Related papers: Dynamic Implicit 3D Adaptive Mesh Refinement for N…
Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space and computational cost increases geometrically with…
We present a general formalism for computing self-consistent, numerical solutions to the time-dependent radiative transfer equation in low velocity, multi-level ions undergoing radiative interactions. Recent studies of time-dependent…
Context. Time-dependent, 3D radiation transfer calculations are important for the modeling of a variety of objects, from supernovae and novae to simulations of stellar variability and activity. Furthermore, time-dependent calculations can…
Numerical radiation-hydrodynamics (RHD) for non-relativistic flows is a challenging problem because it encompasses processes acting over a very broad range of timescales, and where the relative importance of these processes often varies by…
We develop an asymptotic preserving scheme for the gray radiative transfer equation. Two asymptotic regimes are considered: one is a diffusive regime described by a nonlinear diffusion equation for the material temperature; the other is a…
We present here the first systematic treatment of the problems posed by the visualization and analysis of large-scale, parallel adaptive mesh refinement (AMR) simulations on an Eulerian grid. When compared to those obtained by constructing…
In this paper we explore the possibility for solving the 3D Maxwell's equations in the presence of nonlinear and/or inhomogeneous material response. We propose using a hybrid approach which combines a bound- ary integral representation with…
We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm…
Variational inequalities play a pivotal role in a wide array of scientific and engineering applications. This project presents two techniques for adaptive mesh refinement (AMR) in the context of variational inequalities, with a specific…
We describe a grid-based numerical method for 3D hydrodynamic cosmological simulations which is adaptive in space and time and combines the best features of higher order--accurate Godunov schemes for Eulerian hydrodynamics with adaptive…
In this work, we extend the meshfree generalized multiscale exponential integration framework introduced in Nikiforov et al. (2025) to the simulation of three-dimensional advection--diffusion problems in heterogeneous and high-contrast…
We provide a preliminary comparison of the dispersion properties, specifically the time-amplification factor, the scaled group velocity and the error in the phase speed of four spatiotemporal discretization schemes utilized for solving the…
I survey the use and impact of adaptive mesh refinement (AMR) simulations in numerical astrophysics and cosmology. Two basic techniques are in use to extend the dynamic range of Eulerian grid simulations in multi-dimensions: cell…
Highly accurate simulation of plasma transport is needed for the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers…
Parallel implementation of numerical adaptive mesh refinement (AMR)strategies for solving 3D elastostatic contact mechanics problems is an essential step toward complex simulations that exceed current performance levels. This paper…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
Interfractional geometric uncertainties can lead to deviations of the actual delivered dose from the prescribed dose distribution. To better handle these uncertainties during treatment, the authors propose a dynamic framework for robust…
In this article we present robust, efficient and accurate fully implicit time-stepping schemes and nonlinear solvers for systems of reaction-diffusion equations. The applications of reaction-diffusion systems is abundant in the literature,…
Implicit time integration is key to robustly simulating stiff materials and large deformations, but its performance is often dominated by repeatedly solving large linear systems. Adaptive coarsening can reduce this cost by concentrating…
As the deep learning revolution marches on, masked modeling has emerged as a distinctive approach that involves predicting parts of the original data that are proportionally masked during training, and has demonstrated exceptional…