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On a numerical sensitivity approach involving Minkowski deformations for solving shape optimization problems constrained by a semi-linear PDE
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Analysis and application of a lower envelope method for sharp-interface multiphase problems
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Antoine Laurain and Pedro T. P. Lopes Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 382(2277) (2024) https://doi.org/10.1098/rsta.2023.0300
A. Garon, M.C. Delfour: “Transfinite Interpolations and Eulerian/Lagrangian Dynamics”
Stress-based topological shape optimization for thick shells using the level set method and trimmed non-conforming multi-patch isogeometric analysis
Fernando Hübner Scherer, Malek Zarroug, Hakim Naceur and Andrei Constantinescu Structural and Multidisciplinary Optimization 67(10) (2024) https://doi.org/10.1007/s00158-024-03892-x
An improved numerical approach for solving shape optimization problems on convex domains
Reconstruction of Voronoi diagrams in inverse potential problems
Ernesto G. Birgin, Antoine Laurain and Danilo R. Souza ESAIM: Control, Optimisation and Calculus of Variations 30 85 (2024) https://doi.org/10.1051/cocv/2024072
Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds
Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging
Caroline Geiersbach, Estefania Loayza-Romero and Kathrin Welker Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging 1585 (2023) https://doi.org/10.1007/978-3-030-98661-2_120
Shape Optimization of the Stokes Eigenvalue Problem
Robust Level-Set-Based Topology Optimization Under Uncertainties Using Anchored ANOVA Petrov–Galerkin Method
Christophe Audouze, Aaron Klein, Adrian Butscher, Nigel Morris, Prasanth Nair and Masayuki Yano SIAM/ASA Journal on Uncertainty Quantification 11(3) 877 (2023) https://doi.org/10.1137/22M1524722
Computational Design of Flexible Planar Microstructures
Zhan Zhang, Christopher Brandt, Jean Jouve, Yue Wang, Tian Chen, Mark Pauly and Julian Panetta ACM Transactions on Graphics 42(6) 1 (2023) https://doi.org/10.1145/3618396
An abstract Lagrangian framework for computing shape derivatives
Antoine Laurain, Pedro T.P. Lopes and Jean C. Nakasato ESAIM: Control, Optimisation and Calculus of Variations 29 5 (2023) https://doi.org/10.1051/cocv/2022078
Numerical shape optimization of the Canham-Helfrich-Evans bending energy
A Shape-Newton Approach to the Problem of Covering with Identical Balls
Ernesto G. Birgin, Antoine Laurain, Rafael Massambone and Arthur G. Santana SIAM Journal on Scientific Computing 44(2) A798 (2022) https://doi.org/10.1137/21M1426067
Shape Sensitivity of Eigenvalue Functionals for Scalar Problems: Computing the Semi-derivative of a Minimum
Lipschitz Stable Determination of Polyhedral Conductivity Inclusions from Local Boundary Measurements
Andrea Aspri, Elena Beretta, Elisa Francini and Sergio Vessella SIAM Journal on Mathematical Analysis 54(5) 5182 (2022) https://doi.org/10.1137/22M1480550
Improved Discrete Boundary Type Shape Gradients for PDE-constrained Shape Optimization
Non-Smooth and Complementarity-Based Distributed Parameter Systems
Volker H. Schulz and Kathrin Welker International Series of Numerical Mathematics, Non-Smooth and Complementarity-Based Distributed Parameter Systems 172 397 (2022) https://doi.org/10.1007/978-3-030-79393-7_16
Shape optimization in acoustic–structure interaction
Modeling, Simulation and Optimization in the Health- and Energy-Sector
Nicolas Dietrich, Thomas Marx and René Pinnau SEMA SIMAI Springer Series, Modeling, Simulation and Optimization in the Health- and Energy-Sector 14 105 (2022) https://doi.org/10.1007/978-3-030-99983-4_6
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Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging
Caroline Geiersbach, Estefania Loayza-Romero and Kathrin Welker Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging 1 (2022) https://doi.org/10.1007/978-3-030-03009-4_120-1
The strip method for shape derivatives
Sean Hardesty, Harbir Antil, Drew P. Kouri and Denis Ridzal International Journal for Numerical Methods in Engineering 123(7) 1606 (2022) https://doi.org/10.1002/nme.6908
Multiobjective design optimization of a quadrupole resonator under uncertainties
Mathematical Modeling, Simulation and Optimization for Power Engineering and Management
Christian Leithäuser and René Pinnau Mathematics in Industry, Mathematical Modeling, Simulation and Optimization for Power Engineering and Management 34 123 (2021) https://doi.org/10.1007/978-3-030-62732-4_6
Comparison of Shape Derivatives Using CutFEM for Ill-posed Bernoulli Free Boundary Problem
The Shifted Interface Method: A flexible approach to embedded interface computations
Kangan Li, Nabil M. Atallah, G. Alex Main and Guglielmo Scovazzi International Journal for Numerical Methods in Engineering 121(3) 492 (2020) https://doi.org/10.1002/nme.6231
Gradient based biobjective shape optimization to improve reliability and cost of ceramic components
First and Second Order Shape Optimization Based on Restricted Mesh Deformations
Tommy Etling, Roland Herzog, Estefanía Loayza and Gerd Wachsmuth SIAM Journal on Scientific Computing 42(2) A1200 (2020) https://doi.org/10.1137/19M1241465
Shape Derivatives for the Penalty Formulation of Elastic Contact Problems with Tresca Friction
An Equilibrated Fluxes Approach to the Certified Descent Algorithm for Shape Optimization Using Conforming Finite Element and Discontinuous Galerkin Discretizations
Fréchet Differentiability of Unsteady Incompressible Navier--Stokes Flow with Respect to Domain Variations of Low Regularity by Using a General Analytical Framework
Michael Fischer, Florian Lindemann, Michael Ulbrich and Stefan Ulbrich SIAM Journal on Control and Optimization 55(5) 3226 (2017) https://doi.org/10.1137/16M1089563
Certified Descent Algorithm for shape optimization driven by fully-computable a posteriori error estimators
Matteo Giacomini, Olivier Pantz and Karim Trabelsi ESAIM: Control, Optimisation and Calculus of Variations 23(3) 977 (2017) https://doi.org/10.1051/cocv/2016021
A cut finite element method for the Bernoulli free boundary value problem
Erik Burman, Daniel Elfverson, Peter Hansbo, Mats G. Larson and Karl Larsson Computer Methods in Applied Mechanics and Engineering 317 598 (2017) https://doi.org/10.1016/j.cma.2016.12.021