Robert Brownlee's homepage

• Current status

• Research interests

• Publications

• LimB: A 2D nonequilibrium entropy limiter lattice Boltzmann code

• Conferences and meetings

• Talks

• Academic background

• Contact

• Current status
  Former Postdoctoral Research Associate at the Department of Mathematics, University of Leicester. I now do something quite different.
• Research interests
  Approximation theory; multivariate interpolation and approximation; radial basis functions (RBFs); (moving) least squares approximation (MLS); meshless methods; smoothed particle hydrodynamics (SPH). Lattice Boltzmann methods (LBM).
• Publications
  A complete list of Robert Brownlee's publications. This list was compiled on 8^th December, 2011.
  • In preparation/submitted
    1. None
  • Journal articles
    1. R. A. Brownlee, J. Levesley, D. Packwood and A. N. Gorban, Add-ons for Lattice Boltzmann Methods: Regularization, Filtering and Limiters. In Novel Trends in Lattice-Boltzmann Methods - Reactive Flow, Physicochemical Transport and Fluid-Structure Interaction, Progress in Computational Physics, Vol. 3, Bentham Science Publishers, 2012.
    2. R. A. Brownlee, A. N. Gorban and J. Levesley, Nonequilibrium entropy limiters in lattice Boltzmann methods. Physica A, 387(2–3):385–406, 2008 (arXiv:0704.0043);
    3. R. A. Brownlee, A. N. Gorban and J. Levesley, Stable simulation of fluid flows with high-Reynolds number using Ehrenfests' steps. Numer. Algorithms, 45(1–4):389–408, 2007 (arXiv:0705.4371);
    4. R. A. Brownlee, E. H. Georgoulis and J. Levesley, Extending the range of error estimates for radial approximation in Euclidean space and on spheres. SIAM J. Math. Anal., 39(2):554–564, 2007 (arXiv:0705.4368);
    5. R. A. Brownlee, A. N. Gorban and J. Levesley, Stability and stabilisation of the lattice Boltzmann method. Phys. Rev. E, 75(3):036711, 2007 (arXiv:cond-mat/0611444);
    6. R. A. Brownlee, A. N. Gorban and J. Levesley, Stabilisation of the lattice Boltzmann method using the Ehrenfests' coarse-graining idea. Phys. Rev. E, 74(3):037703, 2006 (arXiv:cond-mat/0605359);
    7. R. A. Brownlee, Error estimates for interpolation of rough data using the scattered shifts of a radial basis function. Numer. Algorithms, 39(1–3):57–68, 2005 (arXiv:0705.4300);
    8. R. Brownlee, and W. Light, Approximation orders for interpolation by surface splines to rough functions. IMA J. Numer. Anal., 24(2):179–192, 2004 (arXiv:0705.4281).
  • Conference proceedings
    1. R. A. Brownlee, A. N. Gorban and J. Levesley, The Ehrenfests' coarse-graining as a paradigm for stabilising the lattice-Boltzmann method. In Proc. Russian National Seminar "Modeling of Nonequilibrium Systems", Krasnoyarsk, October 13-15 2006, pages 3-13, Krasnoyarsk State Technical University Press, 2006;
    2. R. Brownlee, J. Levesley, P. Houston, and S. Rosswog. Enhancing SPH using moving least-squares and radial basis functions. In Algorithms for Approximation: Proceedings of the 5th International Conference, Chester UK, July 18-22 2005, pages 103-112, Springer, 2007 (arXiv:0705.4374).
  • PhD thesis & technical reports
    1. R. A. Brownlee, Error estimates for the interpolation of rough and smooth functions using radial basis functions. PhD thesis, 2004;
    2. R. Brownlee, and J. Levesley, A scale of improved error estimates for radial approximation in Euclidean space and on spheres. University of Leicester Mathematics & Computer Science Technical Report, 2004/13, 2004.
  • Shelved/abandoned
    1. R. A. Brownlee, J. Levesley and X. Sun Best approximation in rough native spaces by shifts of a smooth radial basis function. Shelved, 2009.
    2. R. A. Brownlee, A. N. Gorban and J. Levesley, Minimal stable kinetic models for non-isothermal compressible fluid dynamics. Abandoned, 2006;
    3. R. A. Brownlee, A. N. Gorban and J. Levesley, Stable multispeed lattice Boltzmann methods. Submitted to Phys. Rev. Lett., 2006 (arXiv:cond-mat/0611616).
• Conferences and meetings
  
