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An efficient high-order algorithm for acoustic scattering from penetrable thin structures in three dimensions.

Akash Anand1, Fernando Reitich

  • 1Applied and Computational Mathematics, California Institute of Technology, Pasadena, California 91125, USA. anand@acm.caltech.edu

The Journal of the Acoustical Society of America
|June 7, 2007
PubMed
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This study introduces a novel high-order algorithm for volumetric scattering problems. It enhances accuracy for thin structures and material interfaces, improving computational efficiency.

Area of Science:

  • Computational electromagnetics
  • Numerical analysis
  • Applied mathematics

Background:

  • Integral-equation formulations are crucial for volumetric scattering problems.
  • Existing methods often lack high-order accuracy, especially for thin structures and material interfaces.
  • Accelerated algorithms are needed to improve computational efficiency.

Purpose of the Study:

  • To present a high-order accelerated algorithm for solving integral-equation formulations of volumetric scattering.
  • To enhance the accuracy of existing low-order codes for thin structures and material interfaces.
  • To provide a computationally efficient and accurate solution for complex scattering phenomena.

Main Methods:

  • Development of a high-order accelerated algorithm using parametric variable changes and partitions of unity.

Related Experiment Videos

  • Resolution of Green function singularities through parametric variable changes.
  • Implementation of spectrally accurate quadratures away from singular points using partitions of unity.
  • Incorporation of two-face equivalent source approximations on Cartesian grids for accelerated interaction evaluations.

    • Main Results:

    • The algorithm achieves high-order convergence for volumetric scattering problems.
    • It effectively handles thin structures and material interfaces, upgrading existing low-order codes.
    • Numerical results demonstrate the algorithm's accuracy and performance.

    Conclusions:

    • The proposed high-order accelerated algorithm offers a significant advancement in solving volumetric scattering problems.
    • It provides a versatile tool for analyzing thin structures and improving the accuracy of existing computational electromagnetics codes.
    • The method demonstrates strong potential for applications requiring precise scattering analysis.