Complex Computer Simulations, Numerical Artifacts, and Numerical Phenomena
Keywords:
Computer Simulations, Numerical Artifacts, Numerical Phenomena, Self-organizing ProcessesAbstract
The study of some typical complex computer simulations, presenting one or more Complexity features, as the: a) symmetry breaking, b) nonlinear properties, c) dissipative processes, d) high-logical depth, e) selforganizing processes, etc allows to point out some several numerical artifacts, namely the: (i) distortions, (ii) scattering, (iii) pseudo-convergence, (iv) instability, (v) mis-leading (false) symmetry-breaking simulations and others. The detailed analysis of these artifacts allowed clarifying the numerical mechanisms of some such artifacts, which can be named in following numerical phenomena, because their basic features can be exactly predicted.References
R. Skeel, SIAM News, 25(4), p. 11, 1992.
SIAM News, 29(8), pp. 1, 123, 13, 1996, http://www.siam.org/siamnews/general/ariane.htm
a) D. W. McClure "Computer Errors", in D. A. Iordache, D. W. McClure, Selected Works of Computer Aided Applied Sciences, vol. 2, Printech Publishing House, Bucharest, 2002, p. 535;
b) D. W. McClure "Computer errors", Basic notions (chapter 9), Applications (chapter 10), in the frame of textbook E. Bodegom, D. W. McClure et al (D. Iordache, Fl. Pop, C. RoÅŸu - editors) "Computational Physics Guide", Politehnica Presss, Bucharest, 2009.
Cl. S. Fermat "Diophantus' Arithmetica containing (48) observations by P. de Fermat", Toulouse, 1670.
A. Wiles "Modular elliptic curves and Fermat's last theorem", Annals of Mathematics, 142, 443-551(1995). http://dx.doi.org/10.2307/2118559
S. Singh "Fermat's Enigma: the Epic Quest to Solve the World's Greatest Mathematical Problem", Walker Publishing Company, New York, 1997.
R. Courant, K. Friedrichs, H. Lewy, Math. Ann., 100, 32(1928). http://dx.doi.org/10.1007/BF01448839
P.P. Delsanto, T. Whitcombe, H.H. Chaskelis, R.B. Mignogna, Wave Motion, 16, 65(1992). http://dx.doi.org/10.1016/0165-2125(92)90047-6
D. Iordache, P. Delsanto, M. Scalerandi "Pulse Distortions in the FD Simulations of Elastic Wave Propagation", Mathl. Comp. Modelling, 25(6) 31-43, 1997. http://dx.doi.org/10.1016/S0895-7177(97)00037-X
D. Iordache, M. Scalerandi, C. Rugină, V. Iordache "Study of the Stability and Convergence of FD Simulations of Ultrasound Propagation through Non-homogeneous Classical (Zener's) Attenuative Media", Romanian Reports on Physics, 50(10) 703-716, 1998; b) D. A. Iordache, M. Scalerandi, V. Iordache, Romanian Journal of Physics, 45(9-10) 685(2000).
J. C. Strikwerda "Finite Difference Schemes and Partial Difference Equations", Wadsworth- Brooks, 1989.
P. P. Delsanto, G. Kaniadakis, M. Scalerandi, D. Iordache, Comp. Math. Applic., 27(6) 51-61(1994). http://dx.doi.org/10.1016/0898-1221(94)90110-4
P.P. Delsanto, G. Kaniadakis, M. Scalerandi, D. Iordache, Mathl. Comp. Modelling (UK), 19(9) 1-8 (1994). http://dx.doi.org/10.1016/0895-7177(94)90035-3
a) P. P. Delsanto, D. Iordache, C. Iordache, E. Ruffino "Analysis of Stability and Convergence in FD Simulations of the 1-D Ultrasonic Wave Propagation", Mathl. Comp. Modelling, 25(6) 19-29, 1997; http://dx.doi.org/10.1016/S0895-7177(97)00036-8
b) D. Iordache, Şt. Puşcă, C. Toma "Numerical Analysis of some Typical FD Simulations of the Waves Propagation through Different Media", Lecture Notes on Computer Sciences, 3482, 614-620, 2005. http://dx.doi.org/10.1007/11424857_67
D. Iordache "Contributions to the Study of Numerical Phenomena intervening in the Computer Simulations of some Physical Processes", Credis Printing House, Bucharest, 2004.
A. V. Porubov, M. G. Velarde "Strain kinks in an elastic rod embedded in a viscoelastic medium", Wave Motion, 35, 189-204, 2002. http://dx.doi.org/10.1016/S0165-2125(01)00101-9
J. Cuevas, J. C. Eilbeck "Discrete soliton collisions in a waveguide array with saturable nonlinearity", Physics Letters A, 358(1) 15-20, 2006. http://dx.doi.org/10.1016/j.physleta.2006.04.095
D. Iordache, M. Scalerandi, C. Iordache "Mechanisms of Some Numerical Phenomena Specific to the Finite Differences Simulations of the Ultrasound Propagation", Proc. 25th Congress of the American-Romanian Science Academy, Cleveland (US), 2000, pp. 263-266.
a) J. C. Strikwerda "Finite Differences Schemes and Partial Difference Equations", Wadsworth-Brooks, 1989;
b) A. C. Vliegenthart, J. Eng. Math., 3, 81-94, 1969; http://dx.doi.org/10.1007/BF01535512
c) A. C. Vliegenthart, J. Eng. Math., 5, 137-155, 1971. http://dx.doi.org/10.1007/BF01535405
a) P. P. Delsanto, M. Scalerandi, V. Agostini, D. Iordache, Il Nuovo Cimento, B, 114, 1413- 26(1999);
b) D. Iordache, M. Scalerandi M., C. Rugină, V. Iordache, Romanian Reports on Physics, 50(10) 703-716 (1998).
D. Iordache, M. Scalerandi, V. Iordache, Romanian J. of Physics, 45(9-10) 685-704 (2000).
M. Gell-Mann, Europhysics News, 33(1) 17-20 (2002). http://dx.doi.org/10.1051/epn:2002105
D. Iordache, V. Iordache, Romanian Journal of Physics, 48(5-6) 697-704 (2003).
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