Related papers: The Dune Python Module

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…

The dune-functions dune module introduces a new programmer interface for discrete and non-discrete functions. Unlike the previous interfaces considered in the existing dune modules, it is based on overloading operator(), and returning…

We introduce the dune-curvilineargrid module. The module provides the self-contained, parallel grid manager, as well as the underlying elementary curvilinear geometry module dune-curvilineargeometry. This work is motivated by the need for…

In this paper we introduce and describe an implementation of curved (surface) geometries within the Dune framework for grid-based discretizations. Therefore, we employ the abstraction of geometries as local-functions bound to a grid…

Recently, a lot of papers proposed to use neural networks to approximately solve partial differential equations (PDEs). Yet, there has been a lack of flexible framework for convenient experimentation. In an attempt to fill the gap, we…

This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that happened since the release of the first Dune version in 2007…

In this work we extend the Dune solver library with another grid interface to the open-source p4est software. While Dune already supports about a dozen different mesh implementations through its mesh interface Dune-Grid, we undertake this…

In this paper we present the new DUNE-ALUGrid module. This module contains a major overhaul of the sources from the ALUgrid library and the binding to the DUNE software framework. The main changes include user defined load balancing,…

We present our effort to extend and complement the core modules of the Distributed and Unified Numerics Environment DUNE (http://dune-project.org) by a well tested and structured collection of utilities and concepts. We describe key…

Version 2.10 of the Distributed and Unified Numerics Environment DUNE introduces a range of enhancements across its core and extension modules, with a continued emphasis on modern C++ integration and improved usability. This release extends…

We present FoamGrid, a new implementation of the DUNE grid interface. FoamGrid implements one- and two-dimensional grids in a physical space of arbitrary dimension, which allows for grids for curved domains. Even more, the grids are not…

We present a family of Python modules for the numerical integration of ordinary, delay, or stochastic differential equations. The key features are that the user enters the derivative symbolically and it is just-in-time-compiled, allowing…

Solving partial differential equations (PDEs) on complex domains can present significant computational challenges. The Diffuse Domain Method (DDM) is an alternative that reformulates the partial differential equations on a larger, simpler…

This paper introduces PolyDiM, an open-source C++ library tailored for the development and implementation of polytopal discretization methods for partial differential equations. The library provides robust and modular tools to support…

Data gridding is a common task in astronomy and many other science disciplines. It refers to the resampling of irregularly sampled data to a regular grid. We present cygrid, a library module for the general purpose programming language…

Open-source simulation frameworks are evolving rapidly to provide accessible tools for the numerical solution of partial differential equations. Modern finite element (FEM) software such as FEniCS, Firedrake, or dune-fem alleviates the need…

Recently proposed modifications of the standard particle-in-cell (PIC) method resolve long-standing limitations such as exact preservation of physically conserved quantities and unbiased ensemble down-sampling. Such advances pave the way…

Equations, particularly differential equations, are fundamental for understanding natural phenomena and predicting complex dynamics across various scientific and engineering disciplines. However, the governing equations for many complex…

In the numerical solution of partial differential equations (PDEs), a central question is the one of building variational formulations that are inf-sup stable not only at the infinite-dimensional level, but also at the finite-dimensional…

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…