A hierarchical domain decomposition boundary element method with a higher order polynomial expansion for solving 2-D multiregion neutron diffusion equations

A hierarchical domain decomposition boundary element method (HDD-BEM) for solving the multiregion neutron diffusion equation (NDE) has been developed to reduce computation time. The boundary integral equations derived from NDEs defined in homogeneous subregions are discretized with higher order boundary elements. The neutron flux and the neutron currents on boundary elements are expanded by quadratic or cubic polynomials. This expansion allows a large decrease in the number of unknown variables compared with the conventional HDD-BEM with constant boundary elements and reduces the computation time greatly. To obtain high accuracy with a small number of unknowns it is important to assign suitable nodal points on the non-conforming boundary elements. Guidelines for the assignment of nodal points is presented through numerical analysis. The HDD-BEM with higher order boundary elements calculates at least 5 times faster than the conventional HDD-BEM with constant boundary elements and 30 times faster than the finite difference method. The improvements in computation time will enable an extension of the scope of application to a wider variety of problems in reactor analysis.