Xavier Claeys

Contact

Bureau 15-25-310
Université Pierre et Marie Curie
Laboratoire Jacques-Louis Lions
4 place Jussieu
75005 Paris

Tel: +33 (0)1 44 27 72 01
Email: xavier_DOT_claeys_AT_sorbonne_DASH_universite_DOT_fr

Detailed curriculum vitae (updated in March 2022).

Research topics

My research activity is centered on the modelling and numerical analysis of linear wave propagation phenomena, in the context of frequency domain electromagnetics and acoustics. My main interests concern:

• domain decomposition,
• boundary element methods,
• scientific computing,
• multi-scale problems,
• singularities in elliptic problems.

In the past, I have been leading coordinator of the research project NonlocalDD funded by the French National Research Agency (so-called ANR) for investigating boundary integral equations in conjunction with domain decomposition. Before that, I had been involved in the METAMATH project funded by ANR that focused on the modelling and numerical analysis of metamaterials. Below are four presentations that provide a glimpse at my research concerns

• Plenary talk at the WAVES conference, 2022,
• Talk at the seminar on PDE at Versailles university, 2015,
• Talk at the Journées Singulières Augmentées 2013,
• Talk at the seminar of Laboratoire Jacques Louis Lions, 2012.

Software projects

Part of my research activity is dedicated to software projects. My favorite langage is C++. Here are projects I am developing.

Boundary elements

For practical purposes (implementation of multi-trace formulations in particular), I am developping my own boundary element library. It allows easy/fast implementation of multi-trace formulations [Claeys & Hiptmair, 2013]. It is called bemtool and available on GitHub, under the GNU Lesser General Public License. bemtool has recently been interfaced with freefem++.

Domain decomposition

For testing and experimenting Generalized Optimized Schwarz Methods introduced in [Claeys,2021] and [Claeys & Parolin,2022], I co-developped with R.Delville-Atchekzai a versatile C++ finite element library named ddmtool and available on GitLab, under the GNU Lesser General Public License.

Publications

Ph.D. thesis
Asymptotics and numerical analysis for wave diffraction by thin wires,
Université Versailles Saint-Quentin-en-Yvelines, 2008.

Habilitation thesis
Boundary integral equations of time harmonic wave scattering at complex structures,
Université Pierre-et-Marie Curie, 2016.

