• Corpus ID: 246240757

The Helmholtz boundary element method does not suffer from the pollution effect

@article{Galkowski2022TheHB,
  title={The Helmholtz boundary element method does not suffer from the pollution effect},
  author={Jeffrey Galkowski and Euan A. Spence},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.09721}
}
In d dimensions, approximating an arbitrary function oscillating with frequency . k requires ∼ k degrees of freedom. A numerical method for solving the Helmholtz equation (with wavenumber k and in d dimensions) suffers from the pollution effect if, as k → ∞, the total number of degrees of freedom needed to maintain accuracy grows faster than this natural threshold (i.e., faster than k for domain-based formulations, such as finite element methods, and k for boundary-based formulations, such as… 
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