Preconditioned Krylov Subspace Methods for Transport Equations
نویسندگان
چکیده
Transport equations have many important applications. Because the equations are based on highly non-normal operators, they present diiculties in numerical computations. The iterative methods have been shown to be one of eecient numerical methods to solve transport equations. However, because of the nature of transport problems, convergence of iterative methods tends to slow for many important problems. In this paper, we focus on the development of algorithms to accelerate iterative methods. We investigate the applicability and performance of some Krylov subspace methods with preconditioners, particularly, the incomplete LU factorization and the multigrid algorithm. Three cases (isotropic equations without absorption, isotropic equations with absorption, and anisotropic equations) are considered. Our numerical experiments show that the use of an appropriate multilevel preconditioner can make much considerable improvement for Krylov subspace methods, such as GMRES and CGS. x1 Introduction Transport equations are mathematical models which describe the transport of particles , momentum, energy, or any transportable quantity 2]. They originally arose in the study of electron transport in solid, later were found in many other applications, such as neutron transport, gas kinetics, radiative transfer. Many mathematical theories and tools have been developed for the study of transport problems, including 1
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