Numerical Solution of the Problem of the Computational Time Reversal in the Quadrant

Abstract

The problem of the computational time reversal is posed as the inverse problem of the determination of an unknown initial condition with a finite support in a hyperbolic equation, given the Cauchy data at the lateral surface. A stability estimate for this ill-posed problem implies refocusing of the time reversed wave field. Two such two-dimensional inverse problems are solved numerically in the case when the domain is quadrant and the Cauchy data are given at finite parts of coordinate axis. The previously obtained Lipschitz stability estimate (if proven) rigorously explains and numerical results confirm the experimentally observed phenomenon of refocusing of time reversed wave fields.

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Document Details

Document Type
Technical Report
Publication Date
Sep 21, 2005
Accession Number
ADA445094

Entities

People

  • Dmitrii V. Nechaev
  • Michael Klibanov
  • Sergey I. Kabanikhin

Organizations

  • University of North Carolina at Charlotte

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Computational Science
  • Convergence
  • Eigenvalues
  • Electronic Mail
  • Equations
  • Errors
  • Geometry
  • Inverse Problems
  • Mathematics
  • Quadrants
  • Three Dimensional
  • Triangles
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Geodesy