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On second-order tensor representation of derivatives in shape optimization
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
An improved numerical approach for solving shape optimization problems on convex domains
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
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
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
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
Optimal error estimates of the discrete shape gradients for shape optimizations governed by the Stokes-Brinkman equations
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
Improved Discrete Boundary Type Shape Gradients for PDE-constrained Shape Optimization
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
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
Modeling, Simulation and Optimization in the Health- and Energy-Sector
Thomas Marx, Nicolas Dietrich and René Pinnau SEMA SIMAI Springer Series, Modeling, Simulation and Optimization in the Health- and Energy-Sector 14 85 (2022) https://doi.org/10.1007/978-3-030-99983-4_5
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
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
Multiobjective design optimization of a quadrupole resonator under uncertainties
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
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
A level set method for Laplacian eigenvalue optimization subject to geometric constraints
Lipschitz Stable Determination of Polygonal Conductivity Inclusions in a Two-Dimensional Layered Medium from the Dirichlet-to-Neumann Map
Elena Beretta, Elisa Francini and Sergio Vessella SIAM Journal on Mathematical Analysis 53(4) 4303 (2021) https://doi.org/10.1137/20M1369609
A Shape Optimization Approach to the Problem of Covering a Two-Dimensional Region with Minimum-Radius Identical Balls
E. G. Birgin, A. Laurain, R. Massambone and A. G. Santana SIAM Journal on Scientific Computing 43(3) A2047 (2021) https://doi.org/10.1137/20M135950X
Level Set--Based Shape Optimization Approach for Sharp-Interface Reconstructions in Time-Domain Full Waveform Inversion
Yuri F. Albuquerque, Antoine Laurain and Irwin Yousept SIAM Journal on Applied Mathematics 81(3) 939 (2021) https://doi.org/10.1137/20M1378090
Shape Optimization for Superconductors Governed by H(curl)-Elliptic Variational Inequalities
Antoine Laurain, Malte Winckler and Irwin Yousept SIAM Journal on Control and Optimization 59(3) 2247 (2021) https://doi.org/10.1137/19M1294150
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
On Discrete Shape Gradients of Boundary Type for PDE-constrained Shape Optimization
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
A shape optimization approach for electrical impedance tomography with point measurements
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
Convergence analysis of mixed finite element approximations to shape gradients in the Stokes equation
An Equilibrated Fluxes Approach to the Certified Descent Algorithm for Shape Optimization Using Conforming Finite Element and Discontinuous Galerkin Discretizations
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
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
Shape Optimization with Nonsmooth Cost Functions: From Theory to Numerics