Dune-CurvedGrid -- A Dune module for surface parametrization

TL;DR

This paper presents Dune-CurvedGrid, a module that enables surface parametrization within the Dune framework by abstracting geometries as local functions tied to grid elements, facilitating curved surface discretizations.

Contribution

It introduces a novel implementation of curved geometries in Dune, allowing for local surface parametrizations through a new abstraction of geometries and grid connectivity.

Findings

Enables discretization of curved surfaces within Dune.

Provides a flexible abstraction for local surface parametrizations.

Facilitates more accurate surface simulations.

Abstract

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 element, and the abstraction of a grid as connectivity of elements together with a grid-function that can be localized to the elements to provide element local parametrizations of the curved surface.