Exact code scaling
DOI:
https://doi.org/10.1260/175095408786927453Abstract
A new possibility of code scaling is introduced. We show that there are notextreme volumes over which some equations of mathematical physicshave the same eigenvalues and there exists a simple transplantation rule toget the eigenfunction of the first volume once that of the second volume isknown. We present two techniques. In the first, the domain of thenumerical method is a discretized volume. Congruent elements are gluedtogether to get the domain over which the solution is sought. We associatea group and a graph to that volume. When the group is a symmetry of theboundary value problem, one can specify the structure of the solution, andpredict the existance of other equispectral volumes. The second techniqueuses a complex mapping to transplant the solution from volume V1 tovolume V2 and a correction function. Equation for the correction function isgiven. A simple example demonstrates the feasibility of the suggestedmethod. We show that a measurement associated with the fundamentaleigenfunction of a linear operator on a volume is sufficient to predict resultsof a measurement on another volume by a computer program.
References
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Gupta, K. K. Development of a finite element aeroelastic analysis capability, Journal of Aircraft, 33 no.5, 995-1002 (1996). https://doi.org/10.2514/3.47046
Vlahopoulos N., Garza-rios L. O., Mollo C. : Numerical implementation, validation, and marine applications of an Energy Finite Element formulation, Journal of ship research, 43, no3, pp. 143-156 (1999).
H. K. Cho, B. J. Yun, C.-H. Song, G. C. Park: Experimental validation of the modified linear scaling methodology for scaling ECC bypass phenomena in DVI downcomer, Nucl. Eng, Design, 235, 2310-2322 (2005). https://doi.org/10.1016/j.nucengdes.2005.04.005
A. F. Mills: Heat Transfer, Prentice Hall, New Jersey, (1999).
R. P. Martin, L. D. O'Dell: AREVA's realistic large break LOCA analysis methodology, Nucl. Eng. and Design, 235, 1713-1725 (2005). https://doi.org/10.1016/j.nucengdes.2005.02.004
E. Studer, J. P. Magnaud, F. Dabbene, I. Tkatchenko: International standard problem on containment thermal-hydraulics ISP47 Step 1—Results from the MISTRA exercise, Nucl. Eng. and Design, 237, 536-551 (2007). https://doi.org/10.1016/j.nucengdes.2006.08.008
C. N. Madrid, F. Alhama: Discrimination and necessary extension of classical dimensional analysis theory, Heat and Mass Transfer, 33, 287-294 (2006). https://doi.org/10.1016/j.icheatmasstransfer.2005.11.002
A. N. Nahavandi, F. S. Castellana, E. N. Moradkhanian: Scaling Laws for Modeling Nuclear Reactor Systems, Nucl. Sci. Eng. 72, 75-83 (1979). https://doi.org/10.13182/nse79-a19310
M. Ishii, I. Kataoka: Similarity Analysis and Scaling Criteria for LWR's Under Single-Phase and Two-Phase Natural Circulation, NUREG/CR-3267, (1983). https://doi.org/10.2172/6312011
W. Miller: Symmetries and Separation of Variables, Addison-Wesley, Reading, 1977, Chapter 3.1
W. Hereman: Symbolic Software for Lie Symmetry Analysis, in: N. H. Ibragimov (Ed.): CRC Handbook of Lie Group Analysis of Differential Equations, CRC Press, Boca Raton, Florida, (1995).
D. Sattinger: Group Theoretic Methods in Bifurcation Theory, Springer, Berlin, 1979.
M. Makai, Y. Orechwa, “Model Calculations in reconstructions of Measured Fields”, Central European Journal of Physics, 1, 118-131, (2003). https://doi.org/10.2478/bf02475556
Tobin A. Driscoll, Lloyd N. Trefethen: Schwarz-Christoffel Mapping, Cambridge University Press, 2002
C. Gordon and D. Webb: You Can't Hear the Shape of a Drum, American Scientist, 84, 46-55, (1996)
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