A Differentiable Mapping of Mesh Cells Based on Finite Elements on Quadrilateral and Hexahedral Meshes-Reference-Cited by-同舟云学术

A Differentiable Mapping of Mesh Cells Based on Finite Elements on Quadrilateral and Hexahedral Meshes

Published:2020-11-07 Issue:1 Volume:21 Page:1-11
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Arndt Daniel¹^ORCID,Kanschat Guido²^ORCID

Affiliation:

1. Computational Engineering and Energy Sciences Group , Oak Ridge National Laboratory Computing and Computational Sciences Directorate , Oak Ridge , TN 37830 , USA

2. Interdisciplinary Center for Scientific Computing (IWR) , Heidelberg University , Heidelberg , Germany

Abstract

Abstract Finite elements of higher continuity, say conforming in H 2

{H^{2}}

instead of H 1

{H^{1}}

, require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to obtain such mappings given a topologically regular mesh in the standard format of vertex coordinates and a description of the boundary. A variant of the algorithm with orthogonal edges in each vertex is proposed. We introduce necessary modifications in the case of adaptive mesh refinement with nonconforming edges. Furthermore, we discuss efficient storage of the necessary data.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

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