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## Joly, Patrick

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 Author ID: joly.patrick Published as: Joly, P.; Joly, Patrick; July, Patrick Homepage: https://uma.ensta-paris.fr/~pjoly External Links: MGP · Math-Net.Ru · dblp
 Documents Indexed: 175 Publications since 1985, including 4 Books
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#### Co-Authors

 12 single-authored 20 Bécache, Eliane 12 Collino, Francis 11 Haddar, Houssem 10 Bamberger, Alain 10 Rodríguez, Jerónimo 9 Roberts, Jean Elizabeth 9 Tsogka, Chrysoula 8 Imperiale, Sébastien 7 Cohen, Gary 6 Fliss, Sonia 6 Vacus, Olivier 5 Bonnet-Ben Dhia, Anne-Sophie 5 Delourme, Bérangère 5 Diaz, Julien 5 Duruflé, Marc 5 Fouquet, Thierry 5 Kachanovska, Maryna 5 Poirier, Christine 5 Tordeux, Sébastien 4 Derveaux, Grégoire 4 Ha-Duong, Tuong 4 Kern, Michel 4 Tordjman, Nathalie 3 Bermúdez, Alfredo 3 Chabassier, Juliette 3 Duterte, Jean 3 Elmkies, Alexandre 3 Guillot, Jean-Claude 3 Halpern, Laurence 3 Hiptmair, Ralf 3 Hoppe, Ronald H. W. 3 Langer, Ulrich 3 Semin, Adrien 3 Vasilevskaya, Elizaveta 2 Albella Martínez, Jorge 2 Beck, Geoffrey M. 2 Burel, Alienor 2 Cassier, Maxence 2 Chaigne, Antoine 2 Cockburn, Bernardo 2 Engquist, Bjorn E. 2 Ezziani, Abdelaâziz 2 Ghanemi, Souad 2 Goldman, Yale E. 2 Gómez Pedreira, Dolores 2 Grob, P. 2 Hazard, Christophe 2 Joubert, Lauris 2 Millot, Florence 2 Nguyen, Hoai-Minh 2 Pedreira, D. Gómez 2 Rhaouti, Leïla 2 Vinoles, Valentin 2 Weder, Ricardo A. 1 Abboud, Toufic 1 Alboin, Clarisse 1 Anné, Laurent 1 Atamian, C. 1 Barucq, Hélène 1 Bensalah, A. 1 Bonnet, Marc 1 Chalindar, Bruno 1 Clausel, Marianne 1 Coatléven, Julien 1 Cohen, Gary C. 1 Cohen, Gerald D. 1 Collino, P. 1 Delbue, G. 1 Dermenjian, Yves 1 Després, Bruno 1 Dgaygui, Kebir 1 Duong, Tap Ha 1 Eziani, Abdelaâziz 1 Fauqueux, Sandrine 1 Gilbert, Jean Charles 1 Gómez, Dolores 1 Heikkola, Erkki 1 Jaffré, Jérôme 1 Komech, Aleksandr I. 1 Komech, Alexander Ilich 1 Lecouvez, Matthieu 1 Lenoir, Marc 1 Li, Jhuo-Ru 1 Lohrengel, Stephanie 1 Mercier, Jean-François 1 Neittaanmäki, Pekka J. 1 Oñate Ibáñez de Navarra, Eugenio 1 Pedreira, Dolores G. 1 Périaux, Jacques F. 1 Piacentini, Andrea 1 Pironneau, Olivier 1 Scarella, Gilles 1 Schmidt, Kersten 1 Serres, Christophe 1 Teron, Jean Luc 1 Terrasse, Isabelle 1 Thöns-Zueva, Anastasia 1 Tlili, Jamel 1 Tran, Quang Huy 1 Trouvé, Pascal ...and 1 more Co-Authors
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#### Serials

 11 SIAM Journal on Numerical Analysis 8 SIAM Journal on Applied Mathematics 7 Computer Methods in Applied Mechanics and Engineering 7 Comptes Rendus de l’Académie des Sciences. Série I 7 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Journal of Computational Physics 6 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 Mathematical Methods in the Applied Sciences 5 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 4 Numerische Mathematik 4 Communications in Computational Physics 3 Mathematics of Computation 3 Journal of Computational and Applied Mathematics 3 Applied Numerical Mathematics 3 RAIRO. Modélisation Mathématique et Analyse Numérique 3 Numerical Methods for Partial Differential Equations 3 Asymptotic Analysis 3 SIAM Journal on Mathematical Analysis 3 Computational Geosciences 3 Oberwolfach Reports 2 Wave Motion 2 SIAM Journal on Scientific Computing 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Journal of Computational Acoustics 1 Archive for Rational Mechanics and Analysis 1 Computers & Mathematics with Applications 1 Journal of Differential Equations 1 Southeast Asian Bulletin of Mathematics 1 SIAM Journal on Scientific and Statistical Computing 1 Finite Elements in Analysis and Design 1 Applied Mathematics Letters 1 Journal of Scientific Computing 1 Journal of Integral Equations and Applications 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Advances in Computational Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Multiscale Modeling & Simulation 1 Networks and Heterogeneous Media 1 Discrete and Continuous Dynamical Systems. Series S 1 Advances in Applied Mathematics and Mechanics 1 S$$\vec{\text{e}}$$MA Journal 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 SN Partial Differential Equations and Applications
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#### Fields

 110 Partial differential equations (35-XX) 81 Numerical analysis (65-XX) 66 Optics, electromagnetic theory (78-XX) 47 Mechanics of deformable solids (74-XX) 34 Fluid mechanics (76-XX) 9 General and overarching topics; collections (00-XX) 8 Operator theory (47-XX) 8 Geophysics (86-XX) 4 Ordinary differential equations (34-XX) 3 Approximations and expansions (41-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Combinatorics (05-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

135 Publications have been cited 1,320 times in 873 Documents Cited by Year
Stability of perfectly matched layers, group velocities and anisotropic waves. Zbl 1127.74335
Bécache, E.; Fauqueux, S.; Joly, P.
