Related papers: A spectral method algorithm for numerical simulati…
We present techniques for successfully performing numerical relativity simulations of binary black holes with fourth-order accuracy. Our simulations are based on a new coding framework which currently supports higher order finite…
We present the improved Mathematica code which computes quasinormal frequencies with the help of the Bernstein spectral method for a general class of black holes, allowing for asymptotically flat, de Sitter or anti-de Sitter asymptotic. The…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
Second-order self-force calculations will be critical for modelling extreme-mass-ratio inspirals, and they are now known to have high accuracy even for binaries with mass ratios $\sim 1:10$. Many of the challenges facing these calculations…
One of the most suitable methods for modeling fully dynamic earthquake cycle simulations is the spectral boundary integral element method (sBIEM), which takes advantage of the fast Fourier transform (FFT) to make a complex numerical dynamic…
In this paper an approach for decreasing the computational effort required for the split-step Fourier method (SSFM) is introduced. It is shown that using the sparsity property of the simulated signals, the compressive sampling algorithm can…
As a complementary tool to laboratory experiments, discrete numerical simulation, applied to granular materials, provides valuable information on the grain and contact scale microstructure, thereby enabling one to better understand the…
Pseudospectral analyses have broadened our understanding of ringdown waveforms from binary remnants, by providing insight into both the stability of their characteristic frequencies under environmental perturbations, as well as the…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
This paper presents DENSER, an efficient and effective approach leveraging 3D Gaussian splatting (3DGS) for the reconstruction of dynamic urban environments. While several methods for photorealistic scene representations, both implicitly…
We construct a simple algorithm to derive number density of spin 1/2 particles created in spatially flat FLRW spacetimes and resulting renormalized energy-momentum tensor within the framework of adiabatic regularization. Physical quantities…
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
We propose a new smoothing method for obtaining surface densities from discrete particle positions from numerical simulations. This is an essential step for many applications in gravitational lensing. This method is based on the ``scatter''…
We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field…
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…
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has been recently proposed able to generate high velocity gradients…
A spectral method is considered for approximating the fractional Laplacian and solving the fractional Poisson problem in 2D and 3D unit balls. The method is based on the explicit formulation of the eigenfunctions and eigenvalues of the…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
We present a new numerical scheme which combines the Spectral Difference (SD) method up to arbitrary high order with \emph{a-posteriori} limiting using the classical MUSCL-Hancock scheme as fallback scheme. It delivers very accurate…
There has been an increasing interest in developing efficient immersed boundary method (IBM) based on Cartesian grids, recently in the context of high-order methods. IBM based on volume penalization is a robust and easy to implement method…