On the non-equivalence of perfectly matched layers and exterior complex scaling

A. Scrinzi; H. P. Stimming; N. J . Mauser

doi:10.1016/j.jcp.2014.03.007

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arXiv · 1306.6853

On the non-equivalence of perfectly matched layers and exterior complex scaling

A. Scrinzi·H. P. Stimming·N. J . Mauser

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Abstract

The perfectly matched layers (PML) and exterior complex scaling (ECS) methods for absorbing boundary conditions are analyzed using spectral decomposition. Both methods are derived through analytical continuations from unitary to contractive transformations. We find that the methods are mathematically and numerically distinct: ECS is complex stretching that rotates the operator's spectrum into the complex plane, whereas PML is a complex gauge transform which shifts the spectrum. Consequently, the schemes differ in their time-stability. Numerical examples are given.

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A. Scrinzi, H. P. Stimming, N. J . Mauser. 2013-06-28. On the non-equivalence of perfectly matched layers and exterior complex scaling. https://doi.org/10.1016/j.jcp.2014.03.007

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