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

Dedner, Andreas and Klöfkorn, Robert LU orcid (2022) In Communications on Applied Mathematics and Computation 4(2). p.657-696
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 nonlinear partial differential equations (PDEs). 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.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Advection-diffusion, Discontinuous Galerkin, Dune, Dune-Fem, Euler, Finite volume, Navier-Stokes, Python
in
Communications on Applied Mathematics and Computation
volume
4
issue
2
pages
40 pages
publisher
Springer
external identifiers
  • scopus:85128148036
ISSN
2096-6385
DOI
10.1007/s42967-021-00134-5
language
English
LU publication?
yes
id
f1caafc3-bee9-4a5f-ae9e-8a7e2cd1c35c
date added to LUP
2022-12-28 11:21:36
date last changed
2022-12-28 17:05:37
@article{f1caafc3-bee9-4a5f-ae9e-8a7e2cd1c35c,
  abstract     = {{<p>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 nonlinear partial differential equations (PDEs). 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.</p>}},
  author       = {{Dedner, Andreas and Klöfkorn, Robert}},
  issn         = {{2096-6385}},
  keywords     = {{Advection-diffusion; Discontinuous Galerkin; Dune; Dune-Fem; Euler; Finite volume; Navier-Stokes; Python}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{657--696}},
  publisher    = {{Springer}},
  series       = {{Communications on Applied Mathematics and Computation}},
  title        = {{Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Methods}},
  url          = {{http://dx.doi.org/10.1007/s42967-021-00134-5}},
  doi          = {{10.1007/s42967-021-00134-5}},
  volume       = {{4}},
  year         = {{2022}},
}