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Computing scattering resonances using perfectly matched layers with frequency dependent scaling functions.

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Summary
This summary is machine-generated.

Frequency dependent complex scaling reduces spurious resonances in open systems. This method is less sensitive to discretization parameters, simplifying computations compared to standard frequency independent scaling.

Keywords:
Frequency dependent complex scalingHelmholtz resonance problemsPerfectly matched layerSpurious resonances

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Area of Science:

  • Computational physics
  • Quantum mechanics
  • Numerical analysis

Background:

  • Perfectly matched layers (PMLs) are used for resonance computations in open systems.
  • PMLs can introduce artificial or spurious resonances, complicating analysis.

Purpose of the Study:

  • To analyze the dependency of artificial resonances on discretization parameters and complex scaling functions.
  • To compare frequency independent complex scaling with frequency dependent complex scaling.

Main Methods:

  • Investigated artificial resonances in open systems using perfectly matched layers.
  • Analyzed the influence of discretization parameters and complex scaling functions.
  • Compared standard frequency independent complex scaling with frequency dependent complex scaling.

Main Results:

  • Frequency dependent complex scaling leads to a polynomial eigenvalue problem, unlike the linear problem from standard scaling.
  • Artificial resonances are more conveniently located using frequency dependent scaling.
  • Artificial resonances exhibit reduced sensitivity to discretization parameters with frequency dependent scaling.

Conclusions:

  • Frequency dependent complex scaling offers advantages over standard scaling for resonance computations.
  • This method simplifies the selection of discretization parameters, improving computational efficiency and accuracy.