Variational approach to shape derivatives
ESAIM: COCV, 14 3 (2008) 517-539
Published online: 2008-02-07
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:
This article has been cited by the following article(s):
Localization of tumor through a non-conventional numerical shape optimization technique
Julius Fergy Tiongson RabagoApplied Numerical Mathematics 217 135 (2025)
https://doi.org/10.1016/j.apnum.2025.06.005
Detecting an Immersed Obstacle in Stokes Fluid Flow Using the Coupled Complex Boundary Method
J. F. T. Rabago, L. Afraites and H. NotsuSIAM Journal on Control and Optimization 63 (2) 822 (2025)
https://doi.org/10.1137/24M1647369
Approximation of Shape Optimization Problems with Nonsmooth PDE Constraints: An Optimality Conditions Point of View
Livia BetzSIAM Journal on Control and Optimization 63 (3) 1826 (2025)
https://doi.org/10.1137/24M1676181
Numerical Solution to a Free Boundary Problem for the Stokes Equation Using the Coupled Complex Boundary Method in Shape Optimization Setting
Julius Fergy Tiongson Rabago and Hirofumi NotsuApplied Mathematics & Optimization 89 (1) (2024)
https://doi.org/10.1007/s00245-023-10065-7
On shape and topological optimization problems with constraints Helmholtz equation and spectral problems
Mame Gor Ngom, Ibrahima Faye and Diaraf SeckResults in Applied Mathematics 23 100474 (2024)
https://doi.org/10.1016/j.rinam.2024.100474
Numerical solution to the exterior Bernoulli problem using the Dirichlet-Robin energy gap cost functional approach in two and three dimensions
Julius Fergy T. RabagoNumerical Algorithms 94 (1) 175 (2023)
https://doi.org/10.1007/s11075-023-01497-x
Long‐time behavior of shape design solutions for the Navier–Stokes equations
John Sebastian H. SimonZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 103 (2) (2023)
https://doi.org/10.1002/zamm.202100441
Level set‐based shape optimization approach for the inverse optical tomography problem
Zakaria Belhachmi, Rabeb Dhif and Houcine MeftahiZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 103 (3) (2023)
https://doi.org/10.1002/zamm.202200156
Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging
Caroline Geiersbach, Estefania Loayza-Romero and Kathrin WelkerHandbook 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 in acoustic–structure interaction
Philipp Kliewe, Antoine Laurain and Kersten SchmidtEngineering Computations 39 (1) 172 (2022)
https://doi.org/10.1108/EC-07-2021-0379
Simultaneous recovery of Robin boundary and coefficient for the Laplace equation by shape derivative
Weifu FangJournal of Computational and Applied Mathematics 413 114376 (2022)
https://doi.org/10.1016/j.cam.2022.114376
A shape design problem for the Navier–Stokes flow with a convective boundary condition
J. S. H Simon and Hirofumi NotsuComputational and Applied Mathematics 41 (4) (2022)
https://doi.org/10.1007/s40314-022-01876-5
Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging
Caroline Geiersbach, Estefania Loayza-Romero and Kathrin WelkerHandbook 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 optimization problem constrained with the Stokes equations to address maximization of vortices
John Sebastian Simon and Hirofumi NotsuEvolution Equations and Control Theory 11 (6) 1873 (2022)
https://doi.org/10.3934/eect.2022003
Topological Derivative of State-Constrained Objective Functions: A Direct Method
Michel C. DelfourSIAM Journal on Control and Optimization 60 (1) 22 (2022)
https://doi.org/10.1137/20M1368732
Topological derivatives via one-sided derivative of parametrized minima and minimax
Michel C. DelfourEngineering Computations 39 (1) 34 (2022)
https://doi.org/10.1108/EC-06-2021-0318
Stochastic Approximation for Optimization in Shape Spaces
Caroline Geiersbach, Estefania Loayza-Romero and Kathrin WelkerSIAM Journal on Optimization 31 (1) 348 (2021)
