Extendible and Efcient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Methods

doi:10.1007/s42967-021-00134-5

Abstract

Abstract: This paper discusses a Python interface for the recently published Dune-Fem-DG module which provides highly efcient implementations of the discontinuous Galerkin (DG) method for solving a wide range of nonlinear partial diferential equations (PDEs). Although the C++ interfaces of Dune-Fem-DG are highly fexible 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 unifed form language are provided to open Dune-Fem-DG for a broader audience. The Python interfaces are demonstrated for both parabolic and frst-order hyperbolic PDEs.

Key words: Dune, Dune-Fem, Discontinuous Galerkin, Finite volume, Python, Advection-difusion, Euler, Navier-Stokes

CLC Number:

Andreas Dedner, Robert Klöfkorn. Extendible and Efcient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Methods[J]. Communications on Applied Mathematics and Computation, 2022, 4(2): 657-696.

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