2003
Higher order triangular finite elements with mass lumping for the wave equation. Zbl 1019.65077
Cohen, G.; Joly, P.; Roberts, J. E.; Tordjman, N.
2001
On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations. Zbl 0992.78032
Bécache, Eliane; Joly, Patrick
2002
Domain decomposition method for harmonic wave propagation: A general presentation. Zbl 0965.65134
Collino, Francis; Ghanemi, Souad; Joly, Patrick
2000
A time domain analysis of PML models in acoustics. Zbl 1119.76046
Diaz, J.; Joly, P.
2006
Construction and analysis of fourth-order finite difference schemes for the acoustic wave equation in nonhomogeneous media. Zbl 0863.65048
Cohen, Gary; Joly, Patrick
1996
A domain decomposition method for the harmonic Maxwell equations. Zbl 0785.65117
Despres, Bruno; Joly, Patrick; Roberts, Jean E.
1992
Second-order absorbing boundary conditions for the wave equation: A solution for the corner problem. Zbl 0716.35036
Bamberger, Alain; Joly, Patrick; Roberts, Jean E.
1990
Variational methods for time-dependent wave propagation problems. Zbl 1049.78028
Joly, Patrick
2003
Generalized impedance boundary conditions for scattering problems from strongly absorbing obstacles: the case of Maxwell’s equations. Zbl 1170.35094
Haddar, Houssem; Joly, Patrick; Nguyen, Hoai-Minh
2008
Generalized impedance boundary conditions for scattering by strongly absorbing obstacles: the scalar case. Zbl 1084.35102
Haddar, Houssem; Joly, Patrick; Nguyen, Hoai-Minh
2005
A new family of mixed finite elements for the linear elastodynamic problem. Zbl 1032.74049
Bécache, E.; Joly, P.; Tsogka, C.
2002
An analysis of new mixed finite elements for the approximation of wave propagation problems. Zbl 0958.65102
Bécache, E.; Joly, P.; Tsogka, C.
2000
Approximate models for wave propagation across thin periodic interfaces. Zbl 1422.76160
Delourme, Bérangère; Haddar, Houssem; Joly, Patrick
2012
Exact boundary conditions for periodic waveguides containing a local perturbation. Zbl 1125.78008
Joly, P.; Li, J.-R.; Fliss, S.
2006
Parabolic wave equation approximations in heterogeneous media. Zbl 0654.35055
Bamberger, A.; Engquist, B.; Halpern, L.; Joly, P.
1988
Coupling discontinuous Galerkin methods and retarded potentials for transient wave propagation on unbounded domains. Zbl 1416.74081
Abboud, Toufic; Joly, Patrick; Rodrıǵuez, Jerónimo; Terrasse, Isabelle
2011
Matching of asymptotic expansions for wave propagation in media with thin slots I: The asymptotic expansion. Zbl 1132.35347
Joly, Patrick; Tordeux, Sébastien
2006
A conservative space-time mesh refinement method for the 1-D wave equation. I: Construction. Zbl 1048.65089
Collino, F.; Fouquet, T.; Joly, P.
2003
Fictitious domain method for unsteady problems: application to electromagnetic scattering. Zbl 1126.78311
Collino, Francis; Joly, Patrick; Millot, Florence
1997
Higher order paraxial wave equation approximations in heterogeneous media. Zbl 0654.35056
Bamberger, A.; Engquist, B.; Halpern, L.; Joly, P.
1988
Mathematical analysis of guided water waves. Zbl 0787.76007
Bonnet-Ben Dhia, Anne-Sophie; Joly, Patrick
1993
Conservative space-time mesh refinement methods for the FDTD solution of Maxwell’s equations. Zbl 1107.78015
Collino, F.; Fouquet, T.; Joly, P.
2006
Stability of thin layer approximation of electromagnetic waves scattering by linear and nonlinear coatings. Zbl 0998.78008
2002
Fictitious domains, mixed finite elements and perfectly matched layers for 2-D elastic wave propagation. Zbl 1360.74156
Bécache, E.; Joly, P.; Tsogka, C.
2001
A conservative space-time mesh refinement method for the 1-D wave equation. II: Analysis. Zbl 1036.65073
Collino, F.; Fouquet, T.; Joly, P.
2003
Mathematical analysis of elastic surface waves in topographic waveguides. Zbl 0946.74034
Bonnet-Ben Dhia, A. S.; Duterte, J.; Joly, P.
1999
Higher-order finite elements with mass-lumping for the 1D wave equation. Zbl 0865.65072
Cohen, Gary; Joly, Patrick; Tordjman, Nathalie
1994
On the stability analysis of boundary conditions for the wave equation by energy methods. I: The homogeneous case. Zbl 0829.35063
Ha-Duong, T.; Joly, P.
1994
Solutions of the time-harmonic wave equation in periodic waveguides: asymptotic behaviour and radiation condition. Zbl 1333.35260
Fliss, Sonia; Joly, Patrick
2016
Exact boundary conditions for time-harmonic wave propagation in locally perturbed periodic media. Zbl 1165.78311
Fliss, Sonia; Joly, Patrick
2009
Higher order time stepping for second order hyperbolic problems and optimal CFL conditions. Zbl 1149.65070
Gilbert, J. Charles; Joly, Patrick
2008
Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots. Zbl 1220.35174
Joly, Patrick; Tordeux, Sébastien
2006
An analysis of higher order boundary conditions for the wave equation. Zbl 1078.35062
Diaz, Julien; Joly, Patrick
2005
Mathematical and numerical studies of nonlinear ferromagnetic materials. Zbl 0960.78003
Joly, Patrick; Vacus, Olivier
1999
Energy preserving schemes for nonlinear Hamiltonian systems of wave equations: application to the vibrating piano string. Zbl 1231.74146
Chabassier, J.; Joly, P.
2010
Influence of Gauss and Gauss-Lobatto quadrature rules on the accuracy of a quadrilateral finite element method in the time domain. Zbl 1167.65057
Durufle, M.; Grob, P.; Joly, P.
