For many years, it was thought that diffusion synthetic accleration (DSA) of the traditional iterative method used for transport applications, source (or Richardson) iteration, is unconditionally effective if the DSA equations were consistently discretized with the transport equation. It has only recently been discovered that this is not true in general. Examples of situations for which this is the case will be presented, illustrating how source iteration can be replaced with more powerful Krylov methods and how DSA can improve their perfomance when cast as a preconditioner. The talk will begin with a brief review of Krylov subspace iterative methods.
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