论文标题
Cubic域上的完美层层
Perfectly Matched Layers on Cubic Domains forPauli's Equations
论文作者
论文摘要
本文证明了边界值问题的良好姿势，当将PML算法应用于Pauli的方程式（以三维矩形为计算域）时，出现了问题。在边界附近的吸收率阳性，远离边界的零，因此始终依赖于X依赖性。在矩形边界的平坦部分，施加了自然吸收的边界条件。解决的难度是对矩形固体上带有其边缘和角落的矩形固体上产生的可变系数问题的分析。分析theLaplace变换。它打开对通过复杂拉伸正式获得的边界值问题的分析。通过得出平滑域上复杂拉伸的Helmholtz方程的边界值问题，可以证明存在。这是第一个具有X依赖性吸收的稳定性，其边界不光滑的有限域。
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.