2009
A new interface condition in the non-overlapping domain decomposition method for the Maxwell equations. Zbl 0902.65074
Collino, P.; Delbue, G.; Joly, P.; Piacentini, A.
1997
Construction and analysis of improved Kirchhoff conditions for acoustic wave propagation in a junction of thin slots. Zbl 1156.76422
2008
Edge finite elements and mass lumping for Maxwell’s equations: The 2D case. Zbl 0877.65081
Elmkies, Alexandre; Joly, Patrick
1997
Mathematical models for dispersive electromagnetic waves: an overview. Zbl 1397.78004
Cassier, Maxence; Joly, Patrick; Kachanovska, Maryna
2017
Matching of asymptotic expansions for wave propagation in media with thin slots II: The error estimates. Zbl 1132.35348
Joly, Patrick; Tordeux, Sébastien
2008
Edge finite elements and mass lumping for Maxwell’s equations: The 3D case. Zbl 0893.65068
Elmkies, Alexandre; Joly, Patrick
1997
Perfectly matched layers in negative index metamaterials and plasmas. Zbl 1341.78013
Bécache, Éliane; Joly, Patrick; Kachanovska, Maryna; Vinoles, Valentin
2015
An error analysis of conservative space-time mesh refinement methods for the one-dimensional wave equation. Zbl 1097.65095
Joly, Patrick; Rodriguez, Jerónimo
2005
Stabilized perfectly matched layer for advective acoustics. Zbl 1047.76116
Diaz, Julien; Joly, Patrick
2003
Construction and analysis of higher order finite difference schemes for the 1D wave equation. Zbl 0968.65060
Anné, Laurent; Joly, Patrick; Tran, Quang Huy
2000
Construction and analysis of higher order finite elements with mass lumping for the wave equation. Zbl 0814.65096
Cohen, Gary; Joly, Patrick; Tordjman, Nathalie
1993
Fourth order schemes for the heterogeneous acoustics equation. Zbl 0733.76053
Cohen, G.; Joly, P.
1990
On the analysis of perfectly matched layers for a class of dispersive media and application to negative index metamaterials. Zbl 1404.35427
Bécache, Éliane; Joly, Patrick; Vinoles, Valentin
2018
Spectral theory for Maxwell’s equations at the interface of a metamaterial. I: Generalized Fourier transform. Zbl 1387.35426
Cassier, Maxence; Hazard, Christophe; Joly, Patrick
2017
On the well-posedness, stability and accuracy of an asymptotic model for thin periodic interfaces in electromagnetic scattering problems. Zbl 1288.78016
Delourme, Berangere; Haddar, Houssem; Joly, Patrick
2013
Space-time mesh refinement for elastodynamics. Numerical results. Zbl 1095.74030
Bécache, E.; Joly, P.; Rodríguez, J.
2005
Mathematical and numerical aspects of wave propagation, WAVES 2003. Proceedings of the sixth international conference on mathematical and numerical aspects of wave propagation, Jyväskylä, Finland, 30 June – 4 July 2003. Zbl 1029.00072
Cohen, Gary C. (ed.); Heikkola, Erkki (ed.); Joly, Patrick (ed.); Neittaanmäki, Pekka (ed.)
2003
Effective boundary conditions for thin ferromagnetic layers: The one-dimensional model. Zbl 0973.78011
2001
On transitions to stationary states in a Maxwell–Landau–Lifschitz–Gilbert system. Zbl 1025.78005
Joly, Patrick; Komech, Alexander; Vacus, Olivier
2000
A new nonconforming finite element method for the computation of electromagnetic guided waves. I: Mathematical analysis. Zbl 0861.65092
Joly, Patrick; Poirier, Christine; Roberts, J. E.; Trouve, P.
1996
Higher order triangular finite elements with mass lumping for the wave equation. Zbl 0870.65085
Cohen, Gary; Joly, Patrick; Tordjman, Nathalie
1995
Mathematical analysis of the propagation of elastic guided waves in heterogeneous media. Zbl 0714.35045
Bamberger, A.; Dermenjian, Y.; Joly, P.
1990
Mathematical aspects of variational boundary integral equations for time dependent wave propagation. Zbl 1364.35187
Joly, Patrick; Rodríguez, Jerónimo
2017
Mathematical and numerical modelling of piezoelectric sensors. Zbl 1279.78013
Imperiale, Sebastien; Joly, Patrick
2012
Local time stepping and discontinuous Galerkin methods for symmetric first order hyperbolic systems. Zbl 1407.65183
Ezziani, Abdelaâziz; Joly, Patrick
2010
A mixed finite element approach for viscoelastic wave propagation. Zbl 1065.74069
Bécache, Eliane; Ezziani, Abdelaâziz; Joly, Patrick
2004
Mathematical analysis of electromagnetic open waveguides. Zbl 0834.35126
Joly, Patrick; Poirier, Christine
1995
Numerical diffraction by a uniform grid. Zbl 0659.65079
Bamberger, A.; Guillot, Jean-Claude; Joly, Patrick
1988
Effective transmission conditions for thin-layer transmission problems in elastodynamics. the case of a planar layer model. Zbl 1339.35312
Bonnet, Marc; Burel, Aliénor; Duruflé, Marc; Joly, Patrick
2016
Mathematical modeling of electromagnetic wave propagation in heterogeneous lossy coaxial cables with variable cross section. Zbl 1291.78032
Imperiale, Sébastien; Joly, Patrick
2014
An elementary introduction to the construction and the analysis of perfectly matched layers for time domain wave propagation. Zbl 1331.35003
Joly, Patrick
2012
Mathematical and numerical modeling of wave propagation in fractal trees. Zbl 1270.35021
2011
Optimized higher order time discretization of second order hyperbolic problems: construction and numerical study. Zbl 1198.65092
Joly, P.; Rodríguez, J.
2010
Propagation of elastic surface waves along a cylindrical cavity of arbitrary cross section. Zbl 0739.73009
Bamberger, A.; Joly, P.; Kern, M.