https://doi.org/10.1137/20M1316111
Shape Optimization for Superconductors Governed by H(curl)-Elliptic Variational Inequalities
Antoine Laurain, Malte Winckler and Irwin YouseptSIAM Journal on Control and Optimization 59 (3) 2247 (2021)
https://doi.org/10.1137/19M1294150
Shape sensitivity analysis for a microchannel cooling system
Sebastian Blauth, Christian Leithäuser and René PinnauJournal of Mathematical Analysis and Applications 492 (2) 124476 (2020)
https://doi.org/10.1016/j.jmaa.2020.124476
Solutions to a two-dimensional, Neumann free boundary problem
J. A. Gemmer, G. Moon and S. G. RaynorApplicable Analysis 99 (2) 214 (2020)
https://doi.org/10.1080/00036811.2018.1489960
First and Second Order Shape Optimization Based on Restricted Mesh Deformations
Tommy Etling, Roland Herzog, Estefanía Loayza and Gerd WachsmuthSIAM Journal on Scientific Computing 42 (2) A1200 (2020)
https://doi.org/10.1137/19M1241465
Inverse problem of shape identification from boundary measurement for Stokes equations: Shape differentiability of Lagrangian
Victor A. Kovtunenko and Kohji OhtsukaJournal of Inverse and Ill-posed Problems (2020)
https://doi.org/10.1515/jiip-2020-0081
Inverse problem of breaking line identification by shape optimization
Daria Ghilli, Karl Kunisch and Victor A. KovtunenkoJournal of Inverse and Ill-posed Problems 28 (1) 119 (2020)
https://doi.org/10.1515/jiip-2019-0047
Distributed and boundary expressions of first and second order shape derivatives in nonsmooth domains
Antoine LaurainJournal de Mathématiques Pures et Appliquées 134 328 (2020)
https://doi.org/10.1016/j.matpur.2019.09.002
A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functional
Julius Fergy T. Rabago and Hideyuki AzegamiComputational Optimization and Applications 77 (1) 251 (2020)
https://doi.org/10.1007/s10589-020-00199-7
An improved shape optimization formulation of the Bernoulli problem by tracking the Neumann data
Julius Fergy T. Rabago and Hideyuki AzegamiJournal of Engineering Mathematics 117 (1) 1 (2019)
https://doi.org/10.1007/s10665-019-10005-x
Inverse localization of earliest cardiac activation sites from activation maps based on the viscous Eikonal equation
Karl Kunisch, Aurel Neic, Gernot Plank and Philip TrautmannJournal of Mathematical Biology 79 (6-7) 2033 (2019)
https://doi.org/10.1007/s00285-019-01419-3
Two-Dimensional Shape Optimization with Nearly Conformal Transformations
José A. Iglesias, Kevin Sturm and Florian WechsungSIAM Journal on Scientific Computing 40 (6) A3807 (2018)
https://doi.org/10.1137/17M1152711
Shape Optimization for Interface Identification with Obstacle Problems
Björn Führ, Volker Schulz and Kathrin WelkerVietnam Journal of Mathematics 46 (4) 967 (2018)
https://doi.org/10.1007/s10013-018-0312-0
A consistent relaxation of optimal design problems for coupling shape and topological derivatives
Samuel Amstutz, Charles Dapogny and Àlex FerrerNumerische Mathematik 140 (1) 35 (2018)
https://doi.org/10.1007/s00211-018-0964-4
Optimal actuator design based on shape calculus
Dante Kalise, Karl Kunisch and Kevin SturmMathematical Models and Methods in Applied Sciences 28 (13) 2667 (2018)
https://doi.org/10.1142/S0218202518500586
Algorithmic Aspects of Multigrid Methods for Optimization in Shape Spaces
Martin Siebenborn and Kathrin WelkerSIAM Journal on Scientific Computing 39 (6) B1156 (2017)
https://doi.org/10.1137/16M1104561
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 UlbrichSIAM Journal on Control and Optimization 55 (5) 3226 (2017)
https://doi.org/10.1137/16M1089563
Geometric Science of Information
Kathrin WelkerLecture Notes in Computer Science, Geometric Science of Information 10589 65 (2017)
https://doi.org/10.1007/978-3-319-68445-1_8
Hyperbolic Equations with Mixed Boundary Conditions: Shape Differentiability Analysis
Lorena Bociu and Jean-Paul ZolésioApplied Mathematics & Optimization 76 (2) 375 (2017)
