Recent papers and preprints

[by year]
[Multiscale hyperbolic problems]
[Spectral methods for kinetic equations]
[Monte Carlo methods for RGD]
[Stiff differential systems]
[Relaxation approximations]
[Stress intensity factor]
[Lecture notes]

Multiscale hyperbolic problems

  1. 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).
  2. G.Naldi, L.Pareschi, Numerical schemes for kinetic equations in diffusive regimes, Applied Math. Letters, Vol.11, No.2, pp. 29-35, (1998).
  3. 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).
  4. S.Jin, L.Pareschi, Discretization of the multiscale semiconductor Boltzmann equation by diffusive relaxation schemes, J. Comp. Phys. 161, pp.312-330, (2000).
  5. 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.
  6. 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).
  7. S.Jin, L.Pareschi, Asymptotic preserving (AP) schemes for multiscale kinetic equations: a unified approach, International Series of Numerical Mathematics, Birkhauser, 141, (2001), 573-582 (Proceedings Hyperbolic problems: Theory, Numerics, Applications, Magdeburg).

    Spectral methods for kinetic equations
  8. 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).
  9. L.Pareschi, G.Russo, On the stability of spectral methods for the homogeneous Boltzmann equation, Transp. Theo. Stat. Phys. 29, 3-5, 431-447, (2000).
  10. L.Pareschi, G.Russo, Fast spectral methods for Boltzmann and Landau integral operators of gas and plasma kinetic theory. Proceedings Analisi Numerica metodi e software matematico, Annali Università di Ferrara, Sez.VII - Sc. Mat., Vol.XLV, (2000), 329-341.
  11. 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).
  12. L.Pareschi, G.Russo, G.Toscani, Fast spectral methods for the Fokker-Planck-Landau collision operator, J. Comp. Phys. 165, pp. 216-236, (2000).
  13. 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.
  14. 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). (Warning: uncompressed file is 40M!)
  15. 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 (submitted)
  16. L.Pareschi, G.Toscani, C.Villani,Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit, Numerische Mathematik, (2002) (to appear)
  17. L.Pareschi, On the fast evaluation of kinetic equations for driven granular media. Proceedings ENUMATH 2001.

    Monte Carlo methods for RGD
  18. 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).
  19. L.Pareschi, G.Russo, Asymptotic preserving Monte Carlo methods for the Boltzmann equation, Transp. Theo. Stat. Phys. 29, 3-5, pp.415-430, (2000).
  20. L.Pareschi, G.Russo, Time Relaxed Monte Carlo methods for the Boltzmann equation, SIAM J. Sci. Comput. 23 (2001), no 4, 1253--1273
  21. 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).
  22. R.E.Caflisch, L.Pareschi, Towards and hybrid Monte Carlo method for rarefied gasdynamics, IMA Volumes in Mathematics and its Applications (Springer-Verlag) edited by C.D.Levermore, A.Arnold, N.Ben Abdallah, K.T.-R.McLaughlin, P.Degond, I.Gamba, R.Glassey, P.Roe, L.Borucki and C.Ringhofer, Minneapolis (2000) (to appear)

    Stiff differential systems
  23. E.Gabetta, L.Pareschi, G.Toscani, Relaxation schemes for nonlinear kinetic equations, SIAM J. Numerical Analysis, Vol. 34, No. 6, pp. 2168-2194, (1997).
  24. 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).
  25. 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).
  26. 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).
  27. L.Pareschi, Central differencing based numerical schemes for hyperbolic conservation laws with relaxation terms, SIAM J. Numer. Anal. 39 (2001), no. 4, 1395--1417
  28. L.Pareschi, G.Russo, Asimptotically SSP schemes for hyperbolic systems with stiff relaxation, Proceedings Hyperbolic problems: Theory,Numerics, Applications, Caltech, Pasadena 2002.

    Relaxation approximations
  29. 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).
  30. G.Naldi, L.Pareschi, G.Toscani, Convergence of kinetic approximation to nonlinear diffusion problems, Proceedings Conference on Godunov Methods: Theory and Applications, Oxford, Edited by E.F.Toro, Kluwer Academic-Plenum Publishers, 2000 (to appear)
  31. 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.
  32. M.K.Banda, A.Klar, L.Pareschi, M.Seaid, Lattice-Boltzmann type relaxation systems and high order relaxation schemes for the incompressible Navier-Stokes equations, Preprint (2001).
  33. A.Klar, L.Pareschi, M.Seaid, Uniformly accurate schemes for relaxation approximations to fluid dynamic equations, Applied Mathematics Letters (to appear).
  34. M.K.Banda, A.Klar, L.Pareschi, M.Seaid, Compressible and Incompressible Limits for Hyperbolic Systems with Relaxation, Journal of Computational and Applied Mathematics, (to appear).
  35. G.Naldi, L.Pareschi, G.Toscani, Relaxation schemes for PDEs and applications to fourth order diffusion equations, Surveys in Mathematics Applied to Industry, Springer (to appear).
  36. J.A.Carrillo, J.M.Mantas e J.Ortega, L.Pareschi,Parallel Integration of Hydrodinamical Approximations for the Boltzmann Equation on a Cluster of Computers. Proceedings CMMSE 2002: International Conference on Computational and Mathematical Methods in Science and Engineering. (to appear on Journal of Computational and Applied Mathematics)

    Stress Intensity Factor
  37. 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.
  38. O.Ascenzi, L.Pareschi, F.Segala, Convergence of a quadrature formula for the approximation of stress intensity factor for planar cracks, preprint (2002)

    Lecture Notes
  39. L.Pareschi, G.Russo, An introduction to Monte Carlo methods for the Boltzmann equation. ESAIM: Proceedings, Vol.10, pp.35-75 (2001)
  40. L.Pareschi, Computational methods and fast algorithms for Boltzmann equations. Chapter 7, Lecture Notes on the discretization of the Boltzmann equation, ed. N.Bellomo, World Scientific, 46 pagg. (to appear).