Related papers: Adaptive mesh and geodesically sliced Schwarzschil…
The standard approach to the numerical evolution of black hole data using the ADM formulation with maximal slicing and vanishing shift is extended to non-symmetric black hole data containing black holes with linear momentum and spin by…
Given the compact binary evolution problem of numerical relativity, in the finite-difference, block-based, adaptive mesh refinement context, choices must be made on how evolved fields are to be discretized. In GR-Athena++, the space-time…
This article describes a new, fully adaptive Particle-Multiple-Mesh numerical simulation code developed primarily for simulations of small regions (such as a group of galaxies) in a cosmological context. It integrates the equations of…
The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism…
3D Gaussian Splatting (3DGS) has become one of the most influential works in the past year. Due to its efficient and high-quality novel view synthesis capabilities, it has been widely adopted in many research fields and applications.…
The well-known Schwarzschild black hole was first obtained as a stationary, spherically symmetric solution of the Einstein's vacuum field equations. But until thirty years later, efforts were made for the analytic extension from the…
The equations governing null and timelike geodesics are derived within the 3+1 formalism of general relativity. In addition to the particle's position, they encompass an evolution equation for the particle's energy leading to a 3+1…
When fitting Gaussian Mixture Models to 3D geometry, the model is typically fit to point clouds, even when the shapes were obtained as 3D meshes. Here we present a formulation for fitting Gaussian Mixture Models (GMMs) directly to a…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
Given a spherical spacelike three-geometry, there exists a very simple algebraic condition which tells us whether, and in which, Schwarzschild solution this geometry can be smoothly embedded. One can use this result to show that any given…
An implementation of adaptive mesh refinement algorithms is presented for use with multilayer shallow water equations. Currently, adaptive mesh refinement is implemented with a single layer shallow water model in the GeoClaw framework. This…
We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field during materials processing. Our numerical approach uses the systematic renormalization-group formulation of the phase field…
This work introduces Adaptive Density Fields (ADF), a geometric attention framework that formulates spatial aggregation as a query-conditioned, metric-induced attention operator in continuous space. By reinterpreting spatial influence as…
We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS…
We consider 3-point numerical schemes for scalar Conservation Laws, that are oscillatory either to their dispersive or anti-diffusive nature. Oscillations are responsible for the increase of the Total Variation (TV); a bound on which is…
We derive a formalism of numerical relativity for higher-dimensional spacetimes and develop numerical codes for simulating a wide variety of five-dimensional (5D) spacetimes for the first time. First, the Baumgarte-Shapiro-Shibata-Nakamura…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
We present a new pseudospectral code, bamps, for numerical relativity written with the evolution of collapsing gravitational waves in mind. We employ the first order generalized harmonic gauge formulation. The relevant theory is reviewed…
Astrophysical relativistic flow problems require high resolution three-dimensional numerical simulations. In this paper, we describe a new parallel three-dimensional code for simulations of special relativistic hydrodynamics (SRHD) using…
Through full solvability of 2+1 dimensional general relativity we derive out exact dynamic inner metric of collapsing stars with inhomogeneous initial mass distribution but joining with outside Anti-deSitt-Schwarzschild black holes…