Publications

Recent and Preprints
  1. Tino Laidin, Lorenzo Pareschi, Conservative polynomial approximations and applications to Fokker-Planck equations, preprint arXiv:2402.06473, 2024
  2. Lorenzo Pareschi, Optimization by linear kinetic equations and mean-field Langevin dynamics, preprint arXiv:2401.05553, 2024
  3. Lorenzo Pareschi, Mattia Zanella, Reduced variance random batch methods for nonlocal PDEs, preprint arXiv:2401.00493, 2023
  4. Giulia Bertaglia, Lorenzo Pareschi, Giuseppe Toscani, Modelling contagious viral dynamics: a kinetic approach based on mutual utility, Math. Biosci. Eng. 21(3), 4241-4268, 2024.
  5. Giacomo Borghi, Lorenzo Pareschi, Kinetic description and convergence analysis of genetic algorithms for global optimization, preprint arXiv:2310.08562, 2023.
  6. Giulia Bertaglia, Lorenzo Pareschi, Russel E. Caflisch, Gradient-based Monte Carlo methods for relaxation approximations of hyperbolic conservation laws, preprint arXiv:2308.02904, 2023.
  7. Andrea Medaglia, Lorenzo Pareschi, Mattia Zanella, Particle simulation methods for the Landau-Fokker-Planck equation with uncertain data, J. Comp. Phys. 503, 112845, 2024 
  8. Giulia Bertaglia, Lorenzo Pareschi, Multiscale constitutive framework of 1D blood flow modeling: Asymptotic limits and numerical methods, SIAM Multiscale Modeling and Simulation 21(3), 1237-126, 2023
  9. Jonathan Franceschi, Lorenzo Pareschi, Elena Bellodi, Marco Gavanelli, Marco Bresadola, Modeling opinion polarization on social media: application to Covid-19 vaccination hesitancy in Italy, PLoS ONE, 18(10):e0291993, 2023
  10. Giacomo Borghi, Sara Grassi, Lorenzo Pareschi, Consensus based optimization with memory effects: random selection and applications, Chaos, Solitons and Fractals 174, 113859, 2023
  11. Lorenzo Pareschi, Giuseppe Toscani, The kinetic theory of mutation rates, Axioms 12(3), 265, 2023
  12. Manuel R. Izquierdo, Lorenzo Pareschi, Borja Miñano, Joan Massó, Carlos Palenzuela, Global high-order numerical schemes for the time evolution of the general relativistic radiation magneto-hydrodynamics equations, Classical and Quantum Gravity 40, 145014, 2023
  13. Giacomo Borghi, Michael Herty, Lorenzo Pareschi, An adaptive consensus based method for multi-objective optimization with uniform Pareto front approximation, Applied Math. Optim. 88, 58 2023 
  14. Andrea Medaglia, Lorenzo Pareschi, Mattia Zanella, Stochastic Galerkin particle methods for kinetic equations of plasmas with uncertainties, J. Comp. Phys. Volume 479, 112011, 2023
  15. Giacomo Dimarco, Lorenzo Pareschi, Mattia Zanella, Micro-macro stochastic Galerkin methods for nonlinear Fokker-Plank equations with random inputs, SIAM Multiscale Modelling and Simulation, to appear. Preprint arXiv:2207.06494, 2022
  16. Walter Boscheri, Giacomo Dimarco, Lorenzo Pareschi, Locally Structure-Preserving div-curl operators for high order Discontinuous Galerkin schemes, J. Comp. Phys. Vol. 486, 112130, 2023
  17. Giacomo Borghi, Michael Herty, Lorenzo Pareschi, Constrained consensus-based optimization, SIAM J. Optimization 33(1):10.1137, 2023. 

 Lecture notes, book chapters, surveys
  1. Lorenzo Pareschi, Giuseppe Toscani, Dinamiche sociali ed equazioni alle derivate parziali in ambito epidemiologico, Matematica, Cultura e Società - Rivista dell'Unione Matematica Italiana, Serie I, Volume 6, No.3, 2021
  2. Giacomo Dimarco, Liu Liu, Lorenzo Pareschi, Xueyu Zhu, Multi-fidelity methods for uncertainty propagation in kinetic equations, to appear in Panoramas & Synthèses, Société Mathématique de France. Preprint arXiv:2112.00932, 2021.
  3. Giacomo Albi, Walter Boscheri, Giulia Bertaglia, Giacomo Dimarco, Lorenzo Pareschi, Giuseppe Toscani, Mattia Zanella, Kinetic modelling of epidemic dynamics: social contacts, control with uncertain data, and multiscale spatial dynamics Predicting Pandemics in a Globally Connected World, Vol. 1, N. Bellomo and M. Chaplain Editors, Springer-Nature, 43-108, 2022. 
  4. Sara Grassi, Hui Huang, Lorenzo Pareschi, Jinniao Qiu, Mean-field particle swarm optimization, Modeling and Simulation for Collective Dynamics, Vol. 40, IMS Lecture Notes Series, World Scientific, 127-194, 2023.
  5. Lorenzo Pareschi, An introduction to uncertainty quantification for kinetic equations and related problems, in Trails in kinetic theory: foundational aspects and numerical methods, SEMA-SIMAI Springer Series 25:141-181, 2021.
  6. Giacomo Albi, Emiliano Cristiani, Lorenzo Pareschi, Daniele Peri. Mathematical models and methods for crowd dynamics control, Crowd Dynamics Volume 2 - Theory, Models, and Applications. Modeling and Simulation in Science, Engineering and Technology, 159-197, 2020.
  7. Albi, G.; Bellomo, N.; Fermo, L.; Ha, S.-Y.; Kim, J.; Pareschi, L.; Poyato, D.; Soler, J. Vehicular traffic, crowds, and swarms: from kinetic theory and multiscale methods to applications and research perspectives. Math. Models Methods Appl. Sci.  29,  no. 10, 1901-2005, 2019.
