PARALLEL PRECONDITIONING FOR SPARSE LINEAR-EQUATIONS

A popular class of preconditioners is known as incomplete factorizatio ns. They can be thought of as approximating the exact LU factorization of a given matrix A (e.g. computed via Gaussian elimination) by disal lowing certain fill-ins. As opposed to other PDE-based preconditioners such as multigrid and domain decomposition, this class of preconditio ners are primarily algebraic in nature and can in principle be applied to any sparse matrices. In this paper we will discuss some new viewpo ints for the construction of effective preconditioners. In particular, we will discuss parallelization aspects, including re-ordering, serie s expansion and domain decomposition techniques. Generally, this class of preconditioner does not possess a high degree of parallelism in it s original form. Re-ordering and approximations by truncating certain series expansion will increase the parallelism, but usually with a det erioration in convergence rate. Domain decomposition offers a compromi se.