Appendix: Sample Multiphysics Optimization Code

  • Ercan M. DedeEmail author
  • Jaewook Lee
  • Tsuyoshi Nomura
Part of the Simulation Foundations, Methods and Applications book series (SFMA)


In this appendix, example numerical code is provided for a 2-D electrothermal design optimization problem. Here, Joule heating considering side/surface convection of the conductor is assumed. The finite element implementation of the problem follows a description for the finite element analysis of a thermoelectric device, with the exception that Seebeck and Peltier effects are neglected. The code is written in a custom MATLAB® script that exploits a sequential solver for the finite element analysis portion of the problem, where the electrical analysis is first performed and the generated resistive heating thermal loads are passed to the following heat transfer analysis. The code incorporates an optimality criteria optimizer and filtering routine commonly found in the literature for updating the design variables and minimum length scale control. The code is constructed as a continuous script instead of a series of functions, for clarity, and numerous comments have been added throughout the script to explain the various steps implemented in the program.


Finite Element Analysis Joule Heating Design Domain Numerical Code Thermoelectric Device 
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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Toyota Research Institute of North AmericaAnn ArborUSA
  2. 2.Korea Aerospace UniversityGoyang-siKorea, Republic of (South Korea)
  3. 3.Toyota Central R&D LabsNagakuteJapan

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