  8. Giacomo Dimarco, Lorenzo Pareschi, Mattia Zanella, Uncertainty quantification for kinetic models in socio-economic and life sciences, in Uncertainty quantification for kinetic and hyperbolic equations, SEMA-SIMAI Springer Series, vol. 14, 151-191, 2018.
  9. Giacomo Albi, Lorenzo Pareschi, Giuseppe Toscani, Mattia Zanella, Recent advances in opinion modeling: control and social influence, Active particles. Vol. 1. Advances in theory, models, and applications, 49–98, Model. Simul. Sci. Eng. Technol., Birkhäuser/Springer, Cham, 2017.
  10. Giacomo Dimarco, Qin Li, Lorenzo Pareschi, Bokai Yan, Numerical methods for plasma physics in collisional regimes, Journal of Plasma Physics, 2015, pp. 305810106.
  11. Dimarco, G.;  Pareschi, L.  Numerical methods for kinetic equations. Acta Numer.  23  (2014), 369--520.
  12. L.Pareschi, G.Russo, Efficient asymptotic preserving deterministic methods for the Boltzmann equation, AVT-194 RTO AVT/VKI, Models and Computational Methods for Rarefied Flows, Lecture Series held at the von Karman Institute, Rhode St. Genèse, Belgium, 24 -28 January (2011).
  13. C.Piatecki, S.Cordier, D.Maldarella, L.Pareschi, Microscopic and kinetic models for financial markets, Mathematical modelling of collective behavior in socio-economic and life sciences, p. 49-80, Boston: Birkhauser, (2010).
  14. L.Pareschi, G.Russo,  An introduction to the numerical analysis of the Boltzmann equation, Lecture Notes at M&KT 2004, Riv. Mat. Univ. Parma (7) 4** (2005), 145--250.
  15. L.Pareschi, Hybrid multiscale methods for kinetic and hyperbolic problems, ESAIM: Proceedings, Vol.15, T. Goudon, E. Sonnendrucker and D. Talay, Editors, pp.87-120, (2005)
  16. L.Pareschi, G.Toscani, Modelling and numerical methods for granular gases, Chapter 9, Modeling and computational methods for kinetic equations, Series: Modeling and Simulation in Science, Engineering and Technology, Birkhauser (2004), pp.259-286.
  17. P.Markowich, L.Pareschi, W.Bao, Quantum kinetic theory: modelling and numerics for Bose-Einstein condensation, Chapter 10, Modeling and computational methods for kinetic equations, Series: Modeling and Simulation in Science, Engineering and Technology, Birkhauser (2004), pp.287-320.
  18. L.Pareschi, Computational methods and fast algorithms for Boltzmann equations, Chapter 7, Lecture Notes on the discretization of the Boltzmann equation, Series on Advances in Mathematics for Applied Sciences, Vol. 63, World Scientific, (2003). 
  19. L.Pareschi, G.Russo, An introduction to Monte Carlo methods for the Boltzmann equation. ESAIM: Proceedings, Vol.10, pp.35-75 (2001)

Complete list

2019-2022 
  1. Giulia Bertaglia, Chuan Lu, Lorenzo Pareschi, Xueyu Zhu, Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spread, Mathematical Models and Methods in Applied Sciences 32(10):1949-1985, 2022
  2. Giacomo Borghi, Michael Herty, Lorenzo Pareschi, A consensus-based algorithm for multi-objective optimization and its mean-field description, Proceedings of the IEEE Conference on Decision and Control, 4131–4136, 2022
  3. Jonathan Franceschi, Lorenzo Pareschi, Mattia Zanella. From agent-based models to the macroscopic description of fake-news spread: the role of competence in data-driven applications, Partial Differential Equations and Applications 3(68):1-26, 2022
  4. Emanuele Bernardi, Lorenzo Pareschi, Giuseppe Toscani, Mattia Zanella, Effects of vaccination efficacy on wealth distribution in kinetic epidemic models, Entropy 24(2):216, 2022
  5. Giulia Bertaglia, Liu Liu, Lorenzo Pareschi, Xueyu Zhu, Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties, Network and Heterogeneous Media, 17(3): 401-425, 2022
  6. Jonathan Franceschi, Lorenzo Pareschi, Spreading of fake news, competence, and learning: kinetic modeling and numerical approximation, Philosophical Transactions of the Royal Society A 380:2224, 2021.0159, 2022
  7. Liu Liu, Lorenzo Pareschi, Xueyu Zhu, A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs, Journal of Computational Physics 462,  111252, 2022
  8. Walter Boscheri, Maurizio Tavelli, Lorenzo Pareschi, On the construction of conservative semi-Lagrangian IMEX advection schemes for multiscale time dependent PDEs, J. Scientific Computing 90(3), 97, 2022
  9. Lorenzo Pareschi, Thomas Rey, Moment preserving Fourier-Galerkin spectral methods and application to the Boltzmann equation, SIAM J. Num. Analysis 60(6), 10.1137/21M1423452, 2022.
  10. Alessandro Benfenati, Giacomo Borghi, Lorenzo Pareschi, Binary interaction methods for high dimensional global optimization and machine learning, Applied Math. Optim. 86(9):1-41, 2022.
  11. Massimo Fornasier, Hui Huang, Lorenzo Pareschi, Philippe Sünnen, Anisotropic Diffusion in Consensus-based Optimization on the Sphere, SIAM J. Optim. 32(3):1984–2012, 2022.
  12. Lorenzo Pareschi, Torsten Trimborn, Mattia Zanella, Mean-field control variate methods for kinetic equations with uncertainties and applications to socio-economic sciences, Int. J. Uncertainty. Quant. 12(1):61-84, 2022
  13. Giulia Bertaglia, Lorenzo Pareschi, Hyperbolic compartmental models for epidemic spread on networks with uncertain data: application to the emergence of Covid-19 in Italy, Math. Mod. Meth. Appl. Sci. 31(12): 2495-2531, 2021 
  14. Giulia Bertaglia, Walter Boscheri, Giacomo Dimarco, Lorenzo Pareschi, Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty, Math. Biosci. Engin. 18(5): 7028-7059, 2021. 
