A Level Set Based Geometrical Eulerian Approach to Computing High Frequency Radar Cross Sections and Multiphase Semiclassical Limits of the Schrodinger Equation

Abstract

Wave propagation in the high frequency regime can be simplified using the geometrical optics approximation. We obtained an eikonal approximation for the phase and transport equations for the amplitude. The general strategy used to find the phase is to solve for its level sets, called wave fronts. This same strategy works to compute semiclassical solutions of Schrodinger's equation, which is the main topic we studied here. Traditional obstacles faced in numerical approaches are in dealing with multivaluedness and resolution of wave fronts. Under this contract we developed an Eulerian level set based method, solving for the wave fronts using both space and phase.

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Document Details

Document Type
Technical Report
Publication Date
Jun 30, 2008
Accession Number
ADA483927

Entities

People

  • Stanley Osher

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Amplitude
  • Boltzmann Equation
  • Caustics
  • Contracts
  • Department Of Defense
  • Equations
  • Frequency
  • Liouville Equation
  • Molecular Mechanics Methods
  • Optical Lattices
  • Quantum Mechanics
  • Ray Tracing
  • Wave Functions
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Calculus or Mathematical Analysis
  • Wave Propagation and Nonlinear Chaotic Dynamics.

Technology Areas

  • Space