S. Oliveira et Yh. Deng, PRECONDITIONED KRYLOV SUBSPACE METHODS FOR TRANSPORT-EQUATIONS, Progress in nuclear energy (New series), 33(1-2), 1998, pp. 155-174
Transport equations have many important applications. Because these eq
uations are based on highly non-normal operators, they present difficu
lties in numerical computations. Iterative methods have been shown to
be efficient to solve transport equations. However, because of the nat
ure of transport problems, convergence of these methods tends to slow
for many important problems. In this paper, we focus on acceleration t
echniques for iterative methods. Particularly, we investigate the appl
icability and performance of some Krylov subspace methods with precond
itioners, such as the incomplete LU (ILU) factorization (with no fill-
in) and multigrid algorithms (spatial and angular multigrid). Three ca
ses are considered: isotropic equations without absorption, isotropic
equations with absorption, and anisotropic equations. Our numerical ex
periments show that the use of an appropriate multilevel preconditione
r can significantly improve Krylov subspace methods, such as GMRES and
CGS. (C) 1997 Elsevier Science Ltd.