Related papers: GRChombo : Numerical Relativity with Adaptive Mesh…
High-precision regression of physical parameters from black hole images generated by General Relativistic Ray Tracing (GRRT) is essential for investigating spacetime curvature and advancing black hole astrophysics. However, due to…
Numerical codes based on a direct implementation of the standard ADM formulation of Einstein's equations have generally failed to provide long-term stable and convergent evolutions of black hole spacetimes when excision is used to remove…
The detection of gravitational waves has opened a new era for astronomy, allowing for the combined use of gravitational wave and electromagnetic emissions to directly probe the physics of compact objects, still poorly understood. So far,…
We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a…
Standard Bayesian Optimization (BO) assumes uniform smoothness across the search space an assumption violated in multi-regime problems such as molecular conformation search through distinct energy basins or drug discovery across…
When numerically solving partial differential equations, for a given problem and operating condition, adaptive mesh refinement (AMR) has proven its efficiency to automatically build a discretization achieving a prescribed accuracy at low…
We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…
We consider the spherically reduced Einstein-Hilbert action, Einstein field equations and Schwarzschild spacetime modified by a renormalization-group (RG) scale-dependent gravitational Newton coupling, and present a systematic and…
Spherically symmetric (1D) black-hole spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein's equations with the harmonic slicing condition is presented.…
Implementation details and test cases of a newly developed hydrodynamic code, AMRA, are presented. The numerical scheme exploits the adaptive mesh refinement technique coupled to modern high-resolution schemes which are suitable for…
The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…
In recent work we have shown how an accurate reduced model can be utilized to perform mesh refinement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity…
In this paper we present an adaptive discretization technique for solving elliptic partial differential equations via a collocation radial basis function partition of unity method. In particular, we propose a new adaptive scheme based on…
Recent gravitational wave observations of binary black hole mergers and a binary neutron star merger by LIGO and Virgo Collaborations associated with its optical counterpart constrain deviation from General Relativity (GR) both on…
We present a new code, CASTRO, that solves the multicomponent compressible hydrodynamic equations for astrophysical flows including self-gravity, nuclear reactions and radiation. CASTRO uses an Eulerian grid and incorporates adaptive mesh…
Current Adaptive Mesh Refinement (AMR) simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient…
A new extremely simple ensemble-based model with the uniformly generated axis-parallel hyper-rectangles as base models (HRBM) is proposed. Two types of HRBMs are studied: closed rectangles and corners. The main idea behind HRBM is to…
Modified Growth with {\tt CAMB} ({\tt MGCAMB}) is a patch for the Einstein-Boltzmann solver {\tt CAMB} for cosmological tests of gravity. Until now, {\tt MGCAMB} was limited to scales well-described by linear perturbation theory. In this…
We have developed a numerical code to study the evolution of self-gravitating matter in dynamic black hole axisymmetric spacetimes in general relativity. The matter fields are evolved with a high-resolution shock-capturing scheme that uses…
In this paper, we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum (a/c) coupling with finite range interactions in two dimensions. We have…