UTK - M578 - Alexiades

Handouts   ...to come...

Relevant books
  • V Alexiades, AD Solomon
    Mathematical Modeling of Melting and Freezing Processes Hemisphere Publ. Co., 1993
  • MB Allen, I Herrera, and GF Pinder
      Numerical Modeling in Science and Engineering, Wiley, 1988
  • Victor Eijkhout
    Introduction to High Performance Scientific Computing , Lulu.com, 2010, $18 , free download.
  • Richard J Hanson, Tim Hopkins
      Numerical Computing with Modern Fortran, SIAM, 2013 (excellent, on OO methods)
  • Mark H Holmes
    Introduction to the Foundations of Applied Mathematics , Springer, 2009
  • Randall J LeVeque
      Numerical Methods for Conservation Laws, Birkhauser, 1990
  • Randall J LeVeque
    Finite Volume Methods for Hyperbolic Problems, Cambridge U Press, 2002, ISBN 0-521-00924-3
  • WP Petersen, P Arbenz
      Introduction to Parallel Computing, Oxford U Press, 2004 (paperback)
  • Press, Teukolsky, Vetterling and Flannery
    Numerical Recipes in Fortran (or C) , Cambridge U Press, 1992
  • A Tveito and R Winther
    Introduction to Partial Differential Equations - A Computational Approach, Springer, 2005

    Related books
  • MA Celia and WG Gray
      Numerical Methods for Differential Equations, Prentice Hall, 1992
  • KW Morton & DF Mayers
      Numerical Solution of PDEs, Cambridge U Press, 1994
  • Constantine Pozrikidis
      Numerical Computation in Science and Engineering, Oxford U Press, 1998 (I haven't seen it)
  • Mikhail Shashkov
      Conservative Finite-Difference Methods On General Grids, CRC Press, 1996
  • JW Thomas
      Numerical Partial Differential Equations: Finite Difference Methods, Springer-Verlag, 1995
  • David R Wille'
      Advanced Scientific Fortran, Wiley, 1995

    Some interesting relevant papers

  • RE Baker, et.al., 2008
    PDEs for self-organization in cellular and developmental biology , Nonlinearity 21(11): R251, 2008
    (nice survey paper of PDEs in action. Derivation as in class and many others...)
  • Bellomo, Dogbei, 2011
    On the Modeling of Traffic and Crowds, SIAM Review 53(3): 409-463
    (extensive survey of microscopic and macroscopic models, issues)
  • Kadioglu, 2011
    A Gas Dynamics Method Based on Spectral Deferred Corrections (SDC) Time Integration Technique and the Piecewise Parabolic Method (PPM)
      (nice FV paper, with good test problems)
  • Angela Ferrari, C-D Munz, B Weigand, 2011
    A high order sharp-interface method with local time stepping for compressible multiphase flows.,
      Commun. Comput. Phys., 9: 205-230, 2011
    (for shock tracking via combination of high resolution methods, uses FV, WENO, DG, local time-stepping, ...)
  • Alfio Quarteroni, editor, 1998
      Advanced numerical approximation of nonlinear hyperbolic equations
      Springer Lecture Notes Math. no.1697, 1998 QA3.L28 no.1697
  • E Tadmor, Approximate solutions of nonlinear conservation laws
  • C-W Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws
  • Chi-Wang Shu, 2009
    High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems ,
      SIAM Review 51 (1):82-126, 2009   (excellent review by the master)
  • Xiangxiong Zhang and Chi-Wang Shu, 2011
    Maximum-principle-satisfying and positivity-preserving high order schemes for conservation laws: Survey and new developments
      Proc. R. Soc. A, may 2011   (excellent)
  • Xiangxiong Zhang, Yinhua Xia and Chi-Wang Shu, 2012
    Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for Conservation Laws on Triangular Meshes
      Journal of Scientific Computing, 50(1): 29-62, 2012   (excellent, also for FV schemes)
  • Jennifer A Thackham, DL Sean McElwain and Ian W Turner, 2009
    Computational Approaches to Solving Equations Arising from Wound Healing ,
      Bulletin of Mathematical Biology, 71(1):211-246, 2009   (good overview/comparison of FV methods)
  • Bram van Leer, 2006  
    Upwind and High-Resolution Methods for Compressible Flow: From Donor Cell to Residual-Distribution Schemes ,

      Commun. Comput. Phys., 1: 192-206, 2006
    Parallel Distributed scientific computing
  • wikipedia articles on:   parallel computing ,   distributed computing ,   MPI ,   PVM

    MPI (Message Passing Interface) Library
  • Message Passing Interface, chap.8 of Designing and Building Parallel Programs, by Ian Foster
  • open-MPI implementation of MPI-2 and documentation
  • MPICH2 implementation of MPI-1 and MPI-2