A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation

We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares problem into a sequence of local nonlinear problem...

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Detalles Bibliográficos
Autores principales: Caboussat, Alexandre, Glowinski, Roland, Gourzoulidis, Dimitrios
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9402779/
https://www.ncbi.nlm.nih.gov/pubmed/36035316
http://dx.doi.org/10.1007/s10915-022-01968-8
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author Caboussat, Alexandre
Glowinski, Roland
Gourzoulidis, Dimitrios
author_facet Caboussat, Alexandre
Glowinski, Roland
Gourzoulidis, Dimitrios
author_sort Caboussat, Alexandre
collection PubMed
description We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares problem into a sequence of local nonlinear problems and variational linear problems. We develop dedicated solvers for the algebraic problems based on Newton’s method and we solve the differential problems using mixed low-order finite elements. Various numerical experiments demonstrate the accuracy, efficiency and the robustness of the proposed method, compared for instance to augmented Lagrangian approaches.
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spelling pubmed-94027792022-08-26 A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation Caboussat, Alexandre Glowinski, Roland Gourzoulidis, Dimitrios J Sci Comput Article We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares problem into a sequence of local nonlinear problems and variational linear problems. We develop dedicated solvers for the algebraic problems based on Newton’s method and we solve the differential problems using mixed low-order finite elements. Various numerical experiments demonstrate the accuracy, efficiency and the robustness of the proposed method, compared for instance to augmented Lagrangian approaches. Springer US 2022-08-24 2022 /pmc/articles/PMC9402779/ /pubmed/36035316 http://dx.doi.org/10.1007/s10915-022-01968-8 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 Article
Caboussat, Alexandre
Glowinski, Roland
Gourzoulidis, Dimitrios
A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation
title A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation
title_full A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation
title_fullStr A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation
title_full_unstemmed A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation
title_short A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation
title_sort least-squares method for the solution of the non-smooth prescribed jacobian equation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9402779/
https://www.ncbi.nlm.nih.gov/pubmed/36035316
http://dx.doi.org/10.1007/s10915-022-01968-8
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