Extensions and Analysis of an Iterative Solution of the Helmholtz Equation via the Wave Equation

Published in arXiv, 2022

This paper extends analysis of the WaveHoltz iteration, a time-domain iterative method for the solution of the Helmholtz equation, to problems with impedance boundary conditions in a single spatial dimension. We additionally analyze Helmholtz problems with damping, and we additionally show that it is possible to \textit{completely remove} time discretization error from the WaveHoltz solution through careful analysis of the discrete iteration and updated quadrature formulas.