Prof. Dr. Antoine Laurain

​Laurain

​​

Prof. Dr. Antoine Laurain
Universität Duisburg-Essen
Fakultät für Mathematik
Thea-Leymann-Straße 9
D-45127 Essen

Room: WSC-N-4.36

Tel: + 49 201 183 6382

E-mail: antoine.laurain[at]uni-due.de

 

Research Interests

  • shape and topology optimization
  • free boundary problems
  • inverse problems
  • PDE-constrained optimization
  • optimal control
  • asymptotic analysis
  • numerical analysis​​

 

Links

 

Publications in refereed journals

 

46) Analysis and application of a lower envelope method for sharp-interface multiphase problems
Antoine Laurain
Control and Cybernetics 53(1) :189-229 (2025)
DOI : 10.2478/candc-2024-0009
45) Reconstruction of Voronoi diagrams in inverse potential problems
Ernesto G. Birgin, Antoine Laurain, Danilo R. Souza
ESAIM : COCV 30 85 (2024)
DOI : 10.1051/cocv/2024072
44) On second-order tensor representation of derivatives in shape optimization
Antoine Laurain and Pedro T.P. Lopes
Accepted for publication in Philosophical Transactions A (2024), Volume 382,Issue 2277
https://doi.org/10.1098/rsta.2023.0300
43) Bounds on the Optimal Radius When Covering a Set with Minimum Radius Identical Disks
E.G. Birgin, J. L. Gardenghi, A. Laurain
Mathematics of Operations Research 2024 49:3, 1855-1889
https://doi.org/10.1287/moor.2022.0104
42) Optimization of the first Dirichlet Laplacian eigenvalue with respect to a union of balls
E.G. Birgin, L. S. Fernandez, G. Haeser, A. Laurain
The Journal of Geometric Analysis, volume 33, 184 (2023)
https://doi.org/10.1007/s12220-023-01241-w
41) Sensitivity analysis and tailored design of minimization diagrams
E.G. Birgin, A. Laurain, T.C. Menezes
Mathematics of Computation, Volume 92, Number 344, November 2023, Pages 2715-2768
https://doi.org/10.1090/mcom/3839
40) An abstract Lagrangian framework for computing shape derivatives
A. Laurain, P. T. P. Lopes, J. C. Nakasato
ESAIM: Control, Optimisation and Calculus of Variations 29 (2023) 5
https://doi.org/10.1051/cocv/2022078
39) A Shape-Newton approach to the problem of covering with identical balls
E.G. Birgin, A. Laurain, R. Massambone, A.G. Santana
SIAM Journal on Scientific Computing 44, pp. A798-A824, 2022.
https://doi.org/10.1137/21M1426067
38) Shape optimization in acoustic-structure interaction
P. Kliewe, A. Laurain, K. Schmidt
Engineering Computations, , Vol. 39 No. 1, pp. 172-200.
https://doi.org/10.1108/EC-07-2021-0379
37) Optimal control of volume-preserving mean curvature flow
A. Laurain, S.W. Walker
Journal of Computational Physics, Volume 438, 1 August 2021, 110373
https://doi.org/10.1016/j.jcp.2021.110373
36) 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, A.G. Santana
SIAM Journal on Scientific Computing, 43(3), A2047-A2078. (32 pages))
https://doi.org/10.1137/20M135950X
35) Shape optimization for superconductors governed by H(curl)-elliptic variational inequalities
A. Laurain, M. Winckler, and I. Yousept
SIAM Journal on Control and Optimization, 59(3), 2247–2272. (26 pages)
https://doi.org/10.1137/19M1294150
34) Level set-based shape optimization approach for sharp-interface reconstructions in time-domain full waveform inversion
Y. F. Albuquerque, A. Laurain, and I. Yousept
SIAM Journal on Applied Mathematics, 81(3), 939-964
https://doi.org/10.1137/20M1378090
33) A shape optimization approach for electrical impedance tomography with point measurements
