Computational Physics| Computational Physics |
In General > s.a. programming languages [e.g., Maple, Mathematica];
random and stochastic process.
* History: The original
idea of performing numerical experiments was Fermi's, and was first used
in the Fermi-Pasta-Ulam model.
* Status: 1994, Typically,
use × 106 data elements, but ×
108 are possible; The cost may be $1000/hr though.
* Method: Reduce pdes to finite
difference equations (can be done in different ways); Use combinatorial methods.
* Remark: It is useful to practice
with wave equations on a PC and to do related plots.
@ Intros, books: Koonin 85 [BASIC];
Hogg & Huberman PRP(87);
DeVries 94 [FORTRAN],
AJP(96)apr [RL];
Fosdick et al 96;
Weissert 97 [history];
Wong 97 [methods];
Vesely 01;
Steeb et al 04 [C++ and Java];
Giordano & Nakanishi 05;
Yevick 05;
Gibbs 06;
Pang 06;
Landau et al 07;
Thijssen 07;
Landau AJP(08)apr [RL]
and issue AJP(08)apr;
Hoover a0812-Ens [personal view];
Hartmann 09 [practical guide];
Gonnet & Scholl 09
[r PT(10)aug];
Klein & Godunov 10;
Langtangen 12 [Python];
Franklin 13;
Barone et al 13 [in C];
Anagnostopoulos 14 [FORTRAN];
Hutchinson 15 [II, student guide];
Shen 15 [Matlab];
Stewart 17 [Python];
Širca & Horvat 18 [methods].
@ Undergraduate curriculum: Spencer AJP(05)feb [lab sequence];
Chabay & Sherwood AJP(08)apr [in calculus-based physics];
Serbanescu et al AJP(11)sep;
Caballero & Pollock AJP(14)mar [intermediate-level classical mechanics].
@ Physics and computation:
Richtmyer & Metropolis PT(49)oct;
Feynman IJTP(82);
Toffoli IJTP(82);
Geroch & Hartle FP(86)-a1806;
Landauer FP(86);
Langer PT(99)jul [comments];
Rossi ht/06-conf [challenges and opportunities];
Winsberg 10 [philosophical point of view];
Barrett et al npjQI(19)-a1702 [general physical theories].
@ Visualization: Dardashti et al a1604 [Bayesian analysis of scientific inference by simulation].
@ Theoretical physics and PCs: Schmid et al 90;
Stauffer & Stanley 95.
@ Visualization: Earnshaw & Wiseman 92;
PW(93)sep, p48;
Hammond PW(96);
Hege & Polthier 98;
Sanders et al NJP(09) [focus];
Farr JVWR-a0905 [self-gravitating systems, using virtual worlds];
Goodman a0911-proc [status];
Gazis et al PASP(10)-a1008 [large, high-dimensional data sets].
@ Supercomputers: Kaufmann & Smarr 93 [I].
Special Techniques
> s.a. Derivatives [and finite differences]; monte carlo
method; Simulated Annealing [minimization / optimization procedure].
* Mesh enhancement: The process
in which an existing mesh is modified to better meet the requirements of the system.
@ Texts: MacKeown 97 [stochastic];
Mitzenmacher & Upfal 05 [probabilistic].
@ General references:
Knuth 69-73;
Dahlquist & Bjoerck 74;
MacKeown & Newman 87;
Acton 90;
Heermann 90;
MacDonald 94 [REDUCE];
García 00 [Matlab];
Gould et al 06;
Enns & McGuire 07 [recipes, in Maple];
Press et al 07;
Báez-López 09 [Matlab];
Kharab & Guenther 11 [Matlab].
@ Mesh adjustment:
Pretorius & Lehner JCP(04) [adaptive];
Choi et al JCP(04) [refinement boundaries];
Anderson et al JCP(05) [unstructured simplices];
Baker & van Meter PRD(05)gq [in general relativity, reflections from interfaces];
Pretorius & Choptuik JCP(06)gq/05 [adaptive, coupled elliptic-hyperbolic systems];
> s.a. specific areas [adaptive mesh].
@ Related topics: Fulling qp/99,
qp/99 [large integers and remainders];
Hansen et al 05 [mesh enhancement];
Acebrón & Spigler JCP(05) [quasi-random numbers for stochastic systems];
Billo 07 [Excel];
Mazars PRP(11) [correct handling of long-range interactions];
Tripolt et al CPC(19)-a1801 [analytic continuation of Euclidean data];
Tran et al PRL(20)-a1912 [destructive error interference].
> Related topics:
see Courant-Friedrichs-Lewy Condition;
Finite-Element Method; Symplectic Integrators.
Related Topics > see computation [including tensor manipulation]; computational methods in specific areas.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 21 apr 2021