相关论文: Spectral Methods for Numerical Relativity
We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.
We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral…
Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…
In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of spectral methods. The main features of this method are its…
Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…
It was recently demonstrated that time-dependent PDE problems can numerically be solved with a fully pseudospectral scheme, i.e. using spectral expansions with respect to both spatial and time directions (Hennig and Ansorg, 2009 [15]). This…
We derive the evolution equations for the spectra of the Universe. Here "spectra" means the eigenvalues of the Laplacian defined on a space, which contain the geometrical information on the space. These equations are expected to be useful…
We present an overview of recent developments in numerical relativity studies of higher dimensional spacetimes with a focus on time evolutions of black-hole systems. After a brief review of the numerical techniques employed for these…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
Two combined methods for computing solutions of time-varying semilinear differential-algebraic equations (descriptor systems) are obtained. When constructing the methods, time-varying spectral projectors which can be found numerically are…
Orbital solutions for binary or multiple stellar systems that combine astrometry (e.g., position angles and angular separations) with spectroscopy (radial velocities) have important advantages over astrometric-only or spectroscopic-only…
We present a numerical technique for solving evolution equations, as the wave equation, in the description of rotating astrophysical compact objects in comoving coordinates, which avoids the problems associated with the light cylinder. The…
The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on…
Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order…
We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type $\Delta \vec{N} + \lambda…
Self-adjoint operators on infinite-dimensional spaces with continuous spectra are abundant but do not possess a basis of eigenfunctions. Rather, diagonalization is achieved through spectral measures. The SpecSolve package [SIAM Rev., 63(3)…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
We are entering an era where the numerical construction of generic spacetimes is becoming a reality. The use of computer simulations, in principle, allows us to solve Einstein equations in their full generality and unravel important…
We develop a sparse spectral method for a class of fractional differential equations, posed on $\mathbb{R}$, in one dimension. These equations can include sqrt-Laplacian, Hilbert, derivative and identity terms. The numerical method utilizes…
Spectroscopy is one of the most important tools that an astronomer has for studying the universe. This chapter begins by discussing the basics, including the different types of optical spectrographs, with extension to the ultraviolet and…