Y. F. Albuquerque, A. Laurain, and K. Sturm
Inverse Problems, Volume 36, No. 9, September 2020
https ://doi.org/10.1088/1361-6420/ab9f87
32) Distributed and boundary expressions of first and second order shape derivatives in nonsmooth domains
A. Laurain
Journal de Mathématiques Pures et Appliquées, Volume 134, February 2020, Pages 328-368
https://doi.org/10.1016/j.matpur.2019.09.002
31) Analysing smooth and singular domain perturbations in level set methods
A. Laurain
SIAM Journal on Mathematical Analysis, 50(4), 4327-4370. (44 pages) (2018).
https://doi.org/10.1137/17M1118956
30) A level set-based structural optimization code using FEniCS
A. Laurain
Structural and Multidisciplinary Optimization, September 2018, Volume 58, Issue 3, pp 1311--1334.
https://doi.org/10.1007/s00158-018-1950-2
29) Properties of optimizers of the principal eigenvalue with indefinite weight and Robin conditions
J. Lamboley, A. Laurain, G. Nadin and Y. Privat
Calculus of Variations and Partial Differential Equations (2016) 55: 144.
DOI:10.1007/s00526-016-1084-6
28) Stability Analysis of the Reconstruction Step of the Voronoi Implicit Interface Method
A. Laurain,
SIAM Journal on Numerical Analysis, Vol. 55, No. 1, pp. 1--30 (2017).
DOI: http://dx.doi.org/10.1137/15M1046290
27) Shape and parameter reconstruction for the Robin transmission inverse problem
A. Laurain, H. Meftahi,
Journal of Inverse and Ill-posed Problems. Volume 24, Issue 6, Pages 643-662, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219,
DOI: 10.1515/jiip-2015-0008, May 2016
26) A first order approach for worst-case shape optimization of the compliance for a mixture in the low contrast regime
M. Dambrine, A. Laurain,
Structural and Multidisciplinary Optimization (2016) 54:215--231.
DOI: 10.1007/s00158-015-1384-z
25) Shape optimization of an electric motor subject to nonlinear magnetostatics
P. Gangl, U. Langer, A. Laurain, H. Meftahi, K. Sturm,
SIAM J. Sci. Comput. Vol. 37, No. 6, pp. B1002-B1025 (2015)
DOI: 10.1137/15100477X
24) Distributed shape derivative via averaged adjoint method and applications
A. Laurain, K. Sturm,
ESAIM: Mathematical Modelling and Numerical Analysis 50 (2016) 1241-1267
DOI: http://dx.doi.org/10.1051/m2an/2015075
23) A new reconstruction method for the inverse source problem from partial boundary measurements
A. Canelas, A. Laurain, A.A. Novotny,
Inverse Problems 31 (2015) 075009
doi:10.1088/0266-5611/31/7/075009
22) Shape sensitivities for an inverse problem in magnetic induction tomography based on the eddy current model
M. Hintermüller, A. Laurain, I. Yousept,
Inverse Problems 31 (2015) 065006
doi:10.1088/0266-5611/31/6/065006
21) Droplet footprint control
A. Laurain, S. Walker,
SIAM J. Control Optim., 53(2), 771--799. (29 pages)
doi:10.1137/140979721
20) A bilevel shape optimization problem for the exterior Bernoulli free boundary value problem
H. Kasumba, K. Kunisch, A. Laurain,
Interfaces and Free Boundaries 16(2014), 459-487.
19) A new reconstruction method for the inverse potential problem
A. Canelas, A. Laurain, A.A. Novotny,
Journal of Computational Physics 268 (2014), 417-431.
18) Global minimizers of the ground state for two phase conductors in low contrast regime
A. Laurain,
ESAIM : COCV 20 (2014), 362--388.
17) A semismooth Newton method for a class of semilinear optimal control problems with box and volume constraints
S. Amstutz, A. Laurain,
