Iterative Krylov Subspace Methods for Linear Port‐Hamiltonian Systems

ABSTRACT In this work, we present a structure‐preserving Krylov subspace iteration scheme for solving the equation systems that arise from the Gauss integration of linear energy‐conserving and dissipative differential systems (e.g., Poisson systems, gradient systems, and port‐Hamiltonian systems). Exploiting the relation between Gauss integrators and diagonal Padé approximations, the ‐Arnoldi process yields iterates that are not only energy‐preserving up to convergence but also on each iteration level. We extend the approach to cover also energy dissipation. The use of the ‐Arnoldi approximation for Gauss integration enhances the computational efficiency as it allows a termination of the iteration without loss of energy‐associated structures as soon as the desired accuracy of the numerical integrator is reached. We investigate the performance in splitting schemes for linear port‐Hamiltonian systems.