A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations (Q1017593)
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scientific article; zbMATH DE number 5552738
| Language | Label | Description | Also known as |
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| English | A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations |
scientific article; zbMATH DE number 5552738 |
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A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations (English)
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12 May 2009
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The authors propose a numerical method based on high-frequency asymptotics for the Schrödinger equation with a rapidly varying potential. The method starts with the computation of a number of Bloch eigenvalues. The density of each Bloch band is calculated from the zero level set in phase space of the derivative of the phase with respect to the slow spatial variable. The method breaks down in the vicinity of caustics.
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Schrödinger equation
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Bloch waves
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homogenization
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level set method
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semiclassical limit
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high-frequency asymptotics
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Bloch eigenvalues
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