Computational Optimization and Applications 56 (2013), no. 2, 369--403.
16) Topological sensitivity analysis in fluorescence optical tomography
A. Laurain, M. Hintermüller, M. Freiberger, H. Scharfetter,
Inverse Problems 29 (2013) 025003.
15) Minimization of the ground state for two phase conductors in low contrast regime
C. Conca, A. Laurain, R. Mahadevan,
SIAM Journal on Applied Mathematics: Vol. 72, No. 4 (2012), Pages 1238-1259.
14) Principal Eigenvalue Minimization for an Elliptic Problem with Indefinite Weight and Robin Boundary Conditions
M. Hintermüller, C.-Y. Kao, A. Laurain,
Applied Mathematics & Optimization: Volume 65, Issue 1 (2012), Pages 111-146
13) An image space approach to Cartesian based parallel MR imaging with total variation regularization
S.L. Keeling, C. Clason, M. Hintermüller, F. Knoll, A. Laurain, G. Von Winckel,
Medical Image Analysis, Volume 16, Issue 1, January 2012, Pages 189-200.
12) A total variation based approach to correcting surface coil magnetic resonance images
S.L. Keeling, M. Hinterm\"uller, F. Knoll, D. Kraf, A. Laurain,
Applied Mathematics and Computation, Volume 218, Issue 2, 15 September 2011, Pages 219-232
11) Optimal shape design subject to variational inequalities
M. Hintermüller and A. Laurain,
SIAM Journal on Control and Optimization, Vol.49 (2011), No.3, pp. 1015-1047.
10) Second-order topological expansion for electrical impedance tomography
M. Hintermüller, A. Laurain and A.A. Novotny,
Advances in Computational Mathematics 36 (2012), no. 2, 235--265.
9) On a Bernoulli problem with geometric constraints
A. Laurain and Y. Privat,
ESAIM: Control, Optimisation and Calculus of Variations (2012), no. 1, 157--180.
8) Singular perturbations of curved boundaries in dimension three. The spectrum of the Neumann Laplacian
A. Laurain, S. Nazarov and J. Sokolowski,
Journal for Analysis and its Applications, Vol. 30 (2011), No. 2, pp. 148-180.
7) Multiphase image segmentation and modulation recovery based on shape and topological sensitivity
M. Hintermüller and A. Laurain,
Journal of Mathematical Imaging and Vision, Volume 35, Number 1 (September 2009). pp. 1-22.
6) On the analysis of boundary value problems in nonsmooth domains
Frémiot, W. Horn, A. Laurain, M. Rao and J. Sokolowski,
Dissertationes Mathematicae, 462 (2009), 149 pp.
5) Electrical Impedance Tomography: From Topology to Shape
M. Hintermüller and A. Laurain
Control and Cybernetics, special issue on the occasion of Jean-Paul Zoléesio's 60th birthday, Vol. 37, No. 4, 2008.
4) A shape and topology optimization technique for solving a class of linear complementary problems in function space
M. Hintermüller and A. Laurain,
Computational Optimization and Applications, 2010, Vol. 46, No. 3, pp. 535-569.
3) Level set method with topological derivatives in shape optimization
P. Fulmanski, A. Laurain, J.-F. Scheid and J. Sokolowski,
International Journal of Computer Mathematics, Vol. 85, No. 10, October 2008, pp. 1491-1514(24).
2) A level set method in shape and topology optimization for variational inequalities
P. Fulmanski, A. Laurain, J.-F. Scheid and J. Sokolowski,
International Journal of Applied Mathematics and Computer Science, 2007, Vol. 17, No. 3, 413-430.
1) Structure of shape derivatives in non-smooth domains and applications
A. Laurain,
Advances in Mathematical Sciences and Applications, Vol.15, No.1 (2005).

