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Domain decomposition for the \(SP_N\) solver MINOS. (English) Zbl 1273.82081
This paper studies the \(SP_N\) transport equations by using a domain decomposition method based on the Schwarz iterative algorithm. The authors establish the convergence of the method and they develop an asymptotic method to optimize the choice of the Robin matrices that appear in the interface conditions of Robin type. The numerical experiments are done by using the MINOS solver.

82D75 Nuclear reactor theory; neutron transport
82-08 Computational methods (statistical mechanics) (MSC2010)
82-04 Software, source code, etc. for problems pertaining to statistical mechanics
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
Full Text: DOI
[1] Baudron A.-M., Nucl Sci Engineer 155 (2) pp 250– (2007)
[2] Bussac J., Hermann collection enseignement des sciences, Paris (1985)
[3] Duderstadt J. J., Nuclear Reactor Analysis (1976)
[4] Japhet C., Future Generation Comp Syst 18 pp 18– (2001)
[5] Krein M. G., Amer Math Soc Translation (1962)
[6] Lions P.-L., Proceedings of the Third International Symposium on Domain Decomposition Methods for Partial Differential Equations pp 202– (1990)
[7] McLarren R. G., TTSP 39 (2) pp 73– (2011)
[8] Nataf F., Numerische Mathematik 75 (3) pp 357– (1997) · Zbl 0873.65108 · doi:10.1007/s002110050243
[9] Nataf F., C. R. Acad Sci Paris, Ser I 348 pp 1163– (2010) · Zbl 1206.35092 · doi:10.1016/j.crma.2010.10.007
[10] Nédélec J.-C., Numerische Mathematik 50 pp 57– (1986) · Zbl 0625.65107 · doi:10.1007/BF01389668
[11] Pomraning G. C., Ann. Nucl. Energy 20 (9) pp 623– (1993) · doi:10.1016/0306-4549(93)90030-S
[12] Quarteroni A., Domain Decomposition Methods for Partial Differential Equations (1999) · Zbl 0931.65118
[13] Raviart P.-A., Lecture Notes in Mathematics 606 pp 623– (1977)
[14] Schwarz H. A., Ges Math Abh pp 11– (1869)
[15] Van Criekingen S., Ann Nucl Energy 38 (1) pp 145– (2011) · doi:10.1016/j.anucene.2010.08.002
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