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In this paper we extend analysis of the WaveHoltz iteration -- a time-domainiterative method for the solution of the Helmholtz equation. We expand theprevious analysis of energy conserving problems and prove convergence of theWaveHoltz iteration for problems with impedance boundary conditions in a singlespatial dimension. We then consider interior Dirichlet/Neumann problems withdamping in any spatial dimension, and show that for a sufficient level ofdamping the WaveHoltz iteration converges in a number of iteration independentof the frequency. Finally, we present a discrete analysis of the WaveHoltziteration for a family of higher order time-stepping schemes. We show that thefixed-point of the discrete WaveHoltz iteration converges to the discreteHelmholtz solution with the order of the time-stepper chosen. We presentnumerical examples and demonstrate that it is possible to completely removetime discretization error from the WaveHoltz solution through careful analysisof the discrete iteration together with updated quadrature formulas.

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