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Binary level set method for structural topology optimization with MBO type of projection
Author(s) -
Mohamadian Mojtaba,
Shojaee Saeed
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3260
Subject(s) - level set method , binary number , topology optimization , mathematics , mathematical optimization , multiplicative function , robustness (evolution) , projection (relational algebra) , operator (biology) , level set (data structures) , set (abstract data type) , topology (electrical circuits) , convergence (economics) , algorithm , computer science , finite element method , artificial intelligence , image (mathematics) , mathematical analysis , repressor , arithmetic , biochemistry , transcription factor , economics , image segmentation , gene , economic growth , chemistry , thermodynamics , programming language , physics , combinatorics
SUMMARY In this paper, we use binary level set method and Merriman–Bence–Osher scheme for solving structural shape and topology optimization problems. In the binary level set method, the level set function can only take 1 and –1 values at convergence. Thus, it is related to phasefield methods. There is no need to solve the Hamilton–Jacobi equation so it is free of the CFL condition and the reinitialization scheme. This favorable property leads to the great time advantage of this method. We use additive operator splitting (AOS) and multiplicative operator splitting (MOS) schemes for solving optimization problems under some constraints In this work, we also combine the binary level set method with the Merriman–Bence–Osher scheme. The combined scheme is much more efficient than the conventional binary level set method. Several two‐dimensional examples are presented which demonstrate the effectiveness and robustness of proposed method. Copyright © 2011 John Wiley & Sons, Ltd.