 

Extended abstracts

2) Sharp-interface imaging in full waveform inversion using finite elements
K. J. Roberts, Y. Albuquerque, A. Laurain,
82nd EAGE Annual Conference \& Exhibition
1) Reconstruction of Sharp Interfaces in Time-Domain Full Waveform Inversion
Y. Albuquerque, A. Laurain,
Conference Proceedings, 82nd EAGE Annual Conference & Exhibition Workshop Programme, Dec 2020, Volume 2020, p.1 - 5. European Association of Geoscientists & Engineers DOI : https ://doi.org/10.3997/2214-4609.202011976

 

Conference proceedings

10) Topological derivative-based heat sink design with temperature constraints
Giovanna C. Andrade, Antoine Laurain, Antonio A. Novotny,
The 9th European Congress on Computational Methods in Applied Sciences and Engineering,
ECCOMAS Congress 2024, 3-7 June 2024, Lisboa, Portugal.
9) A new method for the inverse potential problem based on the topological derivative
A.A. Novotny, A. Canelas, A. Laurain,
Proceedings of the XXXIV Iberian Latin-American Congress on Computational Methods in Engineering,
Z.J.G.N Del Prado (Editor), ABMEC, Pirenópolis, GO, Brazil, November 10-13, 2013.
8) A Non-Iterative Method for the Inverse Potential Problem Based on the Topological Derivative
A. Canelas, A. Laurain, A.A. Novotny
Mini-Workshop: Geometries, Shapes and Topologies in PDE-based Applications.
Oberwolfach Report No. 57/2012 (DOI: 10.4171/OWR/2012/57)
7) Minimization of the ground state for two phase conductors in low contrast regime
C. Conca, A. Laurain, R. Mahadevan,
Mini-Workshop: Geometries, Shapes and Topologies in PDE-based Applications.
Oberwolfach Report No. 57/2012 (DOI: 10.4171/OWR/2012/57).
6) Using the topological derivative for initializing a Markov-chain Monte Carlo reconstruction in fluorescence tomography
M. Freiberger, A. Laurain, M. Hintermüller, A. Köstinger and H. Scharfetter,
Proceedings of SPIE-OSA Biomedical Optics, SPIE Vol. 8088, 80881Q (2011). (doi:10.1117/12.889609).
5) Topological Derivative for Image Reconstruction in Fluorescence Tomography
M. Freiberger, M. Hintermüller, A. Laurain and H. Scharfetter,
Biomedizinische Technik/Biomedical Engineering. Volume 55, Issue s1, Pages 1--264,
44. DGBMT Jahrestagung Rostock (2010).
DOI: 10.1515/BMT.2010.447, October 2010
4) Numerical algorithms for an inverse problem in shape optimization
M. Grzanek, A. Laurain and K. Szulc,
6th International Conference on Inverse Problems in Engineering: Theory and Practice,
Journal of Physics: Conference series, Vol. 135 (2008) 012047.
3) Using self-adjoint extensions in shape optimization
A. Laurain and K. Szulc,
System modeling and optimization, 331--349, IFIP Adv. Inf. Commun. Technol., 312, Springer, Berlin, 2009.
2) Une méthode levelset en optimisation de formes,
P. Fulmanski, A. Laurain, J.-F. Scheid and J. Sokolowski,
ESAIM proceedings (French), (2008), Vol. 22, 162-168.
1) Level set method for shape optimization of Signorini problem
P. Fulmanski, A. Laurain and J.-F. Scheid,
MMAR proceedings (2004), Vol. 1, 71-75.

 

Chapters in book, reports and miscellaneous

5) Shape optimization for covering problems
E. G. Birgin and A. Laurain,
Notices of the American Mathematical Society 70, pp. 1584-1591, 2023,
DOI: 10.1090/noti2799
4) Topological derivatives and Levelset method in shape optimization
P. Fulmanski, A. Laurain, J-F Scheid, J. Sokolowski, K. Szulc,
in Electrical Capacitance Tomography. Theoretical Basis and Applications, pp 12-67,
Dominik Sankowski and Jan Sikora, Eds, Wydawnictwo Ksiazkowe Instytutu Elektrotechniki,
Warszaw 2010, ISBN 978-83-61956-00-6.
3) Elliptic Mathematical Programs with Equilibrium Constraints in Function Space: Optimality Conditions and Numerical Realization,
M. Hintermüller, A. Laurain, C. Löbhard, C. Rautenberg, T. Surowiec
in Trends in PDE Constrained Optimization, pp 133-153,
Editors: G. Leugering, P. Benner, S. Engell, A. Griewank, H. Harbrecht, M. Hinze, R. Rannacher, S. Ulbrich, International Series of Numerical Mathematics, 165
Springer International Publishing
DOI: 10.1007/978-3-319-05083-6_9
2) Modulation recovery and image reconstruction in Parallel Magnetic Resonance Imaging: a structural study by parameterization,
M. Hintermüller, S.L. Keeling and A. Laurain,
SFB report no. 23, (2008).
1) Where to place a hole?
M. Hintermüller and A. Laurain,
ECMI Newsletter 41, march 2007