  15. Walter Boscheri, Giacomo Dimarco, Lorenzo Pareschi, Modeling and simulating the spatial spread of an epidemic through multiscale kinetic equations, Math. Mod. Meth. App. Sci. 31(6):1059-1097, 2021
  16. Sara Grassi, Lorenzo Pareschi, From particle swarm optimization to consensus based optimization: stochastic modeling and mean-field limit, Math. Mod. Meth. App. Sci. 31(8):1625–1657, 2021
  17. Lorenzo Pareschi, Thomas Rey, On the stability of equilibrium-preserving spectral methods for the homogeneous Boltzmann equation, App. Math. Letters 120:107187, 2021
  18. Walter Boscheri, Lorenzo Pareschi, High order pressure-based semi-implicit IMEX schemes for the 3D Navier-Stokes equations at all Mach numbers, J. Comp. Phys. 434: 110206, 2021
  19. Giulia Bertaglia, Lorenzo Pareschi , Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods, ESAIM: Mathematical Modelling and Numerical Analysis 55:381-407, 2021
  20. Giulia Bertaglia, Valerio Caleffi, Lorenzo Pareschi, Alessandro Valiani, Uncertainty quantification of viscoelastic parameters in arterial hemodynamics with the a-FSI blood flow model, J. Comp. Phys. 430: 110102, 2021
  21. G. Albi, L. Pareschi, M. Zanella, Control with uncertain data of socially structured compartmental epidemic models, J. Math. Bio. 82(7):63, 2021
  22. G. Albi, L. Pareschi, M. Zanella, Modelling lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty, Mathematical Biosciences and Engineering 18, Issue 6: 7161-7190, 2021
  23. Jingwei Hu, Lorenzo Pareschi, Yubo Wang, Uncertainty quantification for the BGK model of the Boltzmann equation using multilevel variance reduced Monte Carlo methods, SIAM/ASA J. Uncer. Quant. 9(2):650-680, 2021
  24. Massimo Fornasier, Hui Huang, Lorenzo Pareschi, Philippe Sünnen, Consensus-based Optimization on the Sphere: Convergence to Global Minimizers and Machine Learning, J. Machine Learning Research 22(237):1−55, 2021 
  25. Giacomo Albi, Lorenzo Pareschi, High order semi-implicit multistep methods for time dependent partial differential equations, Comm. Appl. Math. Comput. vol. 3, pagg.701-718, 2021
  26. G. Dimarco, L. Pareschi, G. Toscani, M. Zanella, Wealth distribution under the spread of infectious diseases, Phys. Rev. E 102, 022303, 2020
  27. Lorenzo Pareschi, Mattia Zanella, Monte Carlo stochastic Galerkin methods for the Boltzmann equation with uncertainties: space-homogeneous case, J. Comp. Phys. 423, (2020), 109822 
  28. Massimo Fornasier, Hui Huang, Lorenzo Pareschi, Philippe Sünnen, Consensus-Based Optimization on Hypersurfaces: Well-Posedness and Mean-Field Limit, Math. Mod. Meth. Appl. Sci. 30(14):2725-2751, 2020
  29. Michael Herty, Lorenzo Pareschi, Giuseppe Visconti, Mean field models for large data-clustering problems, Network and Heterogeneous Media, 15(3): 463-487, (2020)
  30. Albi, Giacomo; Dimarco, Giacomo; Pareschi, Lorenzo, Implicit-explicit multistep methods for hyperbolic systems with multiscale relaxation, SIAM J. Sci. Comput. 42 (2020), no. 4, A2402–A2435.
  31. Giacomo Dimarco, Lorenzo Pareschi, Multi-scale variance reduction methods based on multiple control variates for kinetic equations with uncertainties, Multiscale Model. Simul.  18  (2020),  no. 1, 351-382.
  32. Giacomo Dimarco, Lorenzo Pareschi, Multi-scale control variate methods for uncertainty quantification in kinetic equations, J. Comput. Phys.  388  (2019), 63--89.
  33. Lorenzo Pareschi, Giuseppe Toscani, Andrea Tosin, Mattia Zanella, Hydrodynamic models of preference formation in multi-agent societies, J. Nonlinear Sci.  29  (2019),  no. 6, 2761-2796.
  34. Giacomo Albi, Michael Herty, Lorenzo Pareschi, Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems, Appl. Math. Comput.  354  (2019), 460-477.
  35. Michael Herty, Lorenzo Pareschi, Sonja Steffensen, Control Strategies for the Dynamics of Large Particle Systems. Active particles, Vol. 2., 149-171, Model. Simul. Sci. Eng. Technol., Birkhäuser/Springer, Cham,  (2019).
  36. Giacomo Albi, Lorenzo Pareschi, Mattia Zanella, Boltzmann games in heterogeneous consensus dynamics, J. Stat. Phys.  175  (2019),  no. 1, 97--125.
  37. Torsten Trimborn, Lorenzo Pareschi, Martin Frank, Portfolio Optimization and Model Predictive Control: A Kinetic Approach, Discrete Contin. Dyn. Syst. Ser. B  24  (2019),  no. 11, 6209-6238.
  38. J. A. Carrillo, L. Pareschi, M. Zanella, Particle based gPC methods for mean-field models of swarming with uncertainty, Commun. Comput. Phys., 25 (2019), pp. 508-531. 
  39. José A. Carrillo, Young-Pil Choi, Lorenzo Pareschi, Structure preserving schemes for the continuum Kuramoto model: phase transitions, J. Comp. Phys. 376, (2019), 365-389.

    2015-2018
  40. Shi Jin, Hanqing Lu, Lorenzo Pareschi, A High Order Stochastic Asymptotic Preserving Scheme for Chemotaxis Kinetic Models with Random Inputs, Multiscale Model. Simul.  16  (2018),  no. 4, 1884-1915.
