Related papers: Improving the convergence properties of the moving…
We present the implementation of a three-dimensional, second order accurate Godunov-type algorithm for magneto-hydrodynamic (MHD), in the adaptive-mesh-refinement (AMR) cosmological code {\tt CHARM}. The algorithm is based on the full…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
Numerous formulations of finite volume schemes for the Euler and Navier-Stokes equations exist, but in the majority of cases they have been developed for structured and stationary meshes. In many applications, more flexible mesh geometries…
It was recently established that for convex optimization problems with sparse optimal solutions (be it entry-wise sparsity or matrix rank-wise sparsity) it is possible to design first-order methods with linear convergence rates that depend…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
Gas cooling and accretion in haloes delivers mass and angular momentum onto galaxies. In this work, we investigate the accuracy of the modelling of this important process in several different semi-analytic (SA) galaxy formation models…
We present a smoothed particle hydrodynamic (SPH) simulation that reproduces a galaxy that is a moderate facsimile of those observed. The primary failing point of previous simulations of disk formation, namely excessive transport of angular…
We continue our investigation of finite deformation linear viscoelastodynamics by focusing on constructing accurate and reliable numerical schemes. The concrete thermomechanical foundation developed in the previous study paves the way for…
In [Kopteva, Math. Comp., 2014] a counterexample of an anisotropic triangulation was given on which the exact solution has a second-order error of linear interpolation, while the computed solution obtained using linear finite elements is…
Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most…
Multidimensional hydrodynamical simulations have transformed the study of stellar interiors over the past few decades. Most codes developed during that time use the anelastic approximation, which fixes the thermal structure of simulations…
We discuss some typical problems related to numerical hydrodynamics of a dense interstellar medium. A newly developed hydrodynamical code based on adaptive mesh refinement technique is presented and applied to simulate the evolution of a…
The threshold dynamics algorithm of Merriman, Bence, and Osher is only first order accurate in the two-phase setting. Its accuracy degrades further to half order in the multi-phase setting, a shortcoming it has in common with other related,…
We describe and test a new version of the adaptive mesh refinement (AMR) cosmological code MASCLET. The new version of the code includes all the ingredients of its previous version plus a description of the evolution of the magnetic field…
The Sllod equations of motion enable modeling of homogeneous flow at the atomic scale, and are commonly used to predict fluid properties such as viscosity. However, few publicly available codes support such simulations, and those that do…
Context: Calculating stellar pulsations requires a sufficient accuracy to match the quality of the observations. Many current pulsation codes apply a second order finite-difference scheme, combined with Richardson extrapolation to reach…
There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation…
First-order energy dissipative schemes in time are available in literature for the Poisson-Nernst-Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite…
This paper describes the design and implementation of our new multi-group, multi-dimensional radiation hydrodynamics (RHD) code Fornax and provides a suite of code tests to validate its application in a wide range of physical regimes.…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…