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A third-order accurate implicit-explicit Runge-Kutta time marching numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with arbitrary damping…
Data-driven modeling of nonlinear dynamical systems is often hampered by measurement noise. We propose a denoising framework, called Runge-Kutta and Total Variation Based Implicit Neural Representation (RKTV-INR), that represents the state…
There is a growing interest in investigating numerical approximations of the water wave equation in recent years, whereas the lack of rigorous analysis of its time discretization inhibits the design of more efficient algorithms. In this…
A unified theoretical framework is suggested to examine the energy dissipation properties at all stages of additive implicit-explicit Runge-Kutta (IERK) methods up to fourth-order accuracy for gradient flow problems. We construct some…
The design of numerical integrators for solving stochastic dynamics with high weak order relies on tedious calculations and is subject to a high number of order conditions. The original approaches from the literature consider strong…
Context. The magnetic field in the solar atmosphere continually reconnects and accelerates charged particles to high energies. Simulations of the atmosphere in three dimensions that include the effects of accelerated particles can aid our…
The nonlinear gyrokinetic equations describe plasma turbulence in laboratory and astrophysical plasmas. To solve these equations, massively parallel codes have been developed and run on present-day supercomputers. This paper describes…
We present an extensive study of the effects of neutrino transport in 3-dimensional general relativistic radiation hydrodynamics (GRHD) simulations of binary neutron star (BNS) mergers using our moment-based, energy-integrated neutrino…
A wide range of physical phenomena exhibit auxiliary admissibility criteria, such as conservation of entropy or various energies, which arise implicitly under the exact solution of their governing PDEs. However, standard temporal schemes,…
We design a novel, exactly energy-conserving implicit non-symplectic integration method for an eight-dimensional Hamiltonian system with four degrees of freedom. In our algorithm, each partial derivative of the Hamiltonian with respect to…
Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we…
This review concentrates on the two principle methods used to evolve nuclear abundances within astrophysical simulations, evolution via rate equations and via equilibria. Because in general the rate equations in nucleosynthetic applications…
Neutrinos play an important role in compact star astrophysics: neutrino-heating is one of the main ingredients in core-collapse supernovae, neutrino-matter interactions determine the composition of matter in binary neutron star mergers and…
This paper presents a comprehensive numerical framework for simulating radiation-plasma systems. The radiative transfer process spans multiple flow regimes due to varying fluid opacity across different regions, necessitating a robust…
We present a set of numerical-relativity binary neutron star merger simulations incorporating muons and muonic reactions for two baseline baryonic equations-of-state. In order to investigate the possible impact of muons and muonic weak…
We present general-relativistic radiation magnetohydrodynamics simulations of binary neutron star mergers performed with GR-Athena++. Neutrino transport is treated using a moment-based, energy-integrated scheme (M1), augmented by neutrino…
We present a new implementation of radiation hydrodynamics (RHD) in the adaptive mesh refinement (AMR) code RAMSES. The multi-group radiative transfer (RT) is performed on the AMR grid with a first-order Godunov method using the M1 closure…
We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a non equilibrium part and are exact for relaxation…
We propose an experimental study of adaptive time-stepping methods for efficient modeling of the aggregation-fragmentation kinetics. Precise modeling of this phenomena usually requires utilization of the large systems of nonlinear ordinary…
We present a model for the interaction between dust and radiation fields in the radiation hydrodynamic code AREPO-RT, which solves the moment-based radiative transfer equations on an unstructured moving mesh. Dust is directly treated using…