  41. Bertram Düring, Lorenzo Pareschi, Giuseppe Toscani, Kinetic models for optimal control of wealth inequalities,  Eur. Phys. J. B (2018) 91: 265. [open access].
  42. Giacomo Albi, Michael Herty, Lorenzo Pareschi, Relaxation approximation of optimal control problems and applications to traffic flow models, AIP Conference Proceedings 1975, 020001 (2018) 
  43. Dimarco, G.; Pareschi, L.; Samaey, G.; Asymptotic-Preserving Monte Carlo Methods for Transport Equations in the Diffusive Limit. SIAM J. Sci. Comput. 40 (2018), no. 1, A504–A528.
  44. Shi Jin, Hanqing Lu, Lorenzo Pareschi, Efficient Stochastic Asymptotic-Preserving IMEX Methods for Transport Equations with Diffusive Scalings and Random Inputs, SIAM J. Sci. Comput. 40 (2018), no. 2, A671–A696. 
  45. Lorenzo Pareschi, Mattia Zanella, Structure preserving schemes for nonlinear Fokker-Planck equations and applications, J. Sci. Comput. 74 (2018), no. 3, 1575–1600.
  46. Sebastiano Boscarino, Lorenzo Pareschi, Giovanni Russo, A unified IMEX Runge-Kutta approach for hyperbolic systems with   multiscale relaxation, SIAM J. Numer. Anal. 55 (2017), no. 4, 2085–2109.
  47. Giacomo Albi, Lorenzo Pareschi, Mattia Zanella, Opinion dynamics over complex networks: kinetic modeling and numerical methods, Kinetic and Related Models, 11, 2017, pp. 1-32.
  48. Giacomo Dimarco, Lorenzo Pareschi, Implicit-explicit linear multistep methods for kinetic equations, SIAM J. Numer. Anal. 55 (2017), no. 2, 664–690.
  49. Lorenzo Pareschi, Thomas Rey, Residual equilibrium schemes for time dependent PDEs,  Computer and Fluids, vol. 156, 329-342 (2017). 
  50. Giacomo Albi, Lorenzo Pareschi, Selective model predictive control for flocking systems, Commun. Appl. Ind. Math.  9  (2018),  no. 2, 4-21. 
  51. Sebastiano Boscarino, Lorenzo Pareschi, On the asymptotic properties of IMEX Runge-Kutta schemes for hyperbolic balance laws, Journal of Computational and Applied Mathematics, 316, 2017, pp. 60–73.
  52. Lorenzo Pareschi, Pierluigi Vellucci, Mattia Zanella, Kinetic models of collective decision-making in the presence of equality bias, Physica A, 467,  2017, pp. 201-217
  53. Giacomo Albi, Lorenzo Pareschi, Mattia Zanella, On the optimal control of opinion dynamics on evolving networks, In: System Modeling and Optimization. CSMO 2015. IFIP Advances in Information and Communication Technology, vol 494. Springer, Cham, (2016).
  54. Russ Caflisch, Giacomo Dimarco, Lorenzo Pareschi, An hybrid method for the Boltzmann equation, AIP Conf. Proc. 1786, RGD 30, (2016)
  55. Herty, Michael;  Pareschi, Lorenzo;  Steffensen, Sonja. Mean-field control and Riccati equations. Netw. Heterog. Media  10  (2015),  no. 3, 699--715.
  56. Albi, Giacomo;  Pareschi, Lorenzo;  Zanella, Mattia. Uncertainty quantification in control problems for flocking models. Math. Probl. Eng.  2015, Art. ID 850124, 14 pp.
  57. Albi, Giacomo;  Herty, Michael;  Pareschi, Lorenzo. Kinetic description of optimal control problems and applications to opinion consensus. Commun. Math. Sci.  13  (2015),  no. 6, 1407--1429.
  58. Filbet, Francis;  Pareschi, Lorenzo;  Rey, Thomas. On steady-state preserving spectral methods for homogeneous Boltzmann equations. C. R. Math. Acad. Sci. Paris  353  (2015),  no. 4, 309--314.
  59. Hu, Jingwei;  Li, Qin;  Pareschi, Lorenzo. Asymptotic-preserving exponential methods for the quantum Boltzmann equation with high-order accuracy. J. Sci. Comput.  62  (2015),  no. 2, 555--574.

    2011-2014
  60. Degond P., Dimarco G., Pareschi L.. The Moment Guided Monte Carlo Method. International Journal For Numerical Methods In Fluids, 67, 2, pp 189–213, (2011). 
  61. Dimarco G., Pareschi L., Exponential methods for kinetic equations, SIAM J. Num. Anal, 49, 2057-2077, (2011). 
  62. Boccabella, A., Natalini R., Pareschi L., On a continuous mixed strategy model for evolutionary game-theory, Kinetic and Related Models, 4, 187-213,  (2011)
  63. L.Pareschi, G.Russo, Efficient asymptotic preserving deterministic methods for the Boltzmann equation, AVT-194 RTO AVT/VKI, Models and Computational Methods for Rarefied Flows, Lecture Series held at the von Karman Institute, Rhode St. Genèse, Belgium, 24 -28 January (2011). 
  64. Maldarella, D., Pareschi, L. Kinetic models for socio-economic dynamics of speculative markets, Physica A, 391, 715-730, (2012)  
  65. Kashdan L., Pareschi L., Mean field mutation dynamics and the continuous Luria-Delbruck distribution, Mathematical Biosciences, 240, 223-230 (2012).
  66. Herty M., Pareschi L., Steffensen S., Numerical methods for the optimal control of scalar conservation laws, Lecture Notes in Computer Science, IFIP TC7 Conference on System Modelling and Optimization, (2012)
  67. Dimarco G., Pareschi L., High order asymptotic-preserving schemes for the Boltzmann equation, Comptes Rendus Mathematique, 350, 481-486, (2012)
  68. Albi G., Pareschi L., Modelling self-organized systems interacting with few individuals: from microscopic to macroscopic dynamics, Applied Math. Letters 26, (2013), 397-401.