1991
A mathematical analysis of the resonance of the finite thin slots. Zbl 1237.35033
Clausel, M.; Duruflé, M.; Joly, P.; Tordeux, S.
2006
Mathematical analysis and numerical approximation of optical waveguides. Zbl 0986.78013
Bonnet-Ben Dhia, Anne-Sophie; Joly, Patrick
2001
Fictitious domains, $$\text{H(div)}$$ finite elements and Neumann condition: The inf-sup condition. Zbl 0931.65112
Joly, Patrick; Rhaouti, Leïla
1999
Splitting of operators, alternate directions, and paraxial approximations for the three-dimensional wave equation. Zbl 0839.35074
Collino, F.; Joly, P.
1995
Mathematical modelling of multi conductor cables. Zbl 1321.35218
Beck, Geoffrey; Imperiale, Sebastien; Joly, Patrick
2015
High-order asymptotic expansion for the acoustics in viscous gases close to rigid walls. Zbl 1293.35217
Schmidt, Kersten; Thöns-Zueva, Anastasia; Joly, Patrick
2014
Error estimates for 1D asymptotic models in coaxial cables with non-homogeneous cross-section. Zbl 1262.35188
Imperiale, Sébastien; Joly, Patrick
2012
Wave propagation in locally perturbed periodic media (case with absorption): numerical aspects. Zbl 1408.78007
Fliss, Sonia; Joly, Patrick
2012
The mathematical model for elastic wave propagation. Zbl 1162.74021
Joly, Patrick
2008
Effective boundary conditions for thin ferromagnetic coatings. Asymptotic analysis of the 1D model. Zbl 0995.35072
2001
Existence and uniqueness results for the Helmholtz equation with second order absorbing boundary conditions. Zbl 0929.35031
Joly, Patrick; Lohrengel, Stéphanie; Vacus, Olivier
1999
Domain decomposition method for harmonic wave equations. Zbl 0870.65109
Ghanemi, S.; Collino, F.; Joly, P.
1995
A principle of images for absorbing boundary conditions. Zbl 0822.65061
Duong, T. Ha; Joly, P.
1994
Absorbing boundary conditions for linear gravity waves. Zbl 0799.35182
Dgaygui, Kebir; Joly, Patrick
1994
Maxwell equations in polarizable media. Zbl 0665.65098
Cockburn, Bernardo; Joly, Patrick
1988
Absorbing boundary conditions for Rayleigh waves. Zbl 0655.73013
Bamberger, Alain; Chalindar, Bruno; Joly, Patrick; Roberts, Jean Elizabeth; Teron, Jean Luc
1988
Stable perfectly matched layers for a cold plasma in a strong background magnetic field. Zbl 1376.78003
Bécache, Eliane; Joly, Patrick; Kachanovska, Maryna
2017
Trapped modes in thin and infinite ladder like domains. I: Existence results. Zbl 1378.78029
Delourme, Bérangère; Fliss, Sonia; Joly, Patrick; Vasilevskaya, Elizaveta
2017
Numerical methods for treating unbounded media. Zbl 1286.74039
Joly, Patrick; Tsogka, C.
2008
Numerical simulation of a guitar. Zbl 1047.76115
Bécache, Eliane; Chaigne, Antoine; Derveaux, Grégoire; Joly, Patrick
2003
A method for computing guided waves in integrated optics. II: Numerical approximation and error analysis. Zbl 1017.65085
Gómez Pedreira, Dolores; Joly, Patrick
2002
A new second order 3D edge element on tetrahedra for time dependent Maxwell’s equations. Zbl 0995.78040
Joly, Patrick; Poirier, Christine
2000
Analysis of the fictitious domain method for the exterior Helmholtz problem. Zbl 0807.65069
Atamian, C.; Joly, P.
1993
New results for guided waves in heterogeneous elastic media. Zbl 0756.35108
Joly, Patrick; Weder, Ricardo
1992
Pseudo-transparent boundary conditions for the diffusion equation. I. Zbl 0705.35055
Joly, P.
1989
The electric field in the conductive half space as a model in mining and petroleum prospecting. Zbl 0693.65088
Goldman, Y.; Joly, P.; Kern, M.
1989
Propagation d’ondes élastiques guidées par la surface d’une cavité cylindrique de section arbitraire. (Propagation of elastic surface waves along a cylindrical cavity of arbitrary cross section). Zbl 0617.73029
Bamberger, Alain; Joly, Patrick; Kern, Michel
1987
Wave propagation in fractal trees. Mathematical and numerical issues. Zbl 1427.35018
Joly, Patrick; Kachanovska, Maryna; Semin, Adrien
2019
Time domain simulation of a piano. I: Model description. Zbl 1301.00044
Chabassier, J.; Chaigne, A.; Joly, P.
2014
Exponentially convergent non overlapping domain decomposition methods for the Helmholtz equation. Zbl 1437.65219
Collino, Francis; Joly, Patrick; Lecouvez, Matthieu
2020
Wave propagation in fractal trees. Mathematical and numerical issues. Zbl 1427.35018
Joly, Patrick; Kachanovska, Maryna; Semin, Adrien
2019
On the analysis of perfectly matched layers for a class of dispersive media and application to negative index metamaterials. Zbl 1404.35427
Bécache, Éliane; Joly, Patrick; Vinoles, Valentin
2018
Solving 2D linear isotropic elastodynamics by means of scalar potentials: a new challenge for finite elements. Zbl 1407.65177
Albella Martínez, Jorge; Imperiale, Sébastien; Joly, Patrick; Rodríguez, Jerónimo
2018
Well-posedness of a generalized time-harmonic transport equation for acoustics in flow. Zbl 06901735
Bensalah, A.; Joly, P.; Mercier, J.-f.
