Yet another parameter-free shape optimization method

Swartz, Kenneth E.; Mittal, Ketan; Schmidt, Mathias; Barrera, Jorge-Luis; Watts, Seth; Tortorelli, Daniel A.

doi:10.1007/s00158-023-03684-9

Title: Yet another parameter-free shape optimization method

Journal Article · 20 November 2023 · Structural and Multidisciplinary Optimization

DOI: https://doi.org/10.1007/s00158-023-03684-9 · OSTI ID:2280893

^[1]; Mittal, Ketan ^[1]; Schmidt, Mathias ^[1]; Barrera, Jorge-Luis ^[1]; Watts, Seth ^[1]; Tortorelli, Daniel A. ^[2]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Univ. of Illinois at Urbana-Champaign, IL (United States)

The use of node coordinates as design variables in shape optimization offers a larger design space than computer-aided design (CAD)-based shape parameterizations. It also allows for the optimization of legacy designs, i.e., a finite element mesh from an existing design can be readily optimized to meet new performance requirements without involving a CAD model. However, it is well known that the node coordinate parameterization method is fraught with numerical difficulties, which makes it impractical to use. This has led to several of “parameter-free” shape optimization methods that seek the advantages and avoid the pitfalls of the naïve node coordinate parameterization method. These methods come in two main varieties: sensitivity filtering (or gradient smoothing) and consistent filtering. The latter is analogous to the density filter method used in topology optimization (TO). In this work, we use the PDE filter from TO and energy-based filters to implement consistent shape optimization filtering schemes easily and efficiently. Numerical experiments demonstrate that consistent methods are more robust than sensitivity filtering methods.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2280893

Report Number(s):: LLNL--JRNL-841196; 1062586

Journal Information:: Structural and Multidisciplinary Optimization, Journal Name: Structural and Multidisciplinary Optimization Journal Issue: 12 Vol. 66; ISSN 1615-147X

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (48)

