A fully nonlinear characteristic method for gyrokinetic simulation

Fully electromagnetic nonlinear gyrokinetic equations for tokamak edge turbulence

A Modified Characteristic Finite Element Method for a Fully Nonlinear Formulation of the Semigeostrophic Flow Equations

This paper develops a fully discrete modified characteristic finite element method for a coupled system consisting of the fully nonlinear Monge–Ampère equation and a transport equation. The system is the Eulerian formulation in the dual space for B. J. Hoskins’ semigeostrophic flow equations, which are widely used in meteorology to model frontogenesis. To overcome the difficulty caused by the s...

An Explicit Nonperiodic, Nonlinear Eulerian Gyrokinetic Solver for Microturbulence Simulation

The General Atomics gyrokinetic-Maxwell solver (GYRO) has been largely rewritten replacing implicit but split time steps with explicit high order steps. An orbit-time grid replaces the more familiar fixed poloidal grid in the kinetic equation, allowing full resolution of bounce-point cusps. More systematic, high-accuracy quadrature rules yield superior convergence with number of velocity-space ...

A Probabilistic Numerical Method for Fully Nonlinear

We consider the probabilistic numerical scheme for fully nonlinear partial differential equations suggested in [Comm. Pure Appl. Math. 60 (2007) 1081–1110] and show that it can be introduced naturally as a combination of Monte Carlo and finite difference schemes without appealing to the theory of backward stochastic differential equations. Our first main result provides the convergence of the d...

Perron’s method for nonlocal fully nonlinear equations

This paper is concerned with existence of viscosity solutions of non-translation invariant nonlocal fully nonlinear equations. We construct a discontinuous viscosity solution of such nonlocal equation by Perron’s method. If the equation is uniformly elliptic, we prove the discontinuous viscosity solution is Hölder continuous and thus it is a viscosity solution.