https://doi.org/10.1007/s00245-016-9354-4
Progress in Industrial Mathematics at ECMI 2016
Henry Kasumba, Godwin Kakuba and John Mango MageroMathematics in Industry, Progress in Industrial Mathematics at ECMI 2016 26 657 (2017)
https://doi.org/10.1007/978-3-319-63082-3_99
Sensitivity Analysis for Shape Optimization of a Focusing Acoustic Lens in Lithotripsy
Vanja Nikolić and Barbara KaltenbacherApplied Mathematics & Optimization 76 (2) 261 (2017)
https://doi.org/10.1007/s00245-016-9340-x
Shape and parameter reconstruction for the Robin transmission inverse problem
Antoine Laurain and Houcine MeftahiJournal of Inverse and Ill-posed Problems 24 (6) 643 (2016)
https://doi.org/10.1515/jiip-2015-0008
Shape derivatives for the compressible Navier–Stokes equations in variational form
Matthias Sonntag, Stephan Schmidt and Nicolas R. GaugerJournal of Computational and Applied Mathematics 296 334 (2016)
https://doi.org/10.1016/j.cam.2015.09.010
The shape derivative for an optimization problem in lithotripsy
Gunther Peichl and Barbara KaltenbacherEvolution Equations and Control Theory 5 (3) 399 (2016)
https://doi.org/10.3934/eect.2016011
Shape Optimization of an Electric Motor Subject to Nonlinear Magnetostatics
P. Gangl, U. Langer, A. Laurain, H. Meftahi and K. SturmSIAM Journal on Scientific Computing 37 (6) B1002 (2015)
https://doi.org/10.1137/15100477X
Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences
L. Kaland, M. Sonntag and N. R. GaugerComputational Methods in Applied Sciences, Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences 36 143 (2015)
https://doi.org/10.1007/978-3-319-11541-2_9
Minimax Lagrangian Approach to the Differentiability of Nonlinear PDE Constrained Shape Functions Without Saddle Point Assumption
Kevin SturmSIAM Journal on Control and Optimization 53 (4) 2017 (2015)
https://doi.org/10.1137/130930807
New Trends in Shape Optimization
Kevin SturmInternational Series of Numerical Mathematics, New Trends in Shape Optimization 166 271 (2015)
https://doi.org/10.1007/978-3-319-17563-8_12
Mathematics of nonlinear acoustics
Barbara KaltenbacherEvolution Equations & Control Theory 4 (4) 447 (2015)
https://doi.org/10.3934/eect.2015.4.447
A Transformation Approach in Shape Optimization: Existence and Regularity Results
Bernhard KinigerNumerical Functional Analysis and Optimization 36 (12) 1585 (2015)
https://doi.org/10.1080/01630563.2015.1076001
Shape optimization approaches to free‐surface problems
H. KasumbaInternational Journal for Numerical Methods in Fluids 74 (11) 818 (2014)
https://doi.org/10.1002/fld.3876
On Computation of the Shape Hessian of the Cost Functional Without Shape Sensitivity of the State Variable
H. Kasumba and K. KunischJournal of Optimization Theory and Applications 162 (3) 779 (2014)
https://doi.org/10.1007/s10957-013-0520-4
A New Optimal Control Approach for the Reconstruction of Extended Inclusions
Habib Ammari, Pierre Garapon, François Jouve, et al.SIAM Journal on Control and Optimization 51 (2) 1372 (2013)
https://doi.org/10.1137/100808952
From shape variation to topological changes in constrained minimization: a velocity method-based concept
M. Hintermüller and V. A. KovtunenkoOptimization Methods and Software 26 (4-5) 513 (2011)
https://doi.org/10.1080/10556788.2011.559548
284 (2010)
https://doi.org/10.1109/MMAR.2010.5587219
Goal-Oriented Error Estimation and Adaptivity for Free-Boundary Problems: The Shape-Linearization Approach
K. G. van der Zee, E. H. van Brummelen and R. de BorstSIAM Journal on Scientific Computing 32 (2) 1093 (2010)
https://doi.org/10.1137/080741239
Optimality Conditions for Shape and Topology Optimization Subject to a Cone Constraint
Samuel Amstutz and Marc Ciligot–TravainSIAM Journal on Control and Optimization 48 (6) 4056 (2010)
https://doi.org/10.1137/080722874