Solving 2D/3D Heat Conduction Problems by Combining Topology Optimization and Anisotropic Mesh Adaptation

Kristian Jensen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

Topology optimization was recently combined with anisotropic mesh adaptation to solve 3D minimum compliance problems in a fast and robust way. This paper demonstrates that the methodology is also applicable to 2D/3D heat conduction problems. Nodal design variables are used and the objective function is chosen such that the problem is self-adjoint. There is no way around the book keeping associated with mesh adaptation, so the whole 5527 line MATLAB code is published (https://github.com/kristianE86/trullekrul). The design variables as well as the sensitivities have to be interpolated between meshes, but MATLAB does not support interpolation on simplex meshes and it is thus handled as part of the local operations in the mesh adaptation. This functionality is available for nodal as well as element-wise design variables, but we have found the former to be superior. Results are shown for various discretizations demonstrating that the objective function converges, but comparison to optimizations with fixed meshes indicate that the use of mesh adaptation results in worse objective functions, particularly in 3D. Out of the 5018 statements only 100 is used for the actual optimization loop, 100 for 2D/3D geometry/mesh setup and 50 for the forward problem. It is thus feasible to use the script as a platform for solving other problems or for investigating the details of the methodology itself.
Original languageEnglish
Title of host publicationAdvances in Structural and Multidisciplinary Optimization : Proceedings of the 12th World Congress of Structural and Multidisciplinary Optimization (WCSMO12)
EditorsAxel Schumacher , Thomas Vietor , Sierk Fiebig , Kai-Uwe Bletzinger , Kurt Maute
Number of pages15
PublisherSpringer
Publication date2018
Pages1224-1238
ISBN (Print) 978-3-319-67987-7
ISBN (Electronic)978-3-319-67988-4
DOIs
Publication statusPublished - 2018
Event12th World Congress of Structural and Multidisciplinary Optimisation - Technische Universität Braunschweig, Braunschweig, Germany
Duration: 5 Jun 20179 Jun 2017
Conference number: 12
http://www.wcsmo12.org/

Conference

Conference12th World Congress of Structural and Multidisciplinary Optimisation
Number12
LocationTechnische Universität Braunschweig
CountryGermany
CityBraunschweig
Period05/06/201709/06/2017
Internet address

Keywords

  • Heat conduction
  • Anisotropic
  • Mesh adaptation
  • Topology optimization
  • MATLAB

Cite this

Jensen, K. (2018). Solving 2D/3D Heat Conduction Problems by Combining Topology Optimization and Anisotropic Mesh Adaptation. In A. S., T. V., S. F., K-U. B., & K. M. (Eds.), Advances in Structural and Multidisciplinary Optimization: Proceedings of the 12th World Congress of Structural and Multidisciplinary Optimization (WCSMO12) (pp. 1224-1238). Springer. https://doi.org/10.1007/978-3-319-67988-4_92