Parallel iterative algorithms for large sparse linear systems
Abstract
Numerical handling of partial differential equations (PDEs) plays a crucial role in modeling physical processes. It involves discretization of these PDEs using for example finite difference or finite element methods and often requires the solution of large sparse linear systems. The linear systems at hand may be solved using direct or iterative methods. Direct methods are more reliable and are used when the lower and upper triangular factors do not run out of memory due to fill-in. Iterative algorithms are more amenable to parallelism and may be applied to solve larger linear systems. We focus on the parallel iterative algorithms for large sparse nonsymmetric linear systems. The most popular iterative schemes for these problems are part of the Krylov subspace family of methods and include BiCGStab, GMRES and CGNR methods. We look at their reliability using ILU/IQR-preconditioning techniques and suggest two alternative schemes. The first is a hybrid scheme based on algebraic domain decomposition techniques that uses direct and iterative algorithms to solve in parallel a single linear system. The second is a novel iterative scheme that uses a deflation-based preconditioned block-row projection method with an outer iterative solver to solve in parallel a single linear system.
Degree
Ph.D.
Advisors
Sameh, Purdue University.
Subject Area
Mathematics|Computer science
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