  69. Li Q., Pareschi L.,  Exponential Runge-Kutta schemes for inhomogeneous Boltzmann equations with high order of accuracy, preprint arXiv:1208.2622
  70. Dimarco G., Pareschi L., Asymptotic preserving Implicit-Explicit Runge-Kutta methods for nonlinear kinetic equations, SIAM J. Numer. Anal. 51, (2013), 1064-1087.
  71. Albi G., Pareschi L., Binary interaction algorithms for the simulation of flocking and swarming dynamics, Multiscale Modeling and Simulation 11, (2013), 1-29.  (arXiv:1203.0721)
  72. Herty M., Pareschi L., Steffensen S., Implicit-Explicit Runge-Kutta schemes for numerical discretization of optimal control problems, SIAM J. Numer. Anal. 51, (2013), 1875-1899. (arXiv: 1202.1166)
  73. Mouhot C., Pareschi L., Rey T., Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation, Math. Mod. Num. Anal. 47, 2013, 1515-1531. (arXiv: 1201.3986)
  74. Boscarino S., Pareschi L., Russo G., Implicit-Explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit, SIAM J. Sci. Comp. 35, (2013), 22-51. ( arXiv:1110.4375).
  75. L. Pareschi, Kinetic equations: computation, invited contribution to Springer "Encyclopedia of Applied and Computational Mathematics", ed. by B. Engquist, 2013.
  76. Pareschi, L.;  Toscani, G.  Wealth distribution and collective knowledge: a Boltzmann approach. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.  372  (2014),  no. 2028, 20130396, 15 pp.
  77. Albi, G.;  Pareschi, L.;  Zanella, M.  Boltzmann-type control of opinion consensus through leaders. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.  372  (2014),  no. 2028, 20140138, 18 pp.
  78. Albi, Giacomo;  Herty, Michael;  Jörres, Christian;  Pareschi, Lorenzo. Asymptotic preserving time-discretization of optimal control problems for the Goldstein-Taylor model. Numer. Methods Partial Differential Equations  30  (2014),  no. 6, 1770--1784.
  79. Dimarco, G. ;  Pareschi, L.  Numerical methods for kinetic equations. Acta Numer.  23  (2014), 369--520.
  80. Dimarco, Giacomo;  Pareschi, Lorenzo;  Rispoli, Vittorio. Implicit-explicit Runge-Kutta schemes for the Boltzmann-Poisson system for semiconductors. Commun. Comput. Phys.  15  (2014),  no. 5, 1291--1319.
  81. Li, Qin;  Pareschi, Lorenzo. Exponential Runge-Kutta for the inhomogeneous Boltzmann equations with high order of accuracy. J. Comput. Phys.  259  (2014), 402--420.

    2006-2010
  82. R.Caflisch, H.Chen, E.Luo, L.Pareschi, A Hybrid Method that Interpolates Between DSMC and CFD, 44TH AIAA Aerospace Sciences Meeting and Exhibit, Reno, AIAA-2006-987, (2006).
  83. E.Ferrari, L.Pareschi, Hybrid Monte Carlo schemes for the diffusion of impurities in a gas, Modelling and Numerics of Kinetic Dissipative Systems, Nova-Science, New York (2006). 
  84. L.Pareschi, G.Toscani, Overpopulated tails in non conservative kinetic models, Modelling and Numerics of Kinetic Dissipative Systems, Nova-Science, New York (2006). 
  85. C.Mouhot, L.Pareschi, Fast algorithms for computing the Boltzmann collision operator,Math. Comp. 75 (2006) 1833-1852. 
  86. S.Brull, L.Pareschi, Dissipative hydrodynamic models for the diffusion of impurities in a gas, Appl. Math. Lett. 19 (2006), no. 6, 516--521. 
  87. F.Filbet, C.Mouhot, L.Pareschi, Solving the Boltzmann equation in NlogN, SIAM J. Sci. Comput. 28, 1029 (2006) 
  88. L.Pareschi, G.Toscani, Self-similarity and power-like tails in nonconservative kinetic models, J.Stat. Phys., 124, (2006), pp.747-779. 
  89. G.Dimarco, L.Pareschi, Hybrid methods for multiscale problems I: hyperbolic relaxation system, Commun. Math. Sci. 4 (2006), no. 1, 155--177. 
  90. M.Herty, L.Pareschi, M.Seaid, Discrete velocity models and relaxation schemes for traffic flows, SIAM J. Sci. Comput. 28, 1582 (2006)
  91. Dimarco, Giacomo ; Pareschi, Lorenzo . Hybrid multiscale methods. II. Kinetic equations. Multiscale Model. Simul. 6 (2007/08), no. 4, 1169--1197. 
  92. Herty, Michael ; Pareschi, Lorenzo ; Seaïd, Mohammed . Enskog-like discrete velocity models for vehicular traffic flow. Netw. Heterog. Media 2 (2007), no. 3, 481--496 (electronic). 
  93. Giacomo Dimarco, Piero Foscari, Pareschi L. A Remark On The Finite Number Of Particles Effect In Monte Carlo Methods For Kinetic Equations. Pamm, Vol. 7; (2007) P. 1041003-1041004.
  94. Ferrari, E. ; Pareschi, L. Modelling and numerical methods for the dynamics of impurities in a gas. Internat. J. Numer. Methods Fluids 57 (2008), no. 6, 693--713.
  95. Banda, Mapundi ; Klar, Axel ; Pareschi, Lorenzo ; Seaïd, Mohammed . Lattice-Boltzmann type relaxation systems and high order relaxation schemes for the incompressible Navier-Stokes equations. Math. Comp. 77 (2008), no. 262, 943--965.
  96. Trazzi, Stefano ; Pareschi, Lorenzo ; Wennberg, Bernt . Adaptive and recursive time relaxed Monte Carlo methods for rarefied gas dynamics. SIAM J. Sci. Comput. 31 (2008/09), no. 2, 1379--1398. 
