidelity rendering and vision-based navigation. Existing lunar rendering…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
It is found that the wave functions of the Gross-Pitaevskii equation (GPE) often vary significantly in different spatial regions, with some components exhibiting sharp variations while others remain smooth. Solving the GPE on a single mesh,…
We have applied the Finite Element Method to the self-consistent electronic structure calculations of molecules and solids for the first time. In this approach all the calculations are performed in "real space" and the use of non-uniform…
GW approximation is one of the most popular parameter-free many-body methods that goes beyond the limitations of the standard density functional theory (DFT) to determine the excitation spectra for moderately correlated materials and in…
A parallelized three-dimensional (3D) boundary element method is used to simulate the interaction between an incoming solitary wave and a 3D submerged horizontal plate under the assumption of potential flow. The numerical setup follows…
Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the…
Extreme mass ratio binary systems, binaries involving stellar mass objects orbiting massive black holes, are considered to be a primary source of gravitational radiation to be detected by the space-based interferometer LISA. The numerical…
We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…
We propose an efficient finite-element analysis of the vector wave equation in a class of relatively general curved polygons. The proposed method is suitable for an accurate and efficient calculation of the propagation constants of…