PRECONDITIONED KRYLOV SUBSPACE METHODS FOR TRANSPORT-EQUATIONS

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.