A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev–Petviashvili equation

摘要

In this paper we propose a method to solve the Kadomtsev–Petviashvili equation based on splitting the linear part of the equation from the nonlinear part. The linear part is treated using FFTs, while the nonlinear part is approximated using a semi-Lagrangian discontinuous Galerkin approach of arbitrary order.We demonstrate the efficiency and accuracy of the numerical method by providing a range of numerical simulations. In particular, we find that our approach can outperform the numerical methods considered in the literature by up to a factor of five. Although we focus on the Kadomtsev–Petviashvili equation in this paper, the proposed numerical scheme can be extended to a range of related models as well.