Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Electrical Impedance Tomography Deep Imaging With Dual-Branch U-Net Based on Deformable Convolution and Hyper-Convolution

Zichen Wang, Xiuyan Li, Yukuan Sun and Qi Wang
IEEE Transactions on Instrumentation and Measurement 73 1 (2024)
https://doi.org/10.1109/TIM.2024.3369160

Optimal error estimates of the discrete shape gradients for shape optimizations governed by the Stokes-Brinkman equations

Yingyuan Li, Wenjing Yan, Shengfeng Zhu and Feifei Jing
Applied Numerical Mathematics 190 220 (2023)
https://doi.org/10.1016/j.apnum.2023.04.019

Directional differentiability for shape optimization with variational inequalities as constraints

Victor A. Kovtunenko and Karl Kunisch
ESAIM: Control, Optimisation and Calculus of Variations 29 64 (2023)
https://doi.org/10.1051/cocv/2023056

Shape Optimization of the Stokes Eigenvalue Problem

Jiajie Li and Shengfeng Zhu
SIAM Journal on Scientific Computing 45 (2) A798 (2023)
https://doi.org/10.1137/21M1451543

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 improved numerical approach for solving shape optimization problems on convex domains

Abdelkrim Chakib, Ibrahim Khalil and Azeddine Sadik
Numerical Algorithms (2023)
https://doi.org/10.1007/s11075-023-01660-4

Lagrangian approach and shape gradient for inverse problem of breaking line identification in solid: contact with adhesion

Victor A Kovtunenko
Inverse Problems 39 (8) 084004 (2023)
https://doi.org/10.1088/1361-6420/acdf15

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

Numerical shape optimization of the Canham-Helfrich-Evans bending energy

Michael Neunteufel, Joachim Schöberl and Kevin Sturm
Journal of Computational Physics 488 112218 (2023)
https://doi.org/10.1016/j.jcp.2023.112218

A Unified Approach to Shape and Topological Sensitivity Analysis of Discretized Optimal Design Problems

P. Gangl and M. H. Gfrerer
Applied Mathematics & Optimization 88 (2) (2023)
https://doi.org/10.1007/s00245-023-10016-2

Bounds on the Optimal Radius When Covering a Set with Minimum Radius Identical Disks

Ernesto G. Birgin, John L. Gardenghi and Antoine Laurain
Mathematics of Operations Research (2023)
https://doi.org/10.1287/moor.2022.0104

Numerical Reconstruction of a Discontinuous Diffusive Coefficient in Variable-Order Time-Fractional Subdiffusion

Wei Fan, Xindi Hu and Shengfeng Zhu
Journal of Scientific Computing 96 (1) (2023)
https://doi.org/10.1007/s10915-023-02237-y

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

On mixed finite element approximations of shape gradients in shape optimization with the Navier–Stokes equation

Jiajie Li, Shengfeng Zhu and Xiaoqin Shen
Numerical Methods for Partial Differential Equations 39 (2) 1604 (2023)
https://doi.org/10.1002/num.22947

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

Sensitivity analysis and tailored design of minimization diagrams

E. Birgin, A. Laurain and T. Menezes
Mathematics of Computation 92 (344) 2715 (2023)
https://doi.org/10.1090/mcom/3839

Improved Discrete Boundary Type Shape Gradients for PDE-constrained Shape Optimization

Wei Gong, Jiajie Li and Shengfeng Zhu
SIAM Journal on Scientific Computing 44 (4) A2464 (2022)
https://doi.org/10.1137/21M1457400

A level set method for Laplacian eigenvalue optimization subject to geometric constraints

Meizhi Qian and Shengfeng Zhu
Computational Optimization and Applications 82 (2) 499 (2022)
https://doi.org/10.1007/s10589-022-00371-1

Shape Sensitivity of Eigenvalue Functionals for Scalar Problems: Computing the Semi-derivative of a Minimum

Fabien Caubet, Marc Dambrine and Rajesh Mahadevan
Applied Mathematics & Optimization 86 (1) (2022)
https://doi.org/10.1007/s00245-022-09827-6

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

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 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

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

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

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

Multiobjective design optimization of a quadrupole resonator under uncertainties

Piotr Putek, Shahnam Gorgi Zadeh, Marc Wenskat and Ursula van Rienen
Physical Review Accelerators and Beams 25 (1) (2022)
https://doi.org/10.1103/PhysRevAccelBeams.25.012002

A priori error analysis of shape derivatives of linear functionals in structural topology optimization

Aaron Klein, Prasanth B. Nair and Masayuki Yano
Computer Methods in Applied Mechanics and Engineering 395 114991 (2022)
https://doi.org/10.1016/j.cma.2022.114991

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

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

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 and topology optimization in electrical impedance tomography via moving morphable components method

Dong Liu and Jiangfeng Du
Structural and Multidisciplinary Optimization 64 (2) 585 (2021)
https://doi.org/10.1007/s00158-021-02970-8

Nonlinear Conjugate Gradient Methods for PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics

Sebastian Blauth
SIAM Journal on Optimization 31 (3) 1658 (2021)
https://doi.org/10.1137/20M1367738

Comparison of Shape Derivatives Using CutFEM for Ill-posed Bernoulli Free Boundary Problem

Erik Burman, Cuiyu He and Mats G. Larson
Journal of Scientific Computing 88 (2) (2021)
https://doi.org/10.1007/s10915-021-01544-6

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

On Discrete Shape Gradients of Boundary Type for PDE-constrained Shape Optimization

Wei Gong and Shengfeng Zhu
SIAM Journal on Numerical Analysis 59 (3) 1510 (2021)
https://doi.org/10.1137/20M1323898

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

On accuracy of approximate boundary and distributed H1 shape gradient flows for eigenvalue optimization