2018
Mathematical models for dispersive electromagnetic waves: an overview. Zbl 1397.78004
Cassier, Maxence; Joly, Patrick; Kachanovska, Maryna
2017
Spectral theory for Maxwell’s equations at the interface of a metamaterial. I: Generalized Fourier transform. Zbl 1387.35426
Cassier, Maxence; Hazard, Christophe; Joly, Patrick
2017
Mathematical aspects of variational boundary integral equations for time dependent wave propagation. Zbl 1364.35187
Joly, Patrick; Rodríguez, Jerónimo
2017
Stable perfectly matched layers for a cold plasma in a strong background magnetic field. Zbl 1376.78003
Bécache, Eliane; Joly, Patrick; Kachanovska, Maryna
2017
Trapped modes in thin and infinite ladder like domains. I: Existence results. Zbl 1378.78029
Delourme, Bérangère; Fliss, Sonia; Joly, Patrick; Vasilevskaya, Elizaveta
2017
Solutions of the time-harmonic wave equation in periodic waveguides: asymptotic behaviour and radiation condition. Zbl 1333.35260
Fliss, Sonia; Joly, Patrick
2016
Effective transmission conditions for thin-layer transmission problems in elastodynamics. the case of a planar layer model. Zbl 1339.35312
Bonnet, Marc; Burel, Aliénor; Duruflé, Marc; Joly, Patrick
2016
Time domain simulation of a piano. II: Numerical aspects. Zbl 1381.00017
Chabassier, Juliette; Duruflé, Marc; Joly, Patrick
2016
Perfectly matched layers in negative index metamaterials and plasmas. Zbl 1341.78013
Bécache, Éliane; Joly, Patrick; Kachanovska, Maryna; Vinoles, Valentin
2015
Mathematical modelling of multi conductor cables. Zbl 1321.35218
Beck, Geoffrey; Imperiale, Sebastien; Joly, Patrick
2015
Mathematical modeling of electromagnetic wave propagation in heterogeneous lossy coaxial cables with variable cross section. Zbl 1291.78032
Imperiale, Sébastien; Joly, Patrick
2014
High-order asymptotic expansion for the acoustics in viscous gases close to rigid walls. Zbl 1293.35217
Schmidt, Kersten; Thöns-Zueva, Anastasia; Joly, Patrick
2014
Time domain simulation of a piano. I: Model description. Zbl 1301.00044
Chabassier, J.; Chaigne, A.; Joly, P.
2014
On the well-posedness, stability and accuracy of an asymptotic model for thin periodic interfaces in electromagnetic scattering problems. Zbl 1288.78016
Delourme, Berangere; Haddar, Houssem; Joly, Patrick
2013
Approximate models for wave propagation across thin periodic interfaces. Zbl 1422.76160
Delourme, Bérangère; Haddar, Houssem; Joly, Patrick
2012
Mathematical and numerical modelling of piezoelectric sensors. Zbl 1279.78013
Imperiale, Sebastien; Joly, Patrick
2012
An elementary introduction to the construction and the analysis of perfectly matched layers for time domain wave propagation. Zbl 1331.35003
Joly, Patrick
2012
Error estimates for 1D asymptotic models in coaxial cables with non-homogeneous cross-section. Zbl 1262.35188
Imperiale, Sébastien; Joly, Patrick
2012
Wave propagation in locally perturbed periodic media (case with absorption): numerical aspects. Zbl 1408.78007
Fliss, Sonia; Joly, Patrick
2012
Operator factorization for multiple-scattering problems and an application to periodic media. Zbl 1373.74054
Coatléven, J.; Joly, P.
2012
Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition. Zbl 1299.35184
Burel, Alienor; Impériale, Sebastien; Joly, Patrick
2012
Coupling discontinuous Galerkin methods and retarded potentials for transient wave propagation on unbounded domains. Zbl 1416.74081
Abboud, Toufic; Joly, Patrick; Rodrıǵuez, Jerónimo; Terrasse, Isabelle
2011
Mathematical and numerical modeling of wave propagation in fractal trees. Zbl 1270.35021
2011
Stability of acoustic propagation in 2D duct flows: a low frequency approach. Zbl 1238.35065
Bonnet-Ben Dhia, A.-S.; Durufle, M.; Joly, P.; Joubert, L.
2011
Energy preserving schemes for nonlinear Hamiltonian systems of wave equations: application to the vibrating piano string. Zbl 1231.74146
Chabassier, J.; Joly, P.
2010
Local time stepping and discontinuous Galerkin methods for symmetric first order hyperbolic systems. Zbl 1407.65183
Ezziani, Abdelaâziz; Joly, Patrick
2010
Optimized higher order time discretization of second order hyperbolic problems: construction and numerical study. Zbl 1198.65092
Joly, P.; Rodríguez, J.
2010
Analysis of acoustic wave propagation in a thin moving fluid. Zbl 1211.35225
Joly, Patrick; Weder, Ricardo
2010
Exact boundary conditions for time-harmonic wave propagation in locally perturbed periodic media. Zbl 1165.78311
Fliss, Sonia; Joly, Patrick
2009
Influence of Gauss and Gauss-Lobatto quadrature rules on the accuracy of a quadrilateral finite element method in the time domain. Zbl 1167.65057
Durufle, M.; Grob, P.; Joly, P.
2009
Generalized impedance boundary conditions for scattering problems from strongly absorbing obstacles: the case of Maxwell’s equations. Zbl 1170.35094
Haddar, Houssem; Joly, Patrick; Nguyen, Hoai-Minh
2008
Higher order time stepping for second order hyperbolic problems and optimal CFL conditions. Zbl 1149.65070
Gilbert, J. Charles; Joly, Patrick
2008
Construction and analysis of improved Kirchhoff conditions for acoustic wave propagation in a junction of thin slots. Zbl 1156.76422
2008
Matching of asymptotic expansions for wave propagation in media with thin slots II: The error estimates. Zbl 1132.35348
Joly, Patrick; Tordeux, Sébastien
2008
The mathematical model for elastic wave propagation. Zbl 1162.74021
Joly, Patrick
2008
Numerical methods for treating unbounded media. Zbl 1286.74039
Joly, Patrick; Tsogka, C.
