Related papers: Fast Higher-Order Interpolation and Restriction in…
Gravitational-wave analyses depend heavily on waveforms that model the evolution of compact binary coalescences as seen by observing detectors. In many cases these waveforms are given by waveform approximants, models that approximate the…
We present a novel methodology for deriving high-order volume elements (HOVE) designed for the integration of scalar functions over regular embedded manifolds. For constructing HOVE we introduce square-squeezing --a homeomorphic multilinear…
The physical characteristics and evolution of a large-scale helium plume are examined through a series of numerical simulations with increasing physical resolution using adaptive mesh refinement (AMR). The five simulations each model a 1~m…
Keeping Einstein's equations in second order form can be appealing for computational efficiency, because of the reduced number of variables and constraints. Stability issues emerge, however, which are not present in first order…
We propose a high order numerical homogenization method for dissipative ordinary differential equations (ODEs) containing two time scales. Essentially, only first order homogenized model globally in time can be derived. To achieve a high…
We present an improved high-order weighted compact high resolution (WCHR) scheme that extends the idea of weighted compact nonlinear schemes (WCNS's) using nonlinear interpolations in conjunction with compact finite difference schemes for…
The Event Horizon Telescope (EHT) has recently released high-resolution images of accretion flows onto two supermassive black holes. Our physical understanding of these images depends on accuracy and precision of numerical models of plasma…
Numerical simulations of merging black hole binaries produce the most accurate gravitational waveforms. The availability of hundreds of these numerical relativity (NR) waveforms, often containing many higher spherical harmonic modes, allows…
Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…
Isosurface visualization is fundamental for exploring and analyzing 3D volumetric data. Marching cubes (MC) algorithms with linear interpolation are commonly used for isosurface extraction and visualization. Although linear interpolation is…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…
In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for…
We derive formulas for the leading mass, entropy, and long-range self-force corrections to extremal black holes due to higher-derivative operators. These formulas hold for black holes with arbitrary couplings to gauge fields and moduli,…
Blurred reflection features are commonly observed in the X-ray spectra of accreting black holes. In the presence of high-quality data and with the correct astrophysical model, X-ray reflection spectroscopy is a powerful tool to probe the…
Interpolatory methods offer a powerful framework for generating reduced-order models (ROMs) for non-parametric or parametric systems with time-varying inputs. Choosing the interpolation points adaptively remains an area of active interest.…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
Numerical simulation of the complex plasma dynamics associated with high power, high frequency microwave breakdown at high pressures, leading to the formation of filamentary plasma structures such as self-organized plasma arrays, is a…
Measurements of the angular momentum (spin) of astrophysical black holes are extremely important, as they provide information on the black hole formation and evolution. We present simulated observations of a X-ray binary system with the…