Conditional hyperbolic quadrature method of moments for kinetic equations

Fractional diffusion limit for collisional kinetic equations: A moments method

This paper is devoted to hydrodynamic limits of linear kinetic equations. We consider situations in which the thermodynamical equilibrium is described by a heavy-tail distribution function rather than a maxwellian distribution. A similar problem was addressed in [14] using Fourier transform and it was shown that the long time/small mean free path behavior of the solution of the kinetic equation...

Quadrature-free Implementation of the Discontinuous Galerkin Method for Hyperbolic Equations

A discontinuous Galerkin formulation that avoids the use of discrete quadrature formulas is described and applied to linear and nonlinear test problems in one and two space dimensions. This approach requires less computational time and storage than conventional implementations but preserves the compactness and robustness inherent to the discontinuous Galerkin method. Test problems include both ...

Enhanced Direct Quadrature Based Method of Moments for Nonlinear Filtering

The optimal estimation of a general continuous-discrete system can be achieved through the solution of the Fokker-Planck equation and the Bayesian update. However, solving the Fokker-Planck equation numerically is prohibitive in most cases. Recently a nonlinear filtering algorithm using a direct quadrature method of moments was proposed by the authors, in which the associated Fokker-Planck equa...

AGE Method For Hyperbolic Equations

In this paper, we present a four order unconditionally stable implicit scheme for hyperbolic equations. Based on the scheme a class of parallel alternating group explicit (AGE) iterative method is derived, and convergence analysis is given. Results of numerical experiments show the iterative method can fast converge to the exact solution. Mathematics Subject Classification: 65M06, 74S20

A quadrature-based method of moments for nonlinear filtering