EPJ Plus – New analytic method to solve 2-d Helmholtz equation for irregular boundaries

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Published on 17 August 2011

To date the most successful efforts to solve the irregular boundary Helmholtz equation with Neumann boundary conditions have been computational, but even this general method has its drawbacks. Panda et al. provide a new analytic approach which solves the irregular boundary problem via a perturbative series. As the authors show by working out several nontrivial examples, the benefits of this approach include a precise understanding of the behavior of the solution as the amplitude of the boundary distortion is increased, as well as the control over the analytic precision in the terms computed and its corresponding analytic error estimates. more