Gmres for Sequentially Multiple Nearby Systems

An application of the Generalized Minimal Residual (GMRES) algorithm to the solution of sequentially multiple nearby systems of equations through the reuse of Krylov subspaces is presented. The main focus is on the case when only the right-hand side vector changes. However, the case in which both the matrix and the right-hand side change is also addressed. Applications of these formulations include nonlinear problems, Design Sensitivity Analysis, multiple load cases, and transient analyses. Examples are drawn from systems arising from the discretization of Boundary Integral Equations. Though there is no reason to expect that Krylov subspaces may e ectively be reused for unrelated right-hand sides (except in the trivial full-dimensional limit), recent experience suggests that reuse has broad practical applicability.