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Convolution quadrature methods for time-domain scattering from unbounded penetrable interfaces.

Ignacio Labarca1, Luiz M Faria2, Carlos Pérez-Arancibia1

  • 1Institute for Mathematical and Computational Engineering, School of Engineering and Faculty of Mathematics, Pontificia Universidad Católica de Chile, Santiago, Chile.

Proceedings. Mathematical, Physical, and Engineering Sciences
|August 20, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a novel boundary integral equation method for acoustic and electromagnetic scattering problems. It efficiently solves time-domain scattering with unbounded interfaces using convolution quadrature and windowed Green functions.

Keywords:
boundary integral equationslayered mediatime-domain scatteringwaveguides

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Area of Science:

  • Computational physics
  • Numerical analysis
  • Electromagnetics
  • Acoustics

Background:

  • Time-domain scattering problems with unbounded penetrable interfaces are computationally challenging.
  • Existing methods often struggle with the complexities of infinite domains and penetrable media.

Purpose of the Study:

  • To develop an efficient numerical method for solving acoustic and electromagnetic time-domain scattering problems.
  • To address challenges posed by unbounded penetrable interfaces in two spatial dimensions.

Main Methods:

  • Utilizes convolution quadrature (CQ) schemes to transform time-domain problems into frequency-domain ones.
  • Employs the windowed Green function (WGF) method to handle unbounded interfaces, reducing them to a bounded domain.
  • Solves the resulting integral equations using high-order Nyström methods with Alpert's quadrature rules.

Main Results:

  • The proposed method effectively handles acoustic and electromagnetic time-domain scattering.
  • Errors introduced by the WGF method decrease super-algebraically with increasing window size.
  • Demonstrated capabilities through examples of wave propagation in open waveguides and scattering from layered media.

Conclusions:

  • The combination of CQ and WGF provides a robust and accurate approach for scattering problems with unbounded penetrable interfaces.
  • The method is versatile and applicable to various scenarios, including waveguides and layered media.
  • Offers a powerful tool for numerical simulations in acoustics and electromagnetics.