Pollution and accuracy of solutions of the Helmholtz equation: A novel perspective from the eigenvalues

In researching the Helmholtz equation, focus has either been on accuracy of numerical solution (pollution) or acceleration convergence a preconditioned Krylov-based solver (scalability). While it is widely recognized that properties can be investigated by studying eigenvalues, information from eigenvalues not used in dispersion which drives pollution error. Our aim to bring topics and scalability together for first time; instead approaching error conventional sense being result discrepancy between exact wavenumber, we show also decomposed terms eigenvectors eigenvalues. Using these novel insights, construct sharper upper bounds total independent grid resolution. minimized one-dimension introducing correction, latter possible higher dimensions, even very simple model problems. For our problem, correction enables us remove study full detail, both one- two-dimensions.