Computing multi-valued velocity and electric fields for 1D Euler--Poisson equations

  • Authors:

  • Hailiang Liu;Zhongming Wang

  • Affiliations:

  • Department of Mathematics, Iowa State University, 396 Carver Hall, Ames, IA 50011-2064, USA;Department of Mathematics, Iowa State University, 396 Carver Hall, Ames, IA 50011-2064, USA

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2007

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Abstract

We develop a level set method for the computation of multi-valued velocity and electric fields of one-dimensional Euler-Poisson equations. The system of these equations arises in the semiclassical approximation of Schrodinger-Poisson equations and semiconductor modeling. This method uses an implicit Eulerian formulation in an extended space-called field space, which incorporates both velocity and electric fields into the configuration space. Multi-valued velocity and electric fields are captured through common zeros of two level set functions, which solve a linear homogeneous transport equation in the field space. Numerical examples are presented to validate the proposed level set method.