Cargando…
Quadrature-free immersed isogeometric analysis
This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a newly developed technique for the evaluation of polynomial integrals over spline...
Autores principales: | , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer London
2022
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9653347/ https://www.ncbi.nlm.nih.gov/pubmed/36397879 http://dx.doi.org/10.1007/s00366-022-01644-3 |
_version_ | 1784828661006860288 |
---|---|
author | Antolin, P. Hirschler, T. |
author_facet | Antolin, P. Hirschler, T. |
author_sort | Antolin, P. |
collection | PubMed |
description | This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a newly developed technique for the evaluation of polynomial integrals over spline boundary representations that is exclusively based on analytical computations. First, through a consistent polynomial approximation step, the finite element operators of the Galerkin method are transformed into integrals involving only polynomial integrands. Then, by successive applications of the divergence theorem, those integrals over B-Reps are transformed into the first surface and then line integrals with polynomials integrands. Eventually, these line integrals are evaluated analytically with machine precision accuracy. The performance of the proposed method is demonstrated by means of numerical experiments in the context of 2D and 3D elliptic problems, retrieving optimal error convergence order in all cases. Finally, the methodology is illustrated for 3D CAD models with an industrial level of complexity. |
format | Online Article Text |
id | pubmed-9653347 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer London |
record_format | MEDLINE/PubMed |
spelling | pubmed-96533472022-11-15 Quadrature-free immersed isogeometric analysis Antolin, P. Hirschler, T. Eng Comput Original Article This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a newly developed technique for the evaluation of polynomial integrals over spline boundary representations that is exclusively based on analytical computations. First, through a consistent polynomial approximation step, the finite element operators of the Galerkin method are transformed into integrals involving only polynomial integrands. Then, by successive applications of the divergence theorem, those integrals over B-Reps are transformed into the first surface and then line integrals with polynomials integrands. Eventually, these line integrals are evaluated analytically with machine precision accuracy. The performance of the proposed method is demonstrated by means of numerical experiments in the context of 2D and 3D elliptic problems, retrieving optimal error convergence order in all cases. Finally, the methodology is illustrated for 3D CAD models with an industrial level of complexity. Springer London 2022-04-25 2022 /pmc/articles/PMC9653347/ /pubmed/36397879 http://dx.doi.org/10.1007/s00366-022-01644-3 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Original Article Antolin, P. Hirschler, T. Quadrature-free immersed isogeometric analysis |
title | Quadrature-free immersed isogeometric analysis |
title_full | Quadrature-free immersed isogeometric analysis |
title_fullStr | Quadrature-free immersed isogeometric analysis |
title_full_unstemmed | Quadrature-free immersed isogeometric analysis |
title_short | Quadrature-free immersed isogeometric analysis |
title_sort | quadrature-free immersed isogeometric analysis |
topic | Original Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9653347/ https://www.ncbi.nlm.nih.gov/pubmed/36397879 http://dx.doi.org/10.1007/s00366-022-01644-3 |
work_keys_str_mv | AT antolinp quadraturefreeimmersedisogeometricanalysis AT hirschlert quadraturefreeimmersedisogeometricanalysis |