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].
@ 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); Landauer FP(86); Langer PT(99)jul [comments]; Rossi ht/06-conf [challenges and opportunities]; Winsberg 10 [philosophical point of view]; Barrett et al 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].
> Related topics: see Courant-Friedrichs-Lewy Condition; Finite-Element Method; Symplectic Integrators.

Related Topics > see computational methods in specific areas.


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