Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method

Abstract

Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method *Zhang Rong-Pei( ) a) † , Yu Xi-Jun( ) b) , and Feng Tao ( ) b)

A combined discontinuous Galerkin method for the dipolar Bose–Einstein condensation

“…In above, ·,· K or ·,· ∂ K denotes the inner product integrated in K or on the edge ∂ K and numerical fluxes for solving wave function ψ by using direct DG method [23,33] are chosen as follows:…”

Optimal error estimate of conservative local discontinuous Galerkin method for nonlinear Schrödinger equation

“…Remark 3.2. When θ = 1/2, then by (14) we have |A| = 2 −N (1−(−1) N (k+1) ), which shows that A is invertible if and only if N is odd and k is even. In this case, q = −1 and β N = 1.…”

“…Finally, there is provable cell entropy inequality and L 2 stability, for arbitrary scalar equations in any spatial dimension and any triangulation, for any order of accuracy, without limiters. Some recent attempts have been made to apply the DG discretization to solve the Schrödinger equation, see [6,10,14,15] and references therein. In [10], Xu and Shu developed an LDG method to solve the generalized NLS equation.…”

An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii Equation

“…There are many methods discretizing the normalized gradient flow in the imaginary time. These methods include spectral (pseudospectral) methods [3,5], finite difference method (FDM) [6,7], and discontinuous Galerkin (DG) method [8][9][10].…”