Perfectly Matched Layers on Cubic Domains forPauli's Equations

Laurence Halpern; Jeffrey Rauch

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arXiv · 2006.10340

Perfectly Matched Layers on Cubic Domains forPauli's Equations

Laurence Halpern·Jeffrey Rauch

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Abstract

This article proves the well posedness of the boundary value problemthat arises when PML algorithms are applied to Pauli's equationswith a three dimensional rectangle as computational domain. The absorptionsare positive near the boundary and zero far from the boundary so are always x-dependent. At the flat parts of the boundary of the rectangle, the natural absorbing boundary conditions are imposed.The difficulty addressed is the analysis of the resulting variable coeffi-cient problem on the rectanglar solid with its edges and corners. TheLaplace transform is analysed. It turns on the analysis of a boundaryvalue problem formally obtained by complex stretching. Existence isproved by deriving a boundary value problems for a complex stretchedHelmholtz equation on smoothed domains. This is the first stabilityproof with x-dependent absorptions on a bounded domain whoseboundary is not smooth.

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Laurence Halpern, Jeffrey Rauch. 2020-06-18. Perfectly Matched Layers on Cubic Domains forPauli's Equations. https://arxiv.org/abs/2006.10340

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