Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Method

TL;DR

This paper introduces a Python interface for the DUNE-FEM-DG module, making the efficient Discontinuous Galerkin method more accessible for solving various nonlinear PDEs to a broader audience.

Contribution

It provides a user-friendly Python interface for DUNE-FEM-DG, enabling easier application of the DG method without requiring C++ expertise.

Findings

Python interface simplifies usage of DUNE-FEM-DG

Demonstrated for parabolic and hyperbolic PDEs

Enhances accessibility of DG method in Python environment

Abstract

This paper discusses a Python interface for the recently published DUNE-FEM-DG module which provides highly efficient implementations of the Discontinuous Galerkin (DG) method for solving a wide range of non linear partial differential equations (PDE). Although the C++ interfaces of DUNE-FEM-DG are highly flexible and customizable, a solid knowledge of C++ is necessary to make use of this powerful tool. With this work easier user interfaces based on Python and the Unified Form Language are provided to open DUNE-FEM-DG for a broader audience. The Python interfaces are demonstrated for both parabolic and first order hyperbolic PDEs.