  97. Cordier, Stephane ; Pareschi, Lorenzo ; Piatecki, Cyrille . Mesoscopic modelling of financial markets. J. Stat. Phys. 134 (2009), no. 1, 161--184.
  98. Boscarino S., Pareschi L, Russo G., IMEX Runge-Kutta schemes and hyperbolic systems of conservation laws with stiff diffusive relaxation, ICNAAM, AIP Conference Proceedings 1168, (2009) pp.1106-1111. 
  99. Herty, Michael; Pareschi, Lorenzo. Fokker-Planck asymptotics for traffic flow models. Kinet. Relat. Models 3 (2010), no. 1, 165--179. 
  100. Caflisch R., Dimarco G., Pareschi L., Direct simulation Monte Carlo schemes for Coulomb interactions in plasmas,  Comm. App. Ind. Math., 1, (2010), pp. 72-91. 
  101. Dimarco G., Pareschi L. Fluid Solver Independent Hybrid Methods For Multiscale Kinetic Equations.  Siam Journal On Scientific Computing, Vol. 32; P. 603-634, (2010). 
  102. Maldarella, D., Pareschi, L. Price dynamics in financial markets: a kinetic approach, Science and Culture, 76, p.448-453, (2010)

    2001-2005
  103. S.Jin, L.Pareschi, Asymptotic preserving (AP) schemes for multiscale kinetic equations: a unified approach, Proceedings Hyperbolic problems: Theory, Numerics, Applications, Magdeburg, International Series of Numerical Mathematics, Birkhauser, 141, (2001), 573-582.
  104. L.Pareschi, G.Russo, Time Relaxed Monte Carlo methods for the Boltzmann equation, SIAM J. Sci. Comput. 23 (2001), no 4, 1253--1273 
  105. L.Pareschi, Central differencing based numerical schemes for hyperbolic conservation laws with relaxation terms, SIAM J. Numer. Anal. 39 (2001), no. 4, 1395--1417 
  106. L.Pareschi, G.Russo, An introduction to Monte Carlo methods for the Boltzmann equation. ESAIM: Proceedings, Vol.10, pp.35-75 (2001) 
  107. L.Pareschi, B.Wennberg, A recursive Monte Carlo algorithm for the Boltzmann equation in the Maxwellian case, Monte Carlo Methods and Applications, Vol. 7, no. 3-4, pp.~349-357, (2001). 
  108. G.Naldi, L.Pareschi, G.Toscani, Convergence of kinetic approximation to nonlinear diffusion problems, Proceedings Conference on Godunov Methods (Oxford, 1999), Kluwer Academic-Plenum Publishers, New York (2001), pp.655-662.
  109. O.Ascenzi, L.Pareschi, F.Segala, A precise computation of stress intensity factor on the front of a convex planar crack, International Journal Numerical Methods in Engineering, 54 (2002), pp.241-261. 
  110. F.Filbet, L.Pareschi, Numerical solution of the non homogeneous Fokker-Planck-Landau equation. Progress in Industrial Mathematics at ECMI 2000, A.M.Anile, V.Capasso, A.Greco editors, Springer (2002), 325-331. 
  111. F.Filbet, L.Pareschi, A numerical method for the accurate solution of the Fokker-Planck-Landau equation in the non homogeneous case, Journal of Computational Physics, 179, 1-26 (2002). 
  112. S.Jin, L.Pareschi, M.Slemrod, A relaxation scheme for solving the Boltzmann equation based on the Chapman-Enskog expansion, Acta Mathematicae Applicatae Sinica, Vol. 18, (2002), no.1, 1-26. 
  113. G.Naldi, L.Pareschi, G.Toscani, Relaxation schemes for PDEs and applications to degenerate diffusion problems, Surveys on Mathematics for Industry (now European Journal for Applied Mathematics), 10, pp.315-343, (2002).
  114. L.Pareschi, G.Toscani, C.Villani, Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit, Numerische Mathematik, 93, pp.527-548, (2003). 
  115. G.Naldi, L.Pareschi, G.Toscani, Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit, Mathematical Models and Numerical Analysis, 37, (2003), pp. 73-90. 
  116. R.E.Caflisch, L.Pareschi, Towards and hybrid Monte Carlo method for rarefied gasdynamics, Ben Abdallah, Naoufel (ed.) et al., Transport in transition regimes. New York, NY: Springer. IMA Vol. Math. Appl. 135, pp.57-73 (2004).
  117. L.Pareschi, On the fast evaluation of kinetic equations for driven granular media, Numerical Analysis and Advanced Applications - Proceedings of ENUMATH 2001, the 4th conference on numerical mathematics and advanced applications, Ischia, July 2001, Springer-Italia, (2003).
  118. L.Pareschi, G.Russo, High order asymptotically strong-stability preserving methods for hyperbolic systems with stiff relaxation, Hyperbolic Problems: Theory, Numerics, Applications : Proceedings of the Ninth International Conference on Hyperbolic Problems Held in Caltech, Pasadena, March 25-29, 2002, Springer, (2003), pp.241-255. 
  119. L.Pareschi, Computational methods and fast algorithms for Boltzmann equations, Chapter 7, Lecture Notes on the discretization of the Boltzmann equation, Series on Advances in Mathematics for Applied Sciences, Vol. 63, World Scientific, (2003). 
  120. F.Filbet, L.Pareschi, Numerical solution of the Fokker-Planck-Landau equation by spectral methods. Commun. Math. Sci. 1 (2003), no. 1, 206--207. 
  121. J.A.Carrillo, J.M.Mantas, J.Ortega, L.Pareschi, Parallel Integration of Hydrodinamical Approximations for the Boltzmann Equation on a Cluster of Computers, Journal of Computational Methods in Science and Engineering, Vol. 3, No. 3; pp: 337-346 (2003). 
  122. A.Klar, L.Pareschi, M.Seaid, Uniformly accurate schemes for relaxation approximations to fluid dynamic equations, Applied Mathematics Letters, 16, (2003) pp.1123-1127. 