Articles in peer reviewed journals

• X.Claeys and H.Haddar, Scattering from infinite rough tubular surfaces. Math.Methods Appl. Sci. 30 (2007), no. 4, 389–414. link
• X.Claeys, On the theoretical justification of Pocklington's equation. Math. Models and Meth. Appl. Sci. 19 (2009), no. 8, 1325–1355. link
• X.Claeys and F. Collino, Augmented Galerkin Scheme for the Solution of Scattering by small obstacles, Numer. Math. 116 (2010) no. 2, 246-268. link
• X.Claeys and F. Collino, Asymptotic and numerical analysis for Holland and Simpson’s thin wire formalism, JCAM 235 (2011) 4418–4438. link
• X.Claeys and R.Hiptmair, Electromagnetic scattering at composite objects: a novel multi-trace boundary integral formulation, ESAIM Math.Model. Numer. Anal., 46 (2012) 1421-1445. link
• A-S.Bonnet, L.Chesnel and X.Claeys, Radiation condition for a non-smooth interface between a dielectric and a metamaterial, Math. Models Meth. App. Sci., vol. 23, 9:1629-1662, 2013. link
• X.Claeys and R.Hiptmair, Boundary integral formulation of the first kind for acoustic scattering by composite structures, Comm. Pure Appl. Math., 66(8):1163-1201, 2013 link
• X.Claeys and B.Delourme, High order asymptotics for wave propagation across thin periodic interfaces, Asymptot. Anal., 83(2013), 35-82. link
• X.Claeys and R. Hiptmair, Integral Equations on Multi-Screens, Integral Equations and Operator Theory 77 (2013), no.2, 167-197. link
• X.Claeys and R. Hiptmair and C. Jerez-Hanckes, Multi-trace boundary integral equations, chapter in Direct and Inverse Problems in Wave Propagation and Applications, 51–100, Radon Ser. Comput. Appl. Math., 14, De Gruyter, Berlin, 2013. link
• L.Chesnel, X. Claeys, S.A. Nazarov, A curious instability phenomenon for a rounded corner in presence of a negative material, Asympt. Anal. 88 (2014), no.1-2, 43-74. link
• X. Claeys and R. Hiptmair and E. Spindler, A Second-Kind Galerkin Boundary Element Method for Scattering at Composite Objects, BIT Numer. Math. 55 (2015), no.1, 33–57. link
• X. Claeys, Stability of electromagnetic cavities perturbed by small perfectly conducting inclusions, C. R. Math. Acad. Sci. Paris 353 (2015), no. 2, 139–142. link
• X. Claeys and R. Hiptmair, Integral Equations for Acoustic Scattering by Partially Impenetrable Composite Objects, Integral Equations Operator Theory 81 (2015), no. 2, 151–189. link
• X. Claeys and R. Hiptmair and C. Jerez-Hanckes and S.Pintarelli, Novel Multi-Trace Boundary Integral Equations for Transmission Boundary Value Problems, chapter in Unified Transform for Boundary Value Problems: Applications and Advances, A. S. Fokas, B. Pelloni., SIAM, (2015). link
• X. Claeys, Quasi-local multi-trace boundary integral formulations, Numer. Methods Partial Differential Equations, 31(6):2043–2062, 2015. link.
• L. Chesnel, X. Claeys, S.A. Nazarov, Spectrum for a small inclusion of negative material, Z. Angew. Math. Phys. 66 (2015), no. 5, 2173–2196. link.
• X. Claeys and R.Hiptmair, Integral Equations for Electromagnetic Scattering at Multi-Screens, Integral Equations Operator Theory 84 (2016), no. 1, 33-68. preprint.
• X. Claeys, Asymptotics of the eigenvalues of the Dirichlet-Laplace problem in a domain with thin tube excluded, Quart. Appl. Math. 74 (2016), no. 4, 595–605. HAL.
• L. Chesnel and X. Claeys, A numerical approach for the Poisson equation in a planar domain with a small inclusion, BIT Numerical Mathematics , 56(4):1237-1256, 2016. ArXiv.
• X. Claeys, Essential spectrum of local multi-trace boundary integral operators, IMA J. Appl. Math. (2016) 81 (6): 961-983. ArXiv.
• A.Ayala, X.Claeys, V.Dolean, M.J.Gander (2017) Closed Form Inverse of Local Multi-Trace Operators. In: Lee CO. et al. (eds) Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham
• L.Chesnel, X.Claeys and S.Nazarov, Small obstacle asymptotics for a 2D semi-linear convex problem, Appl. Anal. 97, no.6, 962-981 (2018).
• L.Chesnel, X.Claeys and S.Nazarov, Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner, ESAIM, Math. Model. Numer. Anal. 52, no. 4, 1285-1313 (2018), ArXiv.
• X. Claeys and R. Hiptmair and E. Spindler, Second Kind Boundary Integral Equation for Multi-Subdomain Diffusion Problems, Adv. Comput. Math. 43 (2017), no. 5, 1075-1101, preprint.
• X. Claeys and R. Hiptmair and E. Spindler, Second-Kind Boundary Integral Equations for Scattering at Composite Partly Impenetrable Objects, Commun. Comput. Phys., 23 (2018), pp.264-295, SAM report of ETHZ.
• X. Claeys and R. Hiptmair and E. Spindler, Second-Kind Boundary Integral Equations for Electromagnetic Scattering at Composite Objects, Comput. Math. Appl. 74 (2017), no.11, 2650-2670, available as a SAM report of ETHZ.
• I.Ben-Gharbia, M.Bonazzoli, X.Claeys, P.Marchand, P.-H.Tournier, Fast solution of boundary integral equations for elasticity around a crack network: a comparative study. CEMRACS 2016, 135-151, ESAIM Proc. Surveys, 63, EDP Sci., Les Ulis, 2018.
• X.Claeys, F.Collino and B.Thierry, Integral equation based optimized Schwarz method for electromagnetics. in Domain Decomposition Methods in Science and Engineering XXIV. LNCSE, vol 125. Springer (2018).
• X. Claeys and V. Dolean and M. J. Gander, An introduction to multitrace formulations and associated domain decomposition solvers, Applied Numerical Mathematics, 2019, 135, 69-86., available on HAL.
• X. Claeys and R. Hiptmair, First kind boundary integral formulation for the Hodge-Helmholtz equation, SIAM J. Math. Anal. 51 (2019), no. 1, 197-227, available as a SAM report of ETHZ.
• A.Ayala, X. Claeys and L.Grigori, ALORA: Affine Low-Rank Approximations, J. Sci. Comput. 79 (2019), no. 2, 1135-1160, available on HAL.
• X. Claeys, F. Collino, P. Joly and E. Parolin, A discrete domain decomposition method for acoustics with uniform exponential rate of convergence using non-local impedance operators, Domain decomposition methods in science and engineering XXV, 310–317, Lect. Notes Comput. Sci. Eng., 138, Springer, Cham, 2020.
• A.Ayala, X. Claeys and L.Grigori, Linear-time CUR approximation of BEM matrices, J. Comput. Appl. Math. 368 (2020), 112528, 19 pp, accepted for publication in J. Comput. Appl. Math.
• X. Claeys and R. Hiptmair, First kind Galerkin boundary element method for the Hodge-Laplacian in three dimensions, Math. Methods Appl. Sci. 43 (2020), no. 8, 4974–4994, available as a SAM report.
• X. Claeys and P. Marchand, Boundary integral multi-trace formulations and Optimised Schwarz Methods, Comput. Math. Appl. 79, no. 11, 3241-3256 (2020), available on HAL
• X. Claeys, P. Marchand, P.Jolivet, F.Nataf and P.-H. Tournier, Two-level preconditioning for h-version boundary element approximation of hypersingular operator with GenEO, Numer. Math. 146, no. 3, 597-628 (2020), available on HAL
• X.Claeys, Non-local variant of the Optimized Schwarz Method for arbitrary non-overlapping subdomain partitions, ESAIM Math. Model. Numer. Anal. 55 (2021), no. 2, 429–448. Available on ArXiv.
• X. Claeys, L.Giacomel, R.Hiptmair and C.Urzua-Torres, Quotient-space boundary element methods for scattering at complex screens, BIT Numer. Math. 61, No. 4, 1193-1221 (2021), available as SAM report
• M.Bonazzoli, X.Claeys, F.Nataf and P.-H. Tournier, Analysis of the SORAS Domain Decomposition Preconditioner for Non-self-adjoint or Indefinite Problems, J. Sci. Comput. 89 (2021), no. 1, Paper No. 19. Available on ArXiv.
• X.Claeys, F.Collino, P.Joly & E.Parolin, Non Overlapping Domain Decomposition Methods for Time Harmonic Wave Problems. Available on HAL
• X.Claeys & E.Parolin, Robust treatment of cross points in Optimized Schwarz Methods, Numer. Math. 151 (2022), no. 2, 405–442, available on ArXiv.
• A.Ayala, X.Claeys,P.Escapil-Inchauspé & C.Jerez-Hanckes, Local Multiple Traces Formulation for Electromagnetics: Stability and Preconditioning for Smooth Geometries, J. Comput. Appl. Math. 413 (2022), Paper No. 114356, 17 pp., available on ArXiv.
• X.Claeys, Non-self adjoint impedance in Generalized Optimized Schwarz Methods, IMA J. Numer. Anal. (2023) 43, 3026-3054, available on ArXiv.
• X.Claeys, F.Collino and E.Parolin, Nonlocal optimized Schwarz methods for time-harmonic electromagnetics, Adv Comput Math 48, 72 (2022), available on ArXiv.
• I.Chollet, X.Claeys, P.Fortin & L.Grigori, A directional equispaced interpolation-based fast multipole method for oscillatory kernels, SIAM J. Sci. Comput. 45, No. 1, C20-C48 (2023).
• M.Averseng, X.Claeys & R.Hiptmair, Fractured meshes, accepted in Finite Elem. Anal. Des., available on ArXiv.
• X.Claeys, Non-local optimized Schwarz method for the Helmholtz equation with physical boundaries, SIAM J. Math. Anal., vol.55, no.6, pp.7490-7512, available on ArXiv.
• X.Claeys, M.Hassan and B.Stamm, Continuity estimates for Riesz potentials on polygonal boundaries, available on ArXiv, to appear in SN Partial Differ. Equ. Appl.

