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

## TL;DR

This paper introduces a novel numerical scheme combining Fourier and discontinuous Galerkin methods to efficiently solve the Kadomtsev--Petviashvili equation, demonstrating superior accuracy and speed over existing methods.

## Contribution

The paper presents a new split step Fourier/discontinuous Galerkin scheme that improves efficiency and accuracy for solving the KP equation, with potential extensions to related models.

## Key findings

- The method outperforms existing numerical methods by up to a factor of five.
- The scheme is highly accurate for a range of numerical simulations.
- It can be extended to other related models.

## Abstract

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.