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A unified approach for a posteriori high-order curved mesh generation using solid mechanics

Roman Poya, Rubén Sevilla Orcid Logo, Antonio Gil Orcid Logo

Computational Mechanics, Volume: 58, Issue: 3, Pages: 457 - 490

Swansea University Authors: Roman Poya, Rubén Sevilla Orcid Logo, Antonio Gil Orcid Logo

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Abstract

The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticit...

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Published in: Computational Mechanics
ISSN: 0178-7675 1432-0924
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa28844
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spelling 2021-01-07T14:42:46.3517499 v2 28844 2016-06-12 A unified approach for a posteriori high-order curved mesh generation using solid mechanics 78a0edf15d689ba83c9929767ab93587 Roman Poya Roman Poya true false b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2016-06-12 EEN The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh when considering an isoparametric finite element formulation. Journal Article Computational Mechanics 58 3 457 490 0178-7675 1432-0924 High-order mesh generation, Solid mechanics analogy, Curved elements, Isoparametric finite elements 1 9 2016 2016-09-01 10.1007/s00466-016-1302-2 http://link.springer.com/article/10.1007/s00466-016-1302-2 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2021-01-07T14:42:46.3517499 2016-06-12T17:38:28.3572581 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Roman Poya 1 Rubén Sevilla 0000-0002-0061-6214 2 Antonio Gil 0000-0001-7753-1414 3 0028844-28072016113719.pdf AunifiedapproachSevilla.pdf 2016-07-28T11:37:19.2570000 Output 15891118 application/pdf Version of Record true 2016-07-28T00:00:00.0000000 This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. true
title A unified approach for a posteriori high-order curved mesh generation using solid mechanics
spellingShingle A unified approach for a posteriori high-order curved mesh generation using solid mechanics
Roman Poya
Rubén Sevilla
Antonio Gil
title_short A unified approach for a posteriori high-order curved mesh generation using solid mechanics
title_full A unified approach for a posteriori high-order curved mesh generation using solid mechanics
title_fullStr A unified approach for a posteriori high-order curved mesh generation using solid mechanics
title_full_unstemmed A unified approach for a posteriori high-order curved mesh generation using solid mechanics
title_sort A unified approach for a posteriori high-order curved mesh generation using solid mechanics
author_id_str_mv 78a0edf15d689ba83c9929767ab93587
b542c87f1b891262844e95a682f045b6
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author_id_fullname_str_mv 78a0edf15d689ba83c9929767ab93587_***_Roman Poya
b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Roman Poya
Rubén Sevilla
Antonio Gil
author2 Roman Poya
Rubén Sevilla
Antonio Gil
format Journal article
container_title Computational Mechanics
container_volume 58
container_issue 3
container_start_page 457
publishDate 2016
institution Swansea University
issn 0178-7675
1432-0924
doi_str_mv 10.1007/s00466-016-1302-2
college_str Faculty of Science and Engineering
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hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
url http://link.springer.com/article/10.1007/s00466-016-1302-2
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description The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh when considering an isoparametric finite element formulation.
published_date 2016-09-01T03:34:35Z
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