  • Radial Basis Functions and Beyond: from Meshless Methods to Kernel Learning (Göttingen, Germany), 25^th–26^th November 2005;
  • Algorithms for Approximation V (A4A5) (Chester, UK), 18^th–22^nd July 2005;
  • ECCOMAS Thematic Conference on Meshless Methods (Lisbon, Portugal), 11^th–14^th July 2005;
  • Finite Element Methods and Applications (one day meeting) (Leicester, UK), 30^th March 2005;
  • Radial Basis Function Methods and Applications (one day meeting) (Leicester, UK), 23^rd February 2005;
  • Advances in Dynamical Simulation (one day meeting) (Leicester, UK), 25^th November 2004;
  • LMS-EPSRC XI^th Summer School in Numerical Analysis (Week 2) (Durham, UK), 5^th–9^th July 2004;
  • Workshop on Computation and Numerical Analysis for Multiscale and Multiphysics Modelling (Warwick, UK), 15^th–17^th April 2004;
  • Will Light Conference on Approximation Theory and Applied Analysis (Leicester, UK), 18^th–19^th December 2003;
  • Multivariate Approximation: Theory and Application (MATA 2003) (Cancún, Mexico), 24^th–29^th April 2003;
  • LMS-EPSRC X^thSummer School in Numerical Analysis (Durham, UK), 8^th–19^th July 2002.
• Talks
  
  • Algorithms for Approximation V (A4A5), 18^th July 2005. "Enhancing SPH using moving least-squares and radial basis functions";
  • Will Light Conference on Approximation Theory and Applied Analysis, 19^th December 2003. "The not-so-great-escape";
  • University of Leicester Applied Mathematics Seminar, 27^th November 2003. "Sophisticated RBF error estimates";
  • Multivariate Approximation: Theory and Application (MATA 2003), 24^th April 2003. "Error estimates for interpolation by surface splines to rough functions";
  • University of Leicester Applied Mathematics Seminar, 21^st March 2002. "Error estimates for interpolation by translates of a basic function".
• Academic background
  

  In 2000 I obtained a first class honours degree in mathematics at the University of Leicester. My final year project for my degree was titled "Solving the Interpolation Equations for Radial Basis Functions using the Babuska-Brezzi Approach". Here, I explored an alternative approach to the interpolation problem using radial basis functions. For this project I was supervised by Will Light.

  Upon completion of my degree, I began studying for a PhD in applicable mathematics again in the Department of Mathematics at Leicester funded by way of an award from The Engineering and Physical Science Research Council (EPSRC). My supervisor was Will Light from September 2000 until 8^th December 2002 and Jeremy Levesley from December 2002 onwards. My PhD thesis Error Estimates for Interpolation of Rough and Smooth Functions using Radial Basis Functions was submitted on February 6^th 2004 and successfully defended on April 28^th 2004. My external examiner for my thesis was Armin Iske.
  

  After my PhD, I became a Research Associate working on the development of meshless methods for the modelling of compressible fluid flow. The primary investigators were Jeremy Levesley (and later Alexander Gorban) with co-investigators Paul Houston and Stephan Rosswog.
  

  I now do something quite different.

  My Erdős number is less than or equal to 4, as too is my Erdős number of the second kind.
  
  
• Contact
  rob at symbol rbrownlee dot org dot uk