  123. M.K.Banda, A.Klar, L.Pareschi, M.Seaid, Compressible and Incompressible Limits for Hyperbolic Systems with Relaxation, Journal of Computational and Applied Mathematics, 168 (2004) pp.41-52. 
  124. L.Pareschi, G.Russo, G.Toscani, A kinetic approximation to Hele-Shaw flow, C. R., Math., Acad. Sci. Paris, Ser. I 338, No.2, pp.177-182 (2004). 
  125. L.Pareschi, G.Toscani, Modelling and numerical methods for granular gases, Chapter 9, Modeling and computational methods for kinetic equations, Series: Modeling and Simulation in Science, Engineering and Technology, Birkhauser (2004), pp.259-286. 
  126. P.Markowich, L.Pareschi, W.Bao, Quantum kinetic theory: modelling and numerics for Bose-Einstein condensation, Chapter 10, Modeling and computational methods for kinetic equations, Series: Modeling and Simulation in Science, Engineering and Technology, Birkhauser (2004), pp.287-320. 
  127. L.Pareschi, M.Seaid, A New Monte Carlo Approach for Conservation Laws and Relaxation Systems, Lecture Notes in Computer Science, Vol. 3037, pp:281-288 (2004) 
  128. C.Mouhot, L.Pareschi, Fast methods for the Boltzmann collision integral, C. R., Math., Acad. Sci. Paris, Ser. I 339 (2004) pp.71-76. 
  129. O.Ascenzi, L.Pareschi, F.Segala, Convergence of a quadrature formula for the approximation of stress intensity factor for planar cracks, Applied Mathematics and Computation, Volume 158, Issue 3, 15 (2004), pp 597-617.
  130. L.Pareschi, G.Puppo, G.Russo, Central Runge-Kutta schemes for hyperbolic conservation laws, SIAM J. Sci. Comp. 26, (2005) pp.979-999. 
  131. F.Filbet, L.Pareschi, G.Toscani, Accurate numerical methods for the collisional motion of (heated) granular flows, J. Comp. Phys., 202, (2005), pp.216-235. 
  132. P.Markowich, L.Pareschi, Fast, conservative and entropic numerical methods for the Bosonic Boltzmann equation, Numerische Math. 99 (2005), pp.509--532.
  133. L.Pareschi, G.Russo, S.Trazzi, A.Shevryn, Ye.Bondar, M.Ivanov, Comparison between TRMC and MFS methods for the space homogeneous Boltzmann equation Proceedings 24th International Symposium on Rarefied Gas Dynamics 2004, America Institute of Physics, 762, 571 (2005)
  134. L.Pareschi, G.Russo, S.Trazzi, A.Shevryn, Ye.Bondar, M.Ivanov, Plane Couette Flow Computations by TRMC and MFS Methods, Proceedings 24th International Symposium on Rarefied Gas Dynamics 2004, America Institute of Physics, 762, 577 (2005). 
  135. L.Pareschi, S.Trazzi, Numerical solution of the Boltzmann equation by Time Relaxed Monte Carlo (TRMC) methods, International Journal of Numerical Methods in Fluids, 48, (2005), pp. 947-983. 
  136. S.Cordier, L.Pareschi, G.Toscani, On a kinetic model for a simple market economy, Journal of Statistical Physics, 120, (2005), pp. 253-277. 
  137. A.Klar, M.Herty, L.Pareschi, General kinetic models for vehicular traffic and Monte Carlo methods,Computational Methods in Applied Mathematics, 5, (2005), pp. 154-169. 
  138. L.Pareschi, Hybrid multiscale methods for kinetic and hyperbolic problems, ESAIM: PROCEEDINGS, Vol.15, T. Goudon, E. Sonnendrucker and D. Talay, Editors, pp.87-120, (2005) 
  139. L.Pareschi, G.Russo,  Implicit-Explicit Runge-Kutta methods and applications to hyperbolic systems with relaxation, J. Sci. Comput. 25 (2005), no. 1-2, 129--155. 
  140. L.Pareschi, G.Russo,  An introduction to the numerical analysis of the Boltzmann equation, Lecture Notes at M&KT 2004, Riv. Mat. Univ. Parma (7) 4** (2005), 145--250

    1996-2000
  141. L.Pareschi, Regularity results for the non cutoff Kac equation. Annali Università di Ferrara, Sez.VII -Sc. Mat.,Vol.XLII, (1996), pp.31-50. 
  142. E.Gabetta, L.Pareschi, Boundedness of moments and trend to equilibrium for the non cutoff Kac equation, Proceedings WASCOM 95, Rendiconti del Circolo Matematico di Palermo, Serie II, Suppl. 45, (1996), pp.285-298. 
  143. E.Gabetta, L.Pareschi, G.Toscani, Wild's sums and numerical approximation of nonlinear kinetic equations, Transport Theory and Statistical Physics, Vol.25, No.3-5, (1996), pp.515-531. 
  144. E.Gabetta, L.Pareschi, About the non cut-off Kac equation: Uniqueness and asymptotic behaviour, Communications on Applied Nonlinear Analisys, Vol.4 , No.1, (1997), pp.1-20.
  145. L.Pareschi, B.Perthame, A Fourier spectral method for homogeneous Boltzmann equations, Transport Theory and Statistical Physics, Vol.25, No.3-5, (1996), pp.369-383. 
  146. E.Gabetta, L.Pareschi, G.Toscani, Relaxation schemes for nonlinear kinetic equations, SIAM J. Numerical Analysis, Vol. 34, No. 6, pp. 2168-2194, (1997).
  147. L.Pareschi, Characteristic-based numerical schemes for hyperbolic systems with nonlinear relaxation, Proceedings 9th Int. Conf. on Waves and Stability in Continuous Media, Rendiconti Circolo Matematico di Palermo, Serie II, Suppl. 57, pp. 375-380, (1998). 
