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Spatially varying discrete ordinates methods in $$XY$$-geometry. (English) Zbl 0969.65126
The author treats the classical neutron transport equation on the plane when the domain consists of two squares. The integral formulation of the neutron transport and its solution by the discrete ordinates method are used. The coupling of angular discretizations is considered and the well-posedness of the coupled problem is shown. The main result is that more angular directions are required close to the directions of spatial singularities.

##### MSC:
 65R20 Numerical methods for integral equations 45K05 Integro-partial differential equations 82D75 Nuclear reactor theory; neutron transport
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##### References:
 [1] DOI: 10.1051/m2an:1999160 · Zbl 0931.35010 · doi:10.1051/m2an:1999160 [2] Asadzadeh M., SIAM J. Math. Anal. 23 pp 543– (1986) [3] DOI: 10.1137/0726005 · Zbl 0668.65119 · doi:10.1137/0726005 [4] DOI: 10.1142/S021820259200020X · Zbl 0767.65095 · doi:10.1142/S021820259200020X [5] Bal G., Asymptotic Anal. 20 pp 213– (1999) [6] DOI: 10.1137/S0036141098338855 · Zbl 0937.35007 · doi:10.1137/S0036141098338855 [7] Bal G., Nucl. Sci. Engrg. 127 pp 169– (1997) [8] DOI: 10.1137/0721030 · Zbl 0565.41028 · doi:10.1137/0721030 [9] DOI: 10.1137/0720065 · Zbl 0538.65097 · doi:10.1137/0720065 [10] DOI: 10.1063/1.1666510 · doi:10.1063/1.1666510 [11] DOI: 10.1137/0710018 · Zbl 0257.35004 · doi:10.1137/0710018 [12] DOI: 10.1137/0511085 · Zbl 0458.45001 · doi:10.1137/0511085 [13] DOI: 10.1137/0720064 · Zbl 0533.65096 · doi:10.1137/0720064 [14] DOI: 10.1137/0717010 · Zbl 0454.65087 · doi:10.1137/0717010 [15] Vladimirov V. S., Atomic energy of Canada Ltd, Chalk River, Ont. Report AECL pp 1661– (1963)
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