Model calculations in reconstructions of measured fields

• Authors: Mihály Makai , Yuri Orechwa
• Languages of publication: EN

Abstracts

EN

The state of technological systems, such as reactions in a confined volume, are usually monitored with sensors within as well as outside the volume. To achieve the level of precision required by regulators, these data often need to be supplemented with the solution to a mathematical model of the process. The present work addresses an observed, and until now unexplained, convergence problem in the iterative solution in the application of the finite element method to boundary value problems. We use point group theory to clarify the cause of the non-convergence, and give rule problems. We use the appropriate and consistent orders of approximation on the boundary and within the volume so as to avoid non-convergence.

Keywords

EN

boundary value problem; reactor physics; point group theory; convergence problem; 28.41.Ak; 29.85.+c

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2003
• Volume: 1
• Issue: 1
• Pages: 118-131

Dates

published

1 - 3 - 2003

online

1 - 3 - 2003

Contributors

author

Mihály Makai

• KFKI Atomic Energy Research Institute, H-1525, Budapest 114, POB 49, Hungary

author

Yuri Orechwa

• US Nuclear Regulatory Commission, Washington D.C., USA

References

• [1] C. B. Carrico, E. E. Lewis, G. Palmiotti, (1994): Matrix Rank in Variational Nodal Approximations, Trans. Am. Nucl. Soc. 70, 162
• [2] L. M. Falicov (1966): Group Theory and Its Physical Applications, The University of Chicago Press, Chicago, IL
• [3] G. J. Habetler and M. A. Martino, (1961): Existence Theorems and Spectral Theory for the Multigroup Diffusion Model, Proc. of the Eleventh Symposium in Applied Mathematics of the American Mathematical Society, vol. XI., Nuclear Reactor Theory, American Mathematical Society, Providence, R. I.
• [4] E. E. Lewis, C. B. Carrico and G. Palmiotti, (1996): Variational Nodal Formulation for the Spherical Harmonics Equations, Nucl. Sci. Eng. 122, 194 (1996)
• [5] Makai, (1996): Group Theory Applied to Boundary Value Problems, Report ANL-FRA-1996-5, Argonne, IL, 1996.
• [6] M. Makai, E. Temesvári and Y. Orechwa: Field Reconstruction from Measured Values Using Symmetries, Int. Conf. Mathematics and Computation, September 2001, Salt Lake City, Utah, 2001
• [7] M. Makai and Y. Orechwa: Symmetries of boundary value problems in mathematical physics, J. Math. Phys, 40, 5247 (1999). http://dx.doi.org/10.1063/1.533028[Crossref]
• [8] G. I. Marchuk and V. I. Lebedev, (1971): Numerical Methods in Neutron Transport Theory, Atomizdat, Moscow, in Russian
• [9] G. Palmiotti et al., (1995): VARIANT, Report ANL-95/40, Argonne, IL
• [10] A. Ralston, (1965): A First Course in Numerical Analysis, McGraw-Hill, New York, NY
• [11] M. Schönert et al.: GAP- Groups Algorithms and Programming, Lelhrstuhl für Mathematik, Rheinish Westfälische Technische Hochschule, Aechen, Germany, (1995).
• [12] F. Shipp and W. R. Wade, (1995): Transforms on Normed Spaces, Janus Pannoius University, Pécs (Hungary)
• [13] G. Strang and G. J. Fix (1973): An Analysis of the Finite Element Method (Prentice Hall, Englewood Cliffs, N. J.
• [14] J. L. Walsh (1923): Am. J. Math., 55, 5. http://dx.doi.org/10.2307/2387224[Crossref]

Identifiers

DOI

10.2478/BF02475556