2008
Finite element methods with discontinuous displacement. Zbl 1286.74103
Joly, Patrick; Tsogka, C.
2008
Finite element methods with continuous displacement. Zbl 1138.74048
Joly, Patrick
2008
Space time mesh refinement methods. Zbl 1286.74098
Derveaux, G.; Joly, P.; Rodríguez, J.
2008
Fictitious domain methods for wave diffraction. Zbl 1163.74029
Joly, Patrick; Tsogka, C.
2008
Conservative coupling between finite elements and retarded potentials. Application to vibroacoustics. Zbl 1277.76057
Grob, P.; Joly, P.
2007
A time domain analysis of PML models in acoustics. Zbl 1119.76046
Diaz, J.; Joly, P.
2006
Exact boundary conditions for periodic waveguides containing a local perturbation. Zbl 1125.78008
Joly, P.; Li, J.-R.; Fliss, S.
2006
Matching of asymptotic expansions for wave propagation in media with thin slots I: The asymptotic expansion. Zbl 1132.35347
Joly, Patrick; Tordeux, Sébastien
2006
Conservative space-time mesh refinement methods for the FDTD solution of Maxwell’s equations. Zbl 1107.78015
Collino, F.; Fouquet, T.; Joly, P.
2006
Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots. Zbl 1220.35174
Joly, Patrick; Tordeux, Sébastien
2006
A mathematical analysis of the resonance of the finite thin slots. Zbl 1237.35033
Clausel, M.; Duruflé, M.; Joly, P.; Tordeux, S.
2006
Generalized impedance boundary conditions for scattering by strongly absorbing obstacles: the scalar case. Zbl 1084.35102
Haddar, Houssem; Joly, Patrick; Nguyen, Hoai-Minh
2005
An analysis of higher order boundary conditions for the wave equation. Zbl 1078.35062
Diaz, Julien; Joly, Patrick
2005
An error analysis of conservative space-time mesh refinement methods for the one-dimensional wave equation. Zbl 1097.65095
Joly, Patrick; Rodriguez, Jerónimo
2005
Space-time mesh refinement for elastodynamics. Numerical results. Zbl 1095.74030
Bécache, E.; Joly, P.; Rodríguez, J.
2005
Robust high-order non-conforming finite element formulation for time domain fluid-structure interaction. Zbl 1189.76337
Diaz, Julien; Joly, Patrick
2005
An efficient numerical method for the resolution of the Kirchhoff-Love dynamic plate equation. Zbl 1079.74060
Bécache, Eliane; Derveaux, Grégoire; Joly, Patrick
2005
A mixed finite element approach for viscoelastic wave propagation. Zbl 1065.74069
Bécache, Eliane; Ezziani, Abdelaâziz; Joly, Patrick
2004
Stability of perfectly matched layers, group velocities and anisotropic waves. Zbl 1127.74335
Bécache, E.; Fauqueux, S.; Joly, P.
2003
Variational methods for time-dependent wave propagation problems. Zbl 1049.78028
Joly, Patrick
2003
A conservative space-time mesh refinement method for the 1-D wave equation. I: Construction. Zbl 1048.65089
Collino, F.; Fouquet, T.; Joly, P.
2003
A conservative space-time mesh refinement method for the 1-D wave equation. II: Analysis. Zbl 1036.65073
Collino, F.; Fouquet, T.; Joly, P.
2003
Stabilized perfectly matched layer for advective acoustics. Zbl 1047.76116
Diaz, Julien; Joly, Patrick
2003
Mathematical and numerical aspects of wave propagation, WAVES 2003. Proceedings of the sixth international conference on mathematical and numerical aspects of wave propagation, Jyväskylä, Finland, 30 June – 4 July 2003. Zbl 1029.00072
Cohen, Gary C. (ed.); Heikkola, Erkki (ed.); Joly, Patrick (ed.); Neittaanmäki, Pekka (ed.)
2003
Numerical simulation of a guitar. Zbl 1047.76115
Bécache, Eliane; Chaigne, Antoine; Derveaux, Grégoire; Joly, Patrick
2003
Homogenized model for a laminar ferromagnetic medium. Zbl 1064.78007
2003
On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations. Zbl 0992.78032
Bécache, Eliane; Joly, Patrick
2002
A new family of mixed finite elements for the linear elastodynamic problem. Zbl 1032.74049
Bécache, E.; Joly, P.; Tsogka, C.
2002
Stability of thin layer approximation of electromagnetic waves scattering by linear and nonlinear coatings. Zbl 0998.78008
2002
A method for computing guided waves in integrated optics. II: Numerical approximation and error analysis. Zbl 1017.65085
Gómez Pedreira, Dolores; Joly, Patrick
2002
Stability of thin layer approximation of electromagnetic waves scattering by linear and non linear coatings. Zbl 1142.78308
2002
Higher order triangular finite elements with mass lumping for the wave equation. Zbl 1019.65077
Cohen, G.; Joly, P.; Roberts, J. E.; Tordjman, N.
2001
Fictitious domains, mixed finite elements and perfectly matched layers for 2-D elastic wave propagation. Zbl 1360.74156
Bécache, E.; Joly, P.; Tsogka, C.
2001
Effective boundary conditions for thin ferromagnetic layers: The one-dimensional model. Zbl 0973.78011
2001
Mathematical analysis and numerical approximation of optical waveguides. Zbl 0986.78013
Bonnet-Ben Dhia, Anne-Sophie; Joly, Patrick
2001
Effective boundary conditions for thin ferromagnetic coatings. Asymptotic analysis of the 1D model. Zbl 0995.35072
2001
A method for computing guided waves in integrated optics. I: Mathematical analysis. Zbl 1014.35067
Gómez Pedreira, Dolores; Joly, Patrick
2001
Domain decomposition method for harmonic wave propagation: A general presentation. Zbl 0965.65134
Collino, Francis; Ghanemi, Souad; Joly, Patrick
2000
An analysis of new mixed finite elements for the approximation of wave propagation problems. Zbl 0958.65102
Bécache, E.; Joly, P.; Tsogka, C.
