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We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical…
We present a novel high-order nodal artificial viscosity approach designed for solving Magnetohydrodynamics (MHD) equations. Unlike conventional methods, our approach eliminates the need for ad hoc parameters. The viscosity is…
\large{\bf Abstract-} Unsteady Hall Magnetohydrodynamics (MHD) near a hyperbolic magnetic neutral line is investigated. An exact analytical solution describing a self-similar evolution is given. This solution shows a negligible impact on…
We study the multi-channel sparse blind deconvolution (MCS-BD) problem, whose task is to simultaneously recover a kernel $\mathbf a$ and multiple sparse inputs $\{\mathbf x_i\}_{i=1}^p$ from their circulant convolution $\mathbf y_i =…
This paper proposes and analyzes a gradient-type algorithm based on Burer-Monteiro factorization, called the Asymmetric Projected Gradient Descent (APGD), for reconstructing the point set configuration from partial Euclidean distance…
We describe a method for incorporating ambipolar diffusion in the strong coupling approximation into a multidimensional magnetohydrodynamics code based on the total variation diminishing scheme. Contributions from ambipolar diffusion terms…
In this paper we present an analytical study of a subgrid scale turbulence model of the three-dimensional magnetohydrodynamic (MHD) equations, inspired by the Navier-Stokes-alpha (also known as the viscous Camassa-Holm equations or the…
This paper proposes a new decentralized conjugate gradient (NDCG) method and a decentralized memoryless BFGS (DMBFGS) method for the nonconvex and strongly convex decentralized optimization problem, respectively, of minimizing a finite sum…
The electron inertia term and the off-diagonal electron pressure terms are well-known for the frozen-in condition breakdown in collisionless magnetic reconnection, which are naturally kinetic and difficult to be employed in…
This paper proposes and analyzes arbitrarily high-order discontinuous Galerkin (DG) and finite volume methods which provably preserve the positivity of density and pressure for the ideal MHD on general meshes. Unified auxiliary theories are…
We consider viscous free-boundary magnetohydrodynamics(MHD) under vacuum in $\mathbb{R}^3$, especially when vacuum magnetic field is identically zero. It is a central problem in mathematics to perform vanishing viscosity limit to get a…
We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a…
In this work, we explore the capabilities of multiplexed gradient descent (MGD), a scalable and efficient perturbative zeroth-order training method for estimating the gradient of a loss function in hardware and training it via stochastic…
Many interesting terrestrial and astrophysical scenarios involving magnetic fields can be approached in axial geometry. Even though the Lagrangian smoothed particle hydrodynamics (SPH) technique has been successfully extended to handle…
One of the most important predictions in magnetohydrodynamics (MHD) is that in the presence of a uniform magnetic field $\textbf{b}_{0}$ a transition from weak to strong wave turbulence should occur when going from large to small…
We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. The particles move with the fluid, so the time…
In this paper, a high order free-stream preserving finite difference weighted essentially non-oscillatory (WENO) scheme is developed for the ideal magnetohydrodynamic (MHD) equations on curvilinear meshes. Under the constrained transport…
We describe a three-dimensional, Godunov-type numerical magnetohydrodynamics (MHD) method designed for studying disk accretion to a rotating magnetized star in the general case where the star's rotation axis, its magnetic moment, and the…
The paper describes an explicit multi-dimensional numerical scheme for Special Relativistic Two-Fluid Magnetohydrodynamics of electron-positron plasma and a suit of test problems. The scheme utilizes Cartesian grid and the third order WENO…
In this paper, we are concerned with the two-dimensional (2D) incompressible magnetohydrodynamic (MHD) equations with velocity dissipation given by $(-\Delta)^{\alpha}$ and magnetic diffusion given by reducing about logarithmic diffusion…