Journal of Scientific Computing

, Volume 35, Issue 2–3, pp 192–218 | Cite as

Superposition of Multi-Valued Solutions in High Frequency Wave Dynamics

  • Hailiang Liu
  • Zhongming Wang


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.


Level set method WKB system Multi-valued solution Superposition 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Mathematics DepartmentIowa State UniversityAmesUSA

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