Abstract
The three-dimensional neutron diffusion equation has been solved using the boundary element method employing quadratic isoparametric boundary elements. Direct computation of the singular integral which arises in the present formulation can be avoided using standard mapping techniques, i.e., polar coordinates transformation is introduced after the quadrilateral element is subdivided into four triangles. The domain integral in the boundary integral equation corresponding to the neutron diffusion equation is converted into an equivalent boundary one when the integral is related to a uniform source or a slowing-down source. No boundary elements are required on the outer surface of an infinite reflector. The boundary elements for a symmetry plane can be also omitted when the method of images is adopted. Test calculations show that the present techniques provide accurate solutions for problems of irregular geometries.
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