2000
Construction and analysis of higher order finite difference schemes for the 1D wave equation. Zbl 0968.65060
Anné, Laurent; Joly, Patrick; Tran, Quang Huy
2000
On transitions to stationary states in a Maxwell–Landau–Lifschitz–Gilbert system. Zbl 1025.78005
Joly, Patrick; Komech, Alexander; Vacus, Olivier
2000
A new second order 3D edge element on tetrahedra for time dependent Maxwell’s equations. Zbl 0995.78040
Joly, Patrick; Poirier, Christine
2000
Higher-order variational finite difference schemes for solving 3-D paraxial wave equations using splitting techniques. Zbl 1074.74647
Bécache, Eliane; Collino, Francis; Joly, Patrick
2000
An explicit finite element scheme for time-dependent Kirchhoff-Love equations. Zbl 1072.74546
Bécache, Éliane; Derveaux, Grégoire; Joly, Patrick
2000
Mathematical and numerical aspects of wave propagation. 5th international conference, Santiago de Compostela, Spain, July 10–14, 2000. Zbl 0943.00077
Bermúdez, Alfredo (ed.); Gómez, Dolores (ed.); Hazard, Christophe (ed.); Joly, Patrick (ed.); Roberts, Jean E. (ed.)
2000
Mathematical analysis of elastic surface waves in topographic waveguides. Zbl 0946.74034
Bonnet-Ben Dhia, A. S.; Duterte, J.; Joly, P.
1999
Mathematical and numerical studies of nonlinear ferromagnetic materials. Zbl 0960.78003
Joly, Patrick; Vacus, Olivier
1999
Fictitious domains, $$\text{H(div)}$$ finite elements and Neumann condition: The inf-sup condition. Zbl 0931.65112
Joly, Patrick; Rhaouti, Leïla
1999
Existence and uniqueness results for the Helmholtz equation with second order absorbing boundary conditions. Zbl 0929.35031
Joly, Patrick; Lohrengel, Stéphanie; Vacus, Olivier
1999
A space-time mesh refinement method for the 1D Maxwell’s system. Zbl 0934.78002
Collino, Francis; Fouquet, Thierry; Joly, Patrick
1999
A numerical method for surface waves in a cylindrically perturbed elastic half-space. I: Construction and analysis. Zbl 0937.35111
Duterte, Jean; Joly, Patrick
1999
A numerical method for the computation of electromagnetic modes in optical fibres. Zbl 0922.65088
Joly, Patrick; Poirier, Christine
1999
Fictitious domain method for unsteady problems: application to electromagnetic scattering. Zbl 1126.78311
Collino, Francis; Joly, Patrick; Millot, Florence
1997
A new interface condition in the non-overlapping domain decomposition method for the Maxwell equations. Zbl 0902.65074
Collino, P.; Delbue, G.; Joly, P.; Piacentini, A.
1997
Edge finite elements and mass lumping for Maxwell’s equations: The 2D case. Zbl 0877.65081
Elmkies, Alexandre; Joly, Patrick
1997
Edge finite elements and mass lumping for Maxwell’s equations: The 3D case. Zbl 0893.65068
Elmkies, Alexandre; Joly, Patrick
1997
Mixed finite elements and mass lumping for linear elastodynamics. I: Construction. Zbl 0895.73064
Bécache, Éliane; Joly, Patrick; Tsogka, Chrysoula
1997
Electromagnetic waves propagation in 1D ferromagnetic medium: An existence and uniqueness result. Zbl 0874.35121
Joly, Patrick; Vacus, Olivier
1997
Construction and analysis of a new mixed finite element allowing mass lumping. Zbl 0877.65072
Bécache, Éliane; Joly, Patrick; Tsogka, Chrysoula
1997
...and 35 more Documents
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#### Cited by 1,236 Authors

 52 Joly, Patrick 23 Nazarov, Sergeĭ Aleksandrovich 21 Li, Jichun 15 Hagstrom, Thomas M. 14 Imperiale, Sébastien 13 Bécache, Eliane 13 Nguyen, Hoai-Minh 13 Schmidt, Kersten 12 Givoli, Dan 11 Grote, Marcus J. 11 Huang, Yunqing 11 Kreiss, Gunilla 10 Collino, Francis 10 Duru, Kenneth 10 Duruflé, Marc 10 Haddar, Houssem 9 Fliss, Sonia 9 Gander, Martin Jakob 9 Geuzaine, Christophe A. 8 Antoine, Xavier 8 Sayas, Francisco-Javier 8 Tsynkov, Semyon V. 7 Bendali, Abderrahmane 7 Bonnet-Ben Dhia, Anne-Sophie 7 Chabassier, Juliette 7 Demkowicz, Leszek F. 7 Diaz, Julien 7 Dolean, Victorita 7 Gimperlein, Heiko 7 Halpern, Laurence 7 Kachanovska, Maryna 7 Lanteri, Stéphane 7 Lombard, Bruno 7 Magoulès, Frédéric 7 Nataf, Frédéric 7 Péron, Victor 7 Piperno, Serge 7 Rodríguez, Jerónimo 7 Semin, Adrien 7 Tordeux, Sébastien 6 Boubendir, Yassine 6 Delourme, Bérangère 6 Hu, Fang Qi 6 Lee, Jin-Fa 6 Mattsson, Ken 6 Monk, Peter B. 6 Schweizer, Ben 6 Toivanen, Jari 6 Tsogka, Chrysoula 5 Barucq, Hélène 5 Bielak, Jacobo 5 Cimrák, Ivan 5 Cockburn, Bernardo 5 Dauge, Monique 5 Després, Bruno 5 Egger, Herbert 5 Geevers, Sjoerd 5 Heikkola, Erkki 5 Lechleiter, Armin 5 Liao, Wenyuan 5 Lisitsa, Vadim 5 Nicaise, Serge 5 Rabinovich, Daniel 5 Slodička, Marián 5 Soares, Delfim jun. 5 Stephan, Ernst Peter 5 Turkel, Eli L. 5 Zhang, Ruming 5 Zhang, Wensheng 4 Abgrall, Rémi 4 Appelö, Daniel 4 Beilina, Larisa 4 Cakoni, Fioralba 4 Claeys, Xavier 4 Craster, Richard V. 4 Dohnal, Tomáš 4 Ehrhardt, Matthias 4 Falletta, Silvia 4 Guddati, Murthy N. 4 Hewett, David P. 4 Hiptmair, Ralf 4 Kaltenbacher, Barbara 4 Lipnikov, Konstantin N. 4 Maday, Yvon 4 Marigo, Jean-Jacques 4 Matuszyk, Paweł Jerzy 4 Maurel, Agnès 4 Modave, Axel 4 Özdemir, Ceyhun 4 Peng, Zhen 4 Pinaud, Olivier 4 Piraux, Joël 4 Radu, Bogdan 4 Rauch, Jeffrey B. 4 Stark, David R. 4 Symes, William W. 4 Taskinen, Jari 4 Tcheverda, Vladimir A. 4 van der Vegt, Jaap J. W. 4 Vial, Grégory ...and 1,136 more Authors
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#### Cited in 147 Serials

