相关论文: Excision and avoiding the use of boundary conditio…

We study the free boundary problem for the equations of compressible Euler equations with a vacuum boundary condition. Our main goal is to recover in Eulerian coordinates the earlier well-posedness result obtained by Lindblad [Lindblad H.,…

We consider the hyperboloidal initial value problem in numerical relativity, motivated by the goal to evolve radiating compact objects such as black hole binaries with a numerical grid that includes null infinity. Unconstrained evolution…

In this paper a new double-domain spectral method to compute binary black hole excision initial data is presented. The method solves a system of elliptic partial differential equations in the exterior of two excised spheres. At the surface…

We investigate expansive solutions of the $N$-body problem in $\mathbb{R}^d$ ($d\ge2$) driven by homogeneous Newtonian potentials of degree $-\alpha$. We establish the existence of half-entire expansive motions with prescribed initial…

We describe in this article a new code for evolving axisymmetric isolated systems in general relativity. Such systems are described by asymptotically flat space-times which have the property that they admit a conformal extension. We are…

Many algorithms require discriminative boundaries, such as separating hyperplanes or hyperballs, or are specifically designed to work on spherical data. By applying inversive geometry, we show that the two discriminative boundaries can be…

A common approach to studying high-dimensional systems with emergent low-dimensional behavior is based on lift-evolve-restrict maps (called equation-free methods): first, a user-defined lifting operator maps a set of low-dimensional…

In our earlier paper [JHEP 0310 (2003) 058], we considered higher dimensional cosmological models with hyperbolic spaces. In particular the eternal accelerating expansion was obtained by studying small perturbation around the critical…

We use the energy method to study the well-posedness of initial-boundary value problems approximated by overset mesh methods in one and two space dimensions for linear constant-coefficient hyperbolic systems. We show that in one space…

The results on the initial boundary value problem for Einstein's vacuum field equation obtained in \cite{friedrich:nagy} rely on an unusual gauge. One of the defining gauge source functions represents the mean extrinsic curvature of the…

We present a strategy for interpreting nonlinear, characteristic-type penalty terms as numerical boundary flux functions that provide provable bounds for solutions to nonlinear hyperbolic initial boundary value problems with open…

We describe an explicit in time, finite-difference code designed to simulate black holes by using the excision method. The code is based upon the harmonic formulation of the Einstein equations and incorporates several features regarding the…

Optimization-based methods are widely used for computing fast, diverse solutions for complex tasks such as collision-free movement or planning in the presence of contacts. However, most of these methods require enforcing non-penetration…

We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a…

For any given spacetime the choice of time coordinate is undetermined. A particular choice is the absolute time associated with a preferred vector field. Using the absolute time Hamilton's equations are $- (\delta H_{c})/(\delta…

We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer…

A study is presented for the non linear evolution of a self gravitating distribution of matter coupled to a massless scalar field. The characteristic formulation for numerical relativity is used to follow the evolution by a sequence of…

There is a growing demand for nonparametric conditional density estimators (CDEs) in fields such as astronomy and economics. In astronomy, for example, one can dramatically improve estimates of the parameters that dictate the evolution of…

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 consider nonlinear hyperbolic conservation laws, posed on a differential (n+1)-manifold with boundary referred to as a spacetime, and in which the "flux" is defined as a flux field of n-forms depending on a parameter (the unknown…