相关论文: NRPyElliptic: A Fast Hyperbolic Relaxation Ellipti…

We study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic problems: data completion problems for Poisson's and heat equations. We define an abstract setting to treat both equations at once. We…

An additive Runge-Kutta method is used for the time stepping, which integrates the linear stiff terms by an explicit singly diagonally implicit Runge-Kutta (ESDIRK) method and the nonlinear terms by an explicit Runge-Kutta (ERK) method. In…

We have developed a new numerical scheme to obtain quasiequilibrium structures of nonaxisymmetric compact stars such as binary neutron star systems as well as the spacetime around those systems in general relativity. Concerning…

We present the first results on the construction of an exascale hyperbolic PDE engine (ExaHyPE), a code for the next generation of supercomputers with the objective to evolve dynamical spacetimes of black holes, neutron stars and binaries.…

We present an algorithm for solving the general relativistic initial value equations for a corotating polytropic star in quasicircular orbit with a nonspinning black hole. The algorithm is used to obtain initial data for cases where the…

Bayesian Physics Informed Neural Networks (BPINN) have attracted considerable attention for inferring the system states and physical parameters of differential equations according to noisy observations. However, in practice, Hamiltonian…

It is well known that multigrid methods are optimally efficient for solution of elliptic equations (O(N)), which means that effort is proportional to the number of points at which the solution is evaluated). Thus this is an ideal method to…

We investigate the interplay between numerical relativity (NR) and point-particle black hole perturbation theory (ppBHPT) for quasi-circular non-spinning binary black holes in the intermediate mass ratio regime: 7<=q<=128 (where…

This paper presents a systematic exploration of exact solutions for electrically charged wormholes, black holes, and black bounces within the hybrid metric-Palatini gravity (HMPG) framework. HMPG combines features of the metric and Palatini…

In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…

The main objective of this work is the construction of regular black hole solutions in the context of the Einstein-Maxwell theory. The strategy is to match an interior regular solution to an exterior electrovacuum solution. With this…

A numerical method for variable coefficient elliptic problems on two dimensional domains is described. The method is based on high-order spectral approximations and is designed for problems with smooth solutions. The resulting system of…

A common strategy in the numerical solution of partial differential equations is to define a uniform discretization of a tensor-product multi-dimensional logical domain, which is mapped to a physical domain through a given coordinate…

Implicit particle-in-cell codes offer advantages over their explicit counterparts in that they suffer weaker stability constraints on the need to resolve the higher frequency modes of the system. This feature may prove particularly valuable…

We present a new approach to the problem of binary black holes in the pre-coalescence stage, i.e. when the notion of orbit has still some meaning. Contrary to previous numerical treatments which are based on the initial value formulation of…

In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic partial differential equations by saddle-point mixed finite element methods of arbitrary polynomial degree $p \ge 0$ on…

We present a new study of remnant black hole properties from 13 binary black hole systems, numerically evolved using the Spectral Einstein Code. The mass, spin, and recoil velocity of each remnant were determined quasi-locally from apparent…

We present improvements to construction of binary black hole initial data used in SpEC (the Spectral Einstein Code). We introduce new boundary conditions for the extended conformal thin sandwich elliptic equations that enforce the excision…

A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the…

Recent works have demonstrated the viability of utilizing over-fitted implicit neural representations (INRs) as alternatives to autoencoder-based models for neural video compression. Among these INR-based video codecs, Neural Video…