 161 Journal of Computational Physics 61 Computer Methods in Applied Mechanics and Engineering 56 Journal of Computational and Applied Mathematics 33 Journal of Scientific Computing 32 Wave Motion 27 Applied Numerical Mathematics 26 SIAM Journal on Scientific Computing 21 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 19 International Journal for Numerical Methods in Engineering 18 Computers & Mathematics with Applications 18 Comptes Rendus. Mathématique. Académie des Sciences, Paris 17 Numerische Mathematik 16 Mathematics of Computation 15 SIAM Journal on Numerical Analysis 15 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 14 Journal of Computational Acoustics 11 Mathematical Methods in the Applied Sciences 11 SIAM Journal on Applied Mathematics 10 Applied Mathematics and Computation 10 Computational Mechanics 10 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 Journal of Mathematical Analysis and Applications 8 Archive for Rational Mechanics and Analysis 8 BIT 8 Numerical Methods for Partial Differential Equations 7 Computers and Fluids 6 Journal of Differential Equations 6 RAIRO. Modélisation Mathématique et Analyse Numérique 6 Engineering Analysis with Boundary Elements 5 Journal of Mathematical Physics 5 St. Petersburg Mathematical Journal 5 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 5 Computational Geosciences 4 Inverse Problems 4 Journal of Fluid Mechanics 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Applied Mathematical Modelling 4 Communications in Partial Differential Equations 4 Journal of Mathematical Sciences (New York) 3 Computer Physics Communications 3 International Journal for Numerical Methods in Fluids 3 Calcolo 3 Japan Journal of Industrial and Applied Mathematics 3 Numerical Algorithms 3 Journal of Elasticity 3 SIAM Journal on Mathematical Analysis 3 SIAM Review 3 Mathematics and Mechanics of Solids 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 European Journal of Mechanics. A. Solids 3 Multiscale Modeling & Simulation 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 SN Partial Differential Equations and Applications 2 Journal of Engineering Mathematics 2 Mathematical Notes 2 Meccanica 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Acta Applicandae Mathematicae 2 COMPEL 2 Applied Mathematics Letters 2 Asymptotic Analysis 2 Calculus of Variations and Partial Differential Equations 2 Numerical Linear Algebra with Applications 2 Advances in Computational Mathematics 2 Discrete and Continuous Dynamical Systems 2 Journal of Applied Mechanics and Technical Physics 2 International Journal of Numerical Modelling 2 Engineering Computations 2 Doklady Physics 2 Archives of Computational Methods in Engineering 2 Central European Journal of Mathematics 2 Inverse Problems and Imaging 2 Discrete and Continuous Dynamical Systems. Series S 2 Mathematical Control and Related Fields 2 SMAI Journal of Computational Mathematics 1 Applicable Analysis 1 Communications in Mathematical Physics 1 Indian Journal of Pure & Applied Mathematics 1 International Journal of Solids and Structures 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Statistical Physics 1 Acta Mathematica Vietnamica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Mathematics and Computers in Simulation 1 Mechanics Research Communications 1 Numerical Functional Analysis and Optimization 1 Proceedings of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 Moscow University Computational Mathematics and Cybernetics 1 Applied Mathematics and Mechanics. (English Edition) 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Optimization 1 Mathematical and Computer Modelling 1 Journal of Integral Equations and Applications 1 Science in China. Series A 1 European Journal of Applied Mathematics 1 The Annals of Applied Probability 1 Concurrency: Practice and Experience 1 Computational Mathematics and Mathematical Physics ...and 47 more Serials
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#### Cited in 40 Fields

 495 Numerical analysis (65-XX) 455 Partial differential equations (35-XX) 248 Optics, electromagnetic theory (78-XX) 198 Mechanics of deformable solids (74-XX) 178 Fluid mechanics (76-XX) 35 Geophysics (86-XX) 23 Statistical mechanics, structure of matter (82-XX) 19 Operator theory (47-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 13 Quantum theory (81-XX) 9 Systems theory; control (93-XX) 8 Ordinary differential equations (34-XX) 7 Approximations and expansions (41-XX) 5 Functions of a complex variable (30-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Integral equations (45-XX) 5 Probability theory and stochastic processes (60-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Special functions (33-XX) 4 Functional analysis (46-XX) 4 Computer science (68-XX) 4 Biology and other natural sciences (92-XX) 4 Information and communication theory, circuits (94-XX) 3 General and overarching topics; collections (00-XX) 3 Measure and integration (28-XX) 3 Potential theory (31-XX) 3 Integral transforms, operational calculus (44-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Mechanics of particles and systems (70-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Relativity and gravitational theory (83-XX) 2 Combinatorics (05-XX) 2 Real functions (26-XX) 2 Astronomy and astrophysics (85-XX) 1 History and biography (01-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Differential geometry (53-XX) 1 Operations research, mathematical programming (90-XX)