Wavelet-based algorithms for solving neutron diffusion equations

This work develops efficient algorithms for numerically solving the neutron diffusion equation by a wavelet Galerkin method (WGM). One of the main pro blems encountered in solving neutron diffusion equation using WGM is the tr eatment of the boundary and interface conditions. In one-dimensional proble ms, the boundaries of the wavelet series expansions are assumed to be the a nalytical boundaries of the problem, and the boundary condition equations a re replaced by end equations in Galerkin system. In two-dimensional problem s, in order to maintain the integrity of the system, the boundaries of the wavelet series are shifted until the end is independent on any expansion co efficients of the scaling function that affect the solution within the real boundaries. Since the scaling functions are compactly supported, only a finite number o f the connection coefficients are nonzero. The resultant matrix has a block diagonal structure, which can be inverted easily, therefore, enables us to extend the solution to two-dimensional heterogeneous cases and make the in ner iteration efficient in the eigenvalue and multigroup problems. We teste d our WGM algorithm with several diffusion problems including two-dimension al heterogeneous problems and multi-group problems. The solutions are very accurate with a proper selection of Daubechies' order and dilation order. O ur WGM algorithm provides very accurate solutions fur one-dimensional and t wo-dimensional heterogeneous problems in which the flux exhibits very steep gradients.