This paper develops a family of preconditioners for pseudospectral approximations of pth-order linear differential operators subject to various types of boundary conditions. The approximations are based on ultraspherical polynomials with special attention being paid to Legendre and Chebyshev polynomial methods based on Gauss–Lobatto quadrature points. The eigenvalue spectrum of the precondition...

ABSTRACT The conservative high-order accurate spectral difference method is presented for simulation of rotating shallowwater equations. The method is formulated using Lagrange interpolations on Gauss-Lobatto points for the desired order of accuracy without suffering numerical dissipation and dispersion errors. The optimal third-order total variation diminishing (TVD) Runge-Kutta algorithm is u...

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System’s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transfor...

We propose a new, energy conserving, spectral element, discontinuous Galerkin method for the approximation of the Vlasov–Poisson system in arbitrary dimension, using Cartesian grids. The method is derived from the one proposed in [ACS12], with two modifications: energy conservation is obtained by a suitable projection operator acting on the solution of the Poisson problem, rather than by solvin...

<p style='text-indent:20px;'>Classical symplectic partitioned Runge–Kutta methods can be obtained from a variational formulation where all the terms in discrete Lagrangian are treated with same quadrature formula. We construct family of allowing use different formulas (primary and secondary) for Lagrangian. In particular, we study using Lobatto (with corresponding IIIA-B pair) as primary ...

A primitive-variable formulation for simulation of time-dependent incompressible flows in cylindrical coordinates is developed. Spectral elements are used to discretise the meridional semi-plane, coupled with Fourier expansions in azimuth. Unlike previous formulations where special distributions of nodal points have been used in the radial direction, the current work adopts standard Gauss–Lobat...

In this work we discuss two different but related aspects of the development of efficient discontinuous Galerkin methods on hybrid element grids for the computational modeling of gas dynamics in complex geometries or with adapted grids. In the first part, a recursive construction of different nodal sets for hp finite elements is presented. The different nodal elements are evaluated by computing...

The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions asso-5 ciated with Lagrange polynomials based on Gauss–Lobatto–Legen...

Abstract A stochastic computing approach is implemented in the present work to solve nonlinear nanofluidics system that occurs model of atomic physics. The process converts partial differential with suitable level similarities transformation into systems equations. For construction datasets, finite difference scheme (Lobatto IIIA) applied through different selection collocation points for havin...