BOUNDARY ELEMENT FORMULATION OF FISSION NEUTRON SOURCE PROBLEMS USING ONLY BOUNDARY INTEGRALS

The present paper describes a general way of transforming domain integrals into equivalent boundary ones in boundary element formulations of fission neutron source problems. The critical eigenvalue, which is defined originally by the ratio of two different domain integrals has been transformed into a ratio involving only boundary integrals. The domain integral of fission source multiplied by the fundamental solution is converted into an equivalent boundary integral by the use of a particular solution technique, in which the source distribution is expanded into a Fourier series. The coefficients required in the expansion are determined using a boundary-only integral which has a recurrence form and is updated throughout the neutron source iteration scheme.