A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev--Petviashvili equation
For researchers solving nonlinear wave equations, this hybrid method offers a more efficient numerical approach, though it is incremental as it combines known techniques.
The authors propose a split-step Fourier/discontinuous Galerkin scheme for the Kadomtsev-Petviashvili equation, demonstrating up to 5x speedup over existing methods in numerical simulations.
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.