On the existence of a solution in a domain identification problem Chenais, Denise Journal of Mathematical Analysis and Applications, Vol. 52, Issue 2 https://doi.org/10.1016/0022-247X(75)90091-8	journal	November 1975
Latest developments in node-based shape optimization using Vertex Morphing parameterization Antonau, Ihar; Warnakulasuriya, Suneth; Bletzinger, Kai-Uwe Structural and Multidisciplinary Optimization, Vol. 65, Issue 7 https://doi.org/10.1007/s00158-022-03279-w	journal	July 2022
Traction Method Approach to Optimal Shape Design Problems Shimoda, Masatoshi; Azegami, Hideyuki; Sakurai, Toshiaki SAE Technical Paper Series https://doi.org/10.4271/971538	conference	April 1997
A Geometric Representation Scheme Suitable for Shape Optimization* † Tortorelli, Daniel A. Mechanics of Structures and Machines, Vol. 21, Issue 1 https://doi.org/10.1080/08905459308905182	journal	January 1993
Shape Optimization in Fluid Mechanics Mohammadi, Bijan; Pironneau, Olivier Annual Review of Fluid Mechanics, Vol. 36, Issue 1 https://doi.org/10.1146/annurev.fluid.36.050802.121926	journal	January 2004
Introducing the Target-Matrix Paradigm for Mesh Optimization via Node-Movement Knupp, Patrick Proceedings of the 19th International Meshing Roundtable https://doi.org/10.1007/978-3-642-15414-0_5	book	January 2010
Topology optimization of non-linear elastic structures and compliant mechanisms Bruns, Tyler E.; Tortorelli, Daniel A. Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 26-27 https://doi.org/10.1016/S0045-7825(00)00278-4	journal	March 2001
Mesh Dependence in PDE-Constrained Optimisation Schwedes, Tobias; Ham, David A.; Funke, Simon W. https://doi.org/10.1007/978-3-319-59483-5	book	January 2017
Numerical analysis perspective in structural shape optimization: A review post 2000 Upadhyay, Bhavik D.; Sonigra, Sunil S.; Daxini, Sachin D. Advances in Engineering Software, Vol. 155 https://doi.org/10.1016/j.advengsoft.2021.102992	journal	May 2021
On the Design of Compliant Mechanisms Using Topology Optimization* Sigmund, Ole Mechanics of Structures and Machines, Vol. 25, Issue 4 https://doi.org/10.1080/08905459708945415	journal	January 1997
A structural mapping technique for geometric parametrization in the optimization of magnetic devices Weeber, Konrad; Ratnajeevan, S.; Hoole, H. International Journal for Numerical Methods in Engineering, Vol. 33, Issue 10 https://doi.org/10.1002/nme.1620331010	journal	July 1992
Vertex assigned morphing for parameter free shape optimization of 3-dimensional solid structures Ertl, Franz-Josef; Dhondt, Guido; Bletzinger, Kai-Uwe Computer Methods in Applied Mechanics and Engineering, Vol. 353 https://doi.org/10.1016/j.cma.2019.05.004	journal	August 2019
A coupled CAD‐free parameterization‐morphing method for adjoint‐based shape optimization Liatsikouras, Athanasios G.; Pierrot, Guillaume; Megahed, Mustafa International Journal for Numerical Methods in Fluids, Vol. 94, Issue 11 https://doi.org/10.1002/fld.5123	journal	June 2022
A gradient-based, parameter-free approach to shape optimization Le, Chau; Bruns, Tyler; Tortorelli, Daniel Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 9-12 https://doi.org/10.1016/j.cma.2010.10.004	journal	February 2011
Shape optimal design using B-splines Braibant, V.; Fleury, C. Computer Methods in Applied Mechanics and Engineering, Vol. 44, Issue 3 https://doi.org/10.1016/0045-7825(84)90132-4	journal	August 1984
Adjoint RANS with filtered shape derivatives for hydrodynamic optimisation Stück, Arthur; Rung, Thomas Computers & Fluids, Vol. 47, Issue 1 https://doi.org/10.1016/j.compfluid.2011.01.041	journal	August 2011
Accuracy of the domain material derivative approach to shape design sensitivities Yang, R. J.; Botkin, M. E. AIAA Journal, Vol. 25, Issue 12 https://doi.org/10.2514/3.9831	journal	December 1987
A fictitious energy approach for shape optimization Scherer, M.; Denzer, R.; Steinmann, P. International Journal for Numerical Methods in Engineering, Vol. 82, Issue 3 https://doi.org/10.1002/nme.2764	journal	October 2009
An integrated approach to shape optimization and mesh adaptivity based on material residual forces Riehl, Stefan; Steinmann, Paul Computer Methods in Applied Mechanics and Engineering, Vol. 278 https://doi.org/10.1016/j.cma.2014.06.010	journal	August 2014
A Smoothing Method for Shape Optimization: Traction Method Using the Robin Condition Azegami, Hideyuki; Takeuchi, Kenzen International Journal of Computational Methods, Vol. 03, Issue 01 https://doi.org/10.1142/S0219876206000709	journal	March 2006
Suitable Spaces for Shape Optimization Welker, Kathrin Applied Mathematics & Optimization, Vol. 84, Issue S1 https://doi.org/10.1007/s00245-021-09788-2	journal	May 2021
A Unified Discrete–Continuous Sensitivity Analysis Method for Shape Optimization Berggren, Martin Computational Methods in Applied Sciences https://doi.org/10.1007/978-90-481-3239-3_4	book	October 2009
Shape Optimization Problems Azegami, Hideyuki Springer Optimization and Its Applications https://doi.org/10.1007/978-981-15-7618-8	book	January 2020
Optimal Shape Design for Elliptic Systems Pironneau, Olivier https://doi.org/10.1007/978-3-642-87722-3	book	January 1984
The Target-Matrix Optimization Paradigm for High-Order Meshes Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio SIAM Journal on Scientific Computing, Vol. 41, Issue 1 https://doi.org/10.1137/18M1167206	journal	January 2019
