Application of Preconditioned Conjugate Gradient-Like Methods to Reactor Kinetics

[[abstract]]Several conjugate gradient-like (CG-like) methods are applied to solve the nonsymmetric linear systems of equations derived from the time-dependent two-dimensional two-energy-group neutron diffusion equations by a finite difference approximation. The CG-like methods are: the generalized conjugate residual method; the generalized conjugate gradient least-square method; the generalized minimal residual method; the conjugate gradient square method; and a variant of the bi-conjugate gradient method. In order to accelerate these CG-like methods, several preconditioning techniques are investigated. Two of the preconditioners are based on pointwise incomplete factorization: the incomplete LU and the modified incomplete LU decompositions. Another two, based on the block tridiagonal structure of the coefficient matrix, are blockwise and modified blockwise incomplete factorizations. Finally, the last two are the alternating-direction implicit and symmetric successive overrelaxation preconditioners, which are derived from the basic iterative schemes. Comparisons are made by using CG-like methods combined with different preconditioners to solve a sequence of time-step reactor transient problems[[fileno]]2060128010009[[department]]工程與系統科學