Scientific Computing Seminar
When: 4:10pm – 5:00pm, Monday, May 16, 2016
Where: Room 3083 Kemper Hall
Abstract: The question of how to choose tolerances in the inner iteration in Newton methods has been answered satisfactorily 20 years ago. In fixed point methods, inner iterations can occur as well and the question has not been answered so far. Examples are the Dirichlet-Neumann iteration in Fluid-Structure interaction, the Picard iteration for nonlinear systems and the inexact Hermitian/skew-Hermitian splitting (IHSS) method for nonhermitian linear systems. We show that when using a nonstandard relative termination criterion, the tolerance in the inner linear solves can be chosen very coarse while still obtaining convergence of the outer iteration to the correct solution. For standard relative and absolute termination criteria, this is not the case. This can cause unexpected results, since when convergent, the fixed point iteration will terminate anyhow, with an error that depends on the tolerance in the inner solver.
Host: Zhaojun Bai
3083 Kemper Hall