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Remedy for round-off error accumulation observed in a neutron diffusion calculation using the multiple reciprocity boundary element method

Authors
Journal
Engineering Analysis with Boundary Elements
0955-7997
Publisher
Elsevier
Publication Date
Volume
10
Issue
4
Identifiers
DOI: 10.1016/0955-7997(92)90149-2

Abstract

Abstract A round-off error accumulation is observed in a multiple reciprocity computation for a fission neutron source iteration problem when a certain convergence condition is not satisfied. The present paper presents a reformulation of the multiple reciprocity method to remove the numerical problem. The neutron diffusion equation (NDE) is arranged using Wielandt's spectral shift technique in such a way that the convergence condition is always satisfied through source iterations. The boundary integral equation in this case requires the fundamental solution to the standard Helmholtz equation, while the fundamental solution corresponding to the correspoding to the original NDE was one to the modified Helmholtz equation. Except for this, the new multiple reciprocity formulation is identical to the original one for the fission source iteration problems. Some test calculation results indicate that a rapid and stable convergence can be realized using the new method and no round-off error accumulation is observed any more.

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