  148. S.Jin, L.Pareschi, G.Toscani, Diffusive relaxation schemes for multiscale discrete-velocity kinetic equations, SIAM J. Numerical Analysis, Vol. 35, No. 6, pp. 2405-2439, (1998). 
  149. G.Naldi, L.Pareschi, Numerical schemes for kinetic equations in diffusive regimes, Applied Math. Letters, Vol.11, No.2, pp. 29-35, (1998). 
  150. R.E.Caflisch, L.Pareschi, An implicit Monte Carlo method for rarefied gas dynamics I: The space homogeneous case, J. Computational Physics, 154, pp. 90-116, (1999). 
  151. G.Naldi, L.Pareschi, G.Toscani, Hyperbolic relaxation approximation to nonlinear parabolic problems, Proceedings 7th Int. Conf. on Hyperbolic Problems: Theory, Numerics, Application, ETH Zurich 1998, Internat. Series of Num. Math., Vol. 130, Birkhauser Verlag Basel, pp. 747-756, (1999).
  152. G.Naldi, L.Pareschi, Numerical schemes for hyperbolic systems of conservation laws with stiff diffusive relaxation, SIAM J. Numerical Analysis, Vol. 37, No. 4, pp. 1246-1270, (2000). 
  153. L.Pareschi, G.Russo, Numerical solution of the Boltzmann equation I: Spectrally accurate approximation of the collision operator, SIAM J. Numerical Analysis, Vol. 37, No. 4, pp. 1217-1245 (2000). 
  154. S.Jin, L. Pareschi, G. Toscani, Uniformly accurate diffusive relaxation schemes for multiscale transport equations, SIAM J. Numerical Analysis, Vol. 38, No. 13, pp. 913-936, (2000). 
  155. L.Pareschi, G.Russo, Asymptotic preserving Monte Carlo methods for the Boltzmann equation, Transp. Theo. Stat. Phys. 29, 3-5, pp.415-430, (2000). 
  156. E.Gabetta, L.Pareschi, M.Ronconi, Central schemes for hydrodynamical limits of discrete-velocity kinetic equations, Transp. Theo. Stat. Phys. 29, 3-5, pp.465-477, (2000). 
  157. L.Pareschi, G.Russo, On the stability of spectral methods for the homogeneous Boltzmann equation, Transp. Theo. Stat. Phys. 29, 3-5, pp.431-447, (2000) 
  158. L.Pareschi, G.Russo, Fast spectral methods for Boltzmann and Landau integral operators of gas and plasma kinetic theory, con G.Russo. Proceedings Analisi Numerica metodi e software matematico, Annali Università di Ferrara, Sez.VII - Sc. Mat., Vol.XLV, (2000), 329-341. 
  159. L.Pareschi, G.Russo, G.Toscani, Methode spectrale rapide pour l'equation de Fokker Planck Landau, C. R. Acad. Sci. Paris, t.330, Serie I, pp.517-522, (2000). 
  160. L.Pareschi, G.Russo, G.Toscani, Fast spectral methods for the Fokker-Planck-Landau collision operator, J. Comp. Phys. 165, pp. 216-236, (2000). 
  161. S.Jin, L.Pareschi, Discretization of the multiscale semiconductor Boltzmann equation by diffusive relaxation schemes, J. Comp. Phys. 161, pp.312-330, (2000).
  162. V.Comincioli, G.Naldi, L.Pareschi, G.Toscani, Numerical methods for multiscale hyperbolic systems and nonlinear parabolic equations, Proceedings Analisi Numerica metodi e software matematico, Annali Università di Ferrara, Sez.VII - Sc. Mat., Vol.XLV, (2000), 255-266. 
  163. L.Pareschi, G.Russo Implicit-Explicit Runge-Kutta schemes for stiff systems of differential equations, Recent Trends in Numerical Analysis, Edited by L.Brugnano and D.Trigiante, Vol. 3, 269-289, (2000).

    1991 - 1995
  164. E.Gabetta, L.Pareschi, Large-time behaviours of some fully discrete kinetic models in bounded domains. Le Matematiche, Vol.XLVI, Fasc. I (1991), pp.147-157.
  165. E.Gabetta, L.Pareschi, Stochastic aspects in nonlinear discrete kinetic theory, Proceedings of the IUTAM Symposium on Nonlinear Stochastic Mechanics, Turin, (1992), Springer-Verlag, Berlin, pp.237-245.
  166. E.Gabetta, L.Pareschi, Approximating the Broadwell model in a strip, Mathematical Models and Methods in Applied Sciences, Vol.2, No.1 (1992), pp.1-19.
  167. B.Bagni, D.Bollini, C.Leoni, C.Pallotti, L.Pareschi, P.Petazzoni, Computerized detection of clustered microcalcification: A modular approach using nonlinear filters, Physica Medica, Vol.IX, No.4, (1994).
  168. L.Pareschi, Kinetic approach to a diffusion problem, Proceedings of the National AIMETA symposium on Stocastic Mechanics, F. Casciati Ed., Taormina, (1994), pp.249-258.
  169. E.Gabetta, L.Pareschi, Nonlinear evolution of probability vectors of interest in discrete kinetic theory, Nonlinear Dynamics, Vol.5, No.3 (1994), pp.375-391.
  170. A.V.Bobylev, E.Gabetta, L.Pareschi, On stationary solutions to plane Broadwell model, Transport Theory and Statistical Physics, Vol.24, No.1-3, (1994), pp.289-305.
  171. A.V.Bobylev, E.Gabetta, L.Pareschi, On a boundary value problem for the plane Broadwell model. Exact solutions and numerical simulation, Mathematical Models and Methods in Applied Sciences, Vol.5, No.3, (1995), pp.253-266.
  172. E.Gabetta, L.Pareschi, The Maxwell gas and its Fourier transform towards a numerical approximation, Proceedings WASCOM 93, Series on Advances in Mathematics for Applied Sciences, Vol.23, (1995), pp.197-201.
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