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A variational principle for the scattered wave.

D E Freund1, R A Farrell

  • 1Applied Physics Laboratory, Johns Hopkins University, Laurel, Maryland 20723.

The Journal of the Acoustical Society of America
|May 1, 1990
PubMed
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This study introduces a new variational principle for scalar wave scattering, extending the Schwinger principle to include near-field and far-field scattered wave behavior for complex objects.

Area of Science:

  • Electromagnetics and Wave Propagation
  • Computational Physics
  • Applied Mathematics

Background:

  • The standard Schwinger variational principle is limited to far-field scattering amplitudes.
  • Accurate numerical solutions for wave scattering by arbitrary shapes are computationally challenging.
  • Dirichlet boundary conditions are common in physical scattering problems.

Purpose of the Study:

  • To develop a generalized Schwinger-type variational principle for the scattered field.
  • To extend variational methods to include near-field and far-field quantities.
  • To create a practical method for constructing trial functions for wave scattering problems.

Main Methods:

  • Formulation of a Schwinger-type variational principle for the scattered field.

Related Experiment Videos

  • Development of a generic procedure for constructing trial functions based on boundary conditions and shadowing.
  • Application and validation of the method using a spherical scatterer.

    • Main Results:

    • A variationally invariant principle applicable from the scatterer surface to the far-field.
    • A physically motivated, generic procedure for designing simple, accurate trial functions.
    • Accurate results for a spherical scatterer across the entire frequency range.

    Conclusions:

    • The presented variational principle offers a significant extension to existing methods for wave scattering.
    • The developed trial function construction provides an efficient approach for solving scattering problems.
    • The method demonstrates accuracy and broad applicability for homogeneous Dirichlet scatterers.