GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem

GMRES with deflated restarting, denoted by GMRES-DR(m,k), is a variant of restarted GMRES for solving nonsymmetric linear systems, which improves the convergence of restarted GMRES by weakening the influence of the eigenvalues incurring poor numerical performance. However, it is difficult to determine the deflation parameter k. In this paper, we present a new deflation strategy which determines k dynamically in different cycles. Numerical results for an electromagnetic cavity problem show that the deflation strategy is efficient.