CS 672Numerical Solution of Large Sparse Systems of Equations

Introduction, example applications from finite element analysis, optimization. Data structures, basic graph theory. Direct methods: symmetric structures, non-symmetric structures, ordering methods; RCM, minimum degree, nested dissection. Iterative methods: steepest descent, conjugate gradient, GMRES, CGSTAB. Preconditioning methods; level of fill, drop tolerance. Methods for high performance architectures.