相关论文: Solving the Grad-Shafranov equation using spectral…

In this paper we consider a Novikov equation, recently shown to describe pseudospherical surfaces, to extend some recent results of regularity of its solutions. By making use of the global well-posedness in Sobolev spaces, for analytic…

The Chapman-Enskog method of solution of kinetic equations, such as the Boltzmann equation, is based on an expansion in gradients of the deviations fo the hydrodynamic fields from a uniform reference state (e.g., local equilibrium). This…

We present Sapphire++, an open-source code designed to numerically solve the Vlasov-Fokker-Planck equation for astrophysical applications. Sapphire++ employs a numerical algorithm based on a spherical harmonic expansion of the distribution…

We study the orbital stability of smooth solitary wave solutions of the Novikov equation, which is a Camassa-Holm type equation with cubic nonlinearities. These solitary waves are shown to exist as a one-parameter family (up to spatial…

A new global two-fluid electromagnetic turbulence code, CENTORI, has been developed for the purpose of studying magnetically-confined fusion plasmas on energy confinement timescales. This code is used to evolve the combined system of…

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal for many years. Advancement of this research has largely progressed on four fronts: (1) Exact integration, (2) Lubich quadrature, (3) smooth temporal…

A new classical TM stability simulation workflow has been developed that solves the resistive inner-layer equations in a plasma slab to yield a linear, quasi-toroidal TM growth rate $\gamma$ and mode rotation frequency $\omega$. This…

In this paper, we develop a provably energy stable and conservative discontinuous spectral element method for the shifted wave equation in second order form. The proposed method combines the advantages and central ideas of very successful…

The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian…

We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…

Robust mixed finite element methods are developed for a quad-curl singular perturbation problem. Lower order H(grad curl)-nonconforming but H(curl)-conforming finite elements are constructed, which are extended to nonconforming finite…

The Novikov equation is an integrable Camassa-Holm type equation with cubic nonlinearity and admits the periodic peakons. In this paper, it is shown that the periodic peakons are the global periodic weak solutions to the Novikov equation…

In the present work the classical problem of the kinetic theory of gases (the Smoluchowsky' problem about temperature jump in rarefied gas) is considered. The rarefied gas fills half-space over a flat firm surface. logarithmic gradient of…

In this paper, we investigate a spectral Petrov-Galerkin method for an optimal control problem governed by a two-sided space-fractional diffusion-advection-reaction equation. Taking into account the effect of singularities near the boundary…

Particle transport due to Ion Temperature Gradient/Trapped Electron (ITG/TE) mode turbulence is investigated using the gyrokinetic code GENE. Both a reduced quasilinear (QL) treatment and nonlinear (NL) simulations are performed for typical…

We consider an application of the tetrad formalism introduced by Cardall et al. [Phys. Rev. D 88 (2013) 023011] to the problem of a rigidly rotating relativistic gas in thermal equilibrium and discuss the possible applications of this…

A free-boundary, axisymmetric magnetohydrodynamic (MHD) equilibrium code, pyIPREQ, has been developed for Tokamak plasmas using finite difference and Green's function approach. The code builds upon the foundational frameworks of the PEST…

We propose a nodal discontinuous Galerkin method for solving the nonlinear Riesz space fractional Schr\"{o}dinger equation and the strongly coupled nonlinear Riesz space fractional Schr\"{o}dinger equations. These problems have been…

A new numerical method is developed to approximate the solution of Laplace's equation in the exterior of the sphere with a strongly nonlinear boundary value of oblique type. A functional analysis attempt to solve this type of boundary…

We discuss a numerical method to compute the homogeneous solutions of the Teukolsky equation which is the basic equation of the black hole perturbation method. We use the formalism developed by Mano, Suzuki and Takasugi, in which the…