UTK - M578 - Alexiades
R E F E R E N C E S
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