A domain method for shape design sensitivity analysis of built-up structures Choi, Kyung K.; Seong, Hwal G. Computer Methods in Applied Mechanics and Engineering, Vol. 57, Issue 1 https://doi.org/10.1016/0045-7825(86)90066-6	journal	August 1986
Shape optimization of an acoustic horn Bängtsson, Erik; Noreland, Daniel; Berggren, Martin Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 11-12 https://doi.org/10.1016/S0045-7825(02)00656-4	journal	March 2003
A novel p-harmonic descent approach applied to fluid dynamic shape optimization Müller, Peter Marvin; Kühl, Niklas; Siebenborn, Martin Structural and Multidisciplinary Optimization, Vol. 64, Issue 6 https://doi.org/10.1007/s00158-021-03030-x	journal	August 2021
Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization de Gournay, Frédéric SIAM Journal on Control and Optimization, Vol. 45, Issue 1 https://doi.org/10.1137/050624108	journal	January 2006
Filters in topology optimization based on Helmholtz-type differential equations Lazarov, B. S.; Sigmund, O. International Journal for Numerical Methods in Engineering, Vol. 86, Issue 6 https://doi.org/10.1002/nme.3072	journal	December 2010
Shape optimization of running shoes with desired deformation properties Nonogawa, Mai; Takeuchi, Kenzen; Azegami, Hideyuki Structural and Multidisciplinary Optimization, Vol. 62, Issue 3 https://doi.org/10.1007/s00158-020-02560-0	journal	April 2020
Three-dimensional shape optimization with variational geometry Chen, S.; Torterelli, D. A. Structural Optimization, Vol. 13, Issue 2-3 https://doi.org/10.1007/BF01199226	journal	April 1997
Survey of Shape Parameterization Techniques for High-Fidelity Multidisciplinary Shape Optimization Samareh, Jamshid A. AIAA Journal, Vol. 39, Issue 5 https://doi.org/10.2514/2.1391	journal	May 2001
Soil mechanics and plastic analysis or limit design Drucker, D. C.; Prager, W. Quarterly of Applied Mathematics, Vol. 10, Issue 2 https://doi.org/10.1090/qam/48291	journal	January 1952
Theory and practice of optimal shape design Mohammadi, Bijan; Pironneau, Olivier European Journal of Computational Mechanics, Vol. 17, Issue 1-2 https://doi.org/10.3166/remn.17.13-30	journal	January 2008
Efficient Aerodynamic Shape Optimization with Deep-Learning-Based Geometric Filtering Li, Jichao; Zhang, Mengqi; Martins, Joaquim R. R. A. AIAA Journal, Vol. 58, Issue 10 https://doi.org/10.2514/1.J059254	journal	October 2020
Boundary shape design by using PDE filtered design variables Matsumori, Tadayoshi; Kawamoto, Atsushi; Kondoh, Tsuguo Structural and Multidisciplinary Optimization, Vol. 56, Issue 3 https://doi.org/10.1007/s00158-017-1678-4	journal	March 2017
The implicit bulk-surface filtering method for node-based shape optimization and a comparison of explicit and implicit filtering techniques Najian Asl, Reza; Bletzinger, Kai-Uwe Structural and Multidisciplinary Optimization, Vol. 66, Issue 5 https://doi.org/10.1007/s00158-023-03548-2	journal	April 2023
MFEM: A modular finite element methods library Anderson, Robert; Andrej, Julian; Barker, Andrew Computers & Mathematics with Applications, Vol. 81 https://doi.org/10.1016/j.camwa.2020.06.009	journal	January 2021
On the discrete variant of the traction method in parameter-free shape optimization Riehl, Stefan; Friederich, Jan; Scherer, Michael Computer Methods in Applied Mechanics and Engineering, Vol. 278 https://doi.org/10.1016/j.cma.2014.05.009	journal	August 2014
High-Order Mesh Morphing for Boundary and Interface Fitting to Implicit Geometries Barrera, Jorge-Luis; Kolev, Tzanio; Mittal, Ketan Computer-Aided Design, Vol. 158 https://doi.org/10.1016/j.cad.2023.103499	journal	May 2023
Shape and topology optimization Allaire, Grégoire; Dapogny, Charles; Jouve, François Geometric Partial Differential Equations - Part II https://doi.org/10.1016/bs.hna.2020.10.004	book	October 2020
A shape optimization approach based on natural design variables and shape functions Belegundu, A. D.; Rajan, S. D. Computer Methods in Applied Mechanics and Engineering, Vol. 66, Issue 1 https://doi.org/10.1016/0045-7825(88)90061-8	journal	January 1988
On a shape control problem for the stationary Navier-Stokes equations Gunzburger, Max D.; Kim, Hongchul; Manservisi, Sandro ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 34, Issue 6 https://doi.org/10.1051/m2an:2000125	journal	November 2000
The inner structure of sensitivities in nodal based shape optimisation Gerzen, Nikolai; Materna, Daniel; Barthold, Franz-Joseph Computational Mechanics, Vol. 49, Issue 3 https://doi.org/10.1007/s00466-011-0648-8	journal	October 2011
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming Wächter, Andreas; Biegler, Lorenz T. Mathematical Programming, Vol. 106, Issue 1 https://doi.org/10.1007/s10107-004-0559-y	journal	April 2005
Analytical and numerical methods in shape optimization Harbrecht, Helmut Mathematical Methods in the Applied Sciences, Vol. 31, Issue 18 https://doi.org/10.1002/mma.1008	journal	March 2008
A consistent frame for sensitivity filtering and the vertex assigned morphing of optimal shape Bletzinger, Kai-Uwe Structural and Multidisciplinary Optimization, Vol. 49, Issue 6 https://doi.org/10.1007/s00158-013-1031-5	journal	January 2014

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Title: Yet another parameter-free shape optimization method

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