Recent preprints

  • A. Wan, A. Bihlo and J.-C. Nave, 2015. The multiplier method to construct conservative finite difference schemes for ordinary and partial differential equations. Accepted in SINUM, arXiv:1411.7720, 27 pp.

Peer-reviewed papers

  • A. Bihlo, R.D. Haynes and E.J. Walsh, 2015. Stochastic domain decomposition for time dependent adaptive mesh generation. J. Math. Study 48 (2), 106-124arXiv:1504.00084.
  • A. Bihlo, E.M. Dos Santos Cardoso-Bihlo and R.O. Popovych, 2015. Algebraic method for finding equivalence groups. J. Phys.: Conf. Ser. 621, 012001 (17 pp), arXiv:1503.06487.
  • A. Bihlo, X. Coiteux-Roy and P. Winternitz, 2015. The Korteweg-de Vries equation and its symmetry-preserving discretization. J. Phys. A 48, 055201 (25 pp), arXiv:1409.4340.
  • A. Bihlo and R.D. Haynes, 2014. Parallel stochastic methods for PDE based grid generation. Comput. Math. Appl. 68 (8), 804-820, arXiv:1310.3435.
  • A. Bihlo and R.D. Haynes, 2014. A stochastic domain decomposition method for time dependent mesh generation. Accepted in LNCSEarxiv:1402.0266, 8 pp.
  • A. Bihlo and J.-C. Nave, 2014. Convecting reference frames and invariant numerical models.  J. Comput. Phys. 271, 656–663, arXiv:1301.5955.
  • A. Bihlo, E.M. Dos Santos Cardoso–Bihlo and R.O. Popovych, 2014. Invariant parameterization and turbulence modeling on the beta-plane. Physica D 269, 48-62, arXiv:1112.1917.
  • S. Szatmari and A. Bihlo, 2014. Symmetry analysis of a system of modified shallow-water equations. Commun. Nonlinear Sci. Numer. Simul. 19 (3), 530-537, arXiv:1212.5823.
  • A. Bihlo and J.-C. Nave, 2013. Invariant discretization schemes using evolution-projection techniques. SIGMA 9, 052, 23 pp, arXiv:1209.5028.
  • A. Bihlo and G. Bluman, 2013. Conservative parameterization schemes. J. Math. Phys. 54, 083101 (24 pp), arXiv:1209.4279.
  • A. Bihlo, 2013. Invariant meshless discretization schemes. J. Phys. A: Math. Theor. 46 (6), 062001 (12 pp), arXiv:1210.2762.
  • A. Bihlo, E.M. Dos Santos Cardoso–Bihlo and R.O. Popovych, 2012. Complete group classification of a class of nonlinear wave equations. J. Math. Phys. 53 (12), 123515, 32 pp, arXiv:1106.4801.
  • A. Bihlo and R.O. Popovych, 2012. Invariant discretization schemes for the shallow-water equations. SIAM J. Sci. Comput. 34 (6), B810-B839, arXiv:1201.0498.
  • R.O. Popovych and A. Bihlo, 2012. Symmetry preserving parameterization schemes.  J. Math. Phys. 53 (7), 073102, 36 pp, arXiv:1010.3010.
  • A. Bihlo and R.O. Popovych, 2012. Lie reduction and exact solutions of the vorticity equation on the rotating sphere. Phys. Lett. A 376 (14), 1179–1184, arXiv:1112.3019.
  • A. Bihlo and R.O. Popovych, 2011. Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem.  J. Math. Phys. 52 (3), 033103, 24 pp, arXiv:1010.1542.
  • E.M. Dos Santos Cardoso–Bihlo, A. Bihlo and R.O. Popovych, 2011. Enhanced preliminary group classification of a class of generalized diffusion equations.  Commun. Nonlinear Sci. Numer. Simul. 16 (9), 3622–3638, arXiv:1012.0297.
  • A. Bihlo and J. Staufer, 2011. Minimal atmospheric finite-mode models preserving symmetry and generalized Hamiltonian structures, Physica D 240 (7), 599–606, arXiv:0909.1957.
  • A. Bihlo and R.O. Popovych, 2011. Point symmetry group of the barotropic vorticity equation. In Proceedings of the 5th workshop “Group Analysis of Differential Equations & Integrable Systems”, 15–27, arXiv:1009.1523.
  • A. Bihlo and R.O. Popovych, 2009. Lie symmetries and exact solutions of the barotropic vorticity equation. J. Math. Phys. 50 (12), 123102, 12 pp, arXiv:0902.4099.
  • A. Bihlo and R.O. Popovych, 2009. Symmetry justification of Lorenz’ maximum simplification. Nonlin. Dyn. 61 (1), 101–107, arXiv:0805.4061.
  • A. Bihlo and R.O. Popovych, 2009. Symmetry analysis of barotropic potential vorticity equation. Commun. Theor. Phys. 52 (4), 697–700, arXiv:0811.3008.
  • A. Bihlo, 2009. Symmetries in atmospheric sciences. In Proceedings of the 4th workshop “Group Analysis of Differential Equations & Integrable Systems”, 6–12, arXiv:0902.4112.
  • A. Bihlo, 2008. Rayleigh-Bénard Convection as a Nambu–metriplectic problem. J. Phys. A: Math. Theor. 41 (29), 292001 (6 pp), arXiv:0803.4458.

Book chapters

  • A. Bihlo., E.M. Dos Santos Cardoso-Bihlo and R.O. Popovych, 2015. Invariant and conservative parameterization schemes, in volume 2 of Parameterization of Atmospheric Convection, (R. S. Plant and J. I. Yano, Eds.), Imperial College Press, 483-524.

Ph.D. thesis

Diploma thesis

  • A. Bihlo, 2007. Solving the vorticity equation with Lie groups. In Wiener Meteorologische Schriften, Vol. 6, facultas.wuv, Wien. (Supervisor: Professor Dr. Michael Hantel)