Submitted

• M.Bonazzoli & X.Claeys, Multi-domain FEM-BEM coupling for acoustic scattering, available on HAL.
• R.Delville-Atchekzai, X.Claeys & M.Lecouvez, Substructuring the Hiptmair-Xu preconditioner for positive Maxwell problems, available on ArXiv.
• A. M. Caetano, S. N. Chandler-Wilde, X. Claeys, A. Gibbs, D. P. Hewett & A. Moiola, Integral equation methods for acoustic scattering by fractals, available on ArXiv.
• R.Delville-Atchekzai & X.Claeys, Accelerating non-local exchange in generalized optimized Schwarz methods, available on ArXiv.

Research reports

• X.Claeys, A single trace integral formulation of the second kind for acoustic scattering in complex geometries, SAM Report 2011-14.
• X.Claeys, Asymptotic analysis for the solution to the Helmholtz problemin the exterior of a finite thin straight wire, INRIA report, no. 6277, July 2007.
• X.Claeys and F.Collino, Augmented Galerkin schemes for the numerical solution of scattering by small obstacles, INRIA report, no. 6195,May 2007.
• X.Claeys, H.Haddar et P.Joly, Étude d’un problème modèle pour la diffraction par des fils minces par développements asymptotiques raccordés. Cas 2D, INRIA report, no. 5839,May 2006.

Proceedings

• X.Claeys, Overview on a selection of recent works in asymptotic analysis for wave propagation problems. Conference on Computational Electromagnetism and Acoustics, OBERWOLFACH Germany, February 2010.
• X.Claeys, Matched Asymptotics in Small Inclusion Problems for a Class of Inhomogeneous Operators, WAVES, Pau France, June 2009.
• X.Claeys and F.Collino, A generalized Holland model for wave diffraction by thin wires, International Conference on Electromagnetics in Advanced Applications, ICEAA, Turin Italie, September 2007.
• X.Claeys, Theoretical justification of Pocklington’s equation for diffraction by thin wires, WAVES, Reading Angleterre, July 2007.
• X. Claeys (2011), “Integral formulation of the second kind for multi–subdomain scattering”, Proc. 10th Int. Conf. on Math. Numer. Aspects of Waves (WAVES 2011), Pacific Institute for the Mathematical Sciences.