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Superposition of Multi-Valued Solutions in High Frequency Wave Dynamics

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Abstract

The weakly coupled WKB system captures high frequency wave dynamics in many applications. For such a system a level set method framework has been recently developed to compute multi-valued solutions to the Hamilton-Jacobi equation and evaluate position density accordingly. In this paper we propose two approaches for computing multi-valued quantities related to density, momentum as well as energy. Within this level set framework we show that physical observables evaluated in Jin et al. (J. Comput. Phys. 210(2):497–518, [2005]; J. Comput. Phys. 205(1):222–241, [2005]) are simply the superposition of their multi-valued correspondents. A series of numerical tests is performed to compute multi-valued quantities and validate the established superposition properties.

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Correspondence to Hailiang Liu.

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Liu, H., Wang, Z. Superposition of Multi-Valued Solutions in High Frequency Wave Dynamics. J Sci Comput 35, 192–218 (2008). https://doi.org/10.1007/s10915-008-9198-4

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  • DOI: https://doi.org/10.1007/s10915-008-9198-4

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