Shengfeng Zhu, Xianliang Hu and Qingbiao Wu
Journal of Computational and Applied Mathematics 365 112374 (2020)
https://doi.org/10.1016/j.cam.2019.112374

Scientific Computing in Electrical Engineering

Peter Gangl, Ulrich Langer, Angelos Mantzaflaris and Rainer Schneckenleitner
Mathematics in Industry, Scientific Computing in Electrical Engineering 32 35 (2020)
https://doi.org/10.1007/978-3-030-44101-2_4

Distributed and boundary expressions of first and second order shape derivatives in nonsmooth domains

Antoine Laurain
Journal de Mathématiques Pures et Appliquées 134 328 (2020)
https://doi.org/10.1016/j.matpur.2019.09.002

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

A shape optimization approach for electrical impedance tomography with point measurements

Yuri Flores Albuquerque, Antoine Laurain and Kevin Sturm
Inverse Problems 36 (9) 095006 (2020)
https://doi.org/10.1088/1361-6420/ab9f87

Shape Derivatives for the Penalty Formulation of Elastic Contact Problems with Tresca Friction

Bastien Chaudet-Dumas and Jean Deteix
SIAM Journal on Control and Optimization 58 (6) 3237 (2020)
https://doi.org/10.1137/19M125813X

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

O. T. Doganay, H. Gottschalk, C. Hahn, et al.
Optimization and Engineering 21 (4) 1359 (2020)
https://doi.org/10.1007/s11081-019-09478-7

Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization

Shengfeng Zhu, Xianliang Hu and Qifeng Liao
BIT Numerical Mathematics 60 (3) 853 (2020)
https://doi.org/10.1007/s10543-019-00782-3

Inverse problem of breaking line identification by shape optimization

Daria Ghilli, Karl Kunisch and Victor A. Kovtunenko
Journal of Inverse and Ill-posed Problems 28 (1) 119 (2020)
https://doi.org/10.1515/jiip-2019-0047

Inverse localization of earliest cardiac activation sites from activation maps based on the viscous Eikonal equation

Karl Kunisch, Aurel Neic, Gernot Plank and Philip Trautmann
Journal of Mathematical Biology 79 (6-7) 2033 (2019)
https://doi.org/10.1007/s00285-019-01419-3

Convergence analysis of mixed finite element approximations to shape gradients in the Stokes equation

Shengfeng Zhu and Zhiming Gao
Computer Methods in Applied Mechanics and Engineering 343 127 (2019)
https://doi.org/10.1016/j.cma.2018.08.024

Higher-Order Moving Mesh Methods for PDE-Constrained Shape Optimization

Alberto Paganini, Florian Wechsung and Patrick E. Farrell
SIAM Journal on Scientific Computing 40 (4) A2356 (2018)
https://doi.org/10.1137/17M1133956

Designing polymer spin packs by tailored shape optimization techniques

Christian Leithäuser, René Pinnau and Robert Feßler
Optimization and Engineering 19 (3) 733 (2018)
https://doi.org/10.1007/s11081-018-9396-3

An Equilibrated Fluxes Approach to the Certified Descent Algorithm for Shape Optimization Using Conforming Finite Element and Discontinuous Galerkin Discretizations

Matteo Giacomini
Journal of Scientific Computing 75 (1) 560 (2018)
https://doi.org/10.1007/s10915-017-0545-1

Analyzing Smooth and Singular Domain Perturbations in Level Set Methods

Antoine Laurain
SIAM Journal on Mathematical Analysis 50 (4) 4327 (2018)
https://doi.org/10.1137/17M1118956

Two-Dimensional Shape Optimization with Nearly Conformal Transformations

José A. Iglesias, Kevin Sturm and Florian Wechsung
SIAM Journal on Scientific Computing 40 (6) A3807 (2018)
https://doi.org/10.1137/17M1152711

A Shape Optimization Algorithm for Interface Identification Allowing Topological Changes

Martin Siebenborn
Journal of Optimization Theory and Applications 177 (2) 306 (2018)
https://doi.org/10.1007/s10957-018-1279-4

Optimum Experimental Design by Shape Optimization of Specimens in Linear Elasticity

Tommy Etling and Roland Herzog
SIAM Journal on Applied Mathematics 78 (3) 1553 (2018)
https://doi.org/10.1137/17M1147743

Effective Shape Optimization of Laplace Eigenvalue Problems Using Domain Expressions of Eulerian Derivatives

Shengfeng Zhu
Journal of Optimization Theory and Applications 176 (1) 17 (2018)
https://doi.org/10.1007/s10957-017-1198-9

Optimal actuator design based on shape calculus

Dante Kalise, Karl Kunisch and Kevin Sturm
Mathematical Models and Methods in Applied Sciences 28 (13) 2667 (2018)
https://doi.org/10.1142/S0218202518500586

Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

Elena Beretta, Stefano Micheletti, Simona Perotto and Matteo Santacesaria
Journal of Computational Physics 353 264 (2018)
https://doi.org/10.1016/j.jcp.2017.10.017

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

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

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

Kevin Sturm
SIAM Journal on Control and Optimization 54 (6) 3319 (2016)
https://doi.org/10.1137/16M1069882

Shape and parameter reconstruction for the Robin transmission inverse problem

Antoine Laurain and Houcine Meftahi
Journal of Inverse and Ill-posed Problems 24 (6) 643 (2016)
https://doi.org/10.1515/jiip-2015-0008

A first order approach for worst-case shape optimization of the compliance for a mixture in the low contrast regime

Marc Dambrine and Antoine Laurain
Structural and Multidisciplinary Optimization 54 (2) 215 (2016)
https://doi.org/10.1007/s00158-015-1384-z