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An Optimized Perfectly Matched Layer for the Schrödinger Equation

Communications in Computational Physics 2011年第1期9卷 147-179页

作者： Anna Nissen gunilla kreiss Department of Information Technology Uppsala UniversityP.O.Box 337SE-75105 UppsalaSweden.

We derive a perfectly matched layer(PML)for the Schrödinger equation using a modal *** derive approximate error formulas for the modeling error from the outer boundary of the PML and the error from the discretization in the layer and show how to choose layer parameters so that these errors are matched and optimal performance of the PML is *** computations in 1D and 2D demonstrate that the optimized PML works efficiently at a prescribed accuracy for the zero potential case,with a layer of width less than a third of the de Broglie wavelength corresponding to the dominating frequency.

关键词： Schrödinger equation perfectly matched layer

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A Well-Posed and Discretely Stable Perfectly Matched Layer for Elastic Wave Equations in Second Order Formulation

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Communications in Computational Physics 2012年第5期11卷 1643-1672页

作者： Kenneth Duru gunilla kreiss Division of Scientific Computing Department of Information TechnologyUppsala UniversityBox 337SE-75105 UppsalaSweden

We present a well-posed and discretely stable perfectly matched layer for the anisotropic(and isotropic)elastic wave equations without first re-writing the governing equations as a first order *** new model is derived by the complex coordinate stretching *** standard perturbation methods we show that complex frequency shift together with a chosen real scaling factor ensures the decay of eigen-modes for all relevant *** buttress the stability properties and the robustness of the proposed model,numerical experiments are presented for anisotropic elastic wave *** model is approximated with a stable node-centered finite difference scheme that is second order accurate both in time and space.

关键词： Perfectly matched layer well-posedness stability hyperbolicity elastic waves

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Coupling of Gaussian Beam and Finite Difference Solvers for Semiclassical Schrodinger Equations

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Advances in Applied Mathematics and Mechanics 2015年第6期7卷 687-714页

作者： Emil Kieri gunilla kreiss Olof Runborg Division of Scientific Computing Department of Information TechnologyUppsala UniversitySweden Department of Mathematics and Swedish e-Science Research Center(SeRC) KTHSweden

In the semiclassical regime,solutions to the time-dependent Schrodinger equation for molecular dynamics are highly *** number of grid points required for resolving the oscillations may become very large even for simple model problems,making solution on a grid *** methods like Gaussian beams can resolve the oscillations with little effort and yield good approximations when the atomic nuclei are heavy and the potential is ***,when the potential has variations on a small length-scale,quantum phenomena become *** asymptotic methods are less *** two classes of methods perform well in different parameter *** opens for hybrid methods,using Gaussian beams where we can and finite differences where we have *** propose a new method for treating the coupling between the finite difference method and Gaussian *** new method reduces the needed amount of overlap regions considerably compared to previous methods,which improves the efficiency.

关键词： Gaussian beams semiclassical Schrodinger equation hybrid methods

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