## Abstract

The Helmholtz equation (Δ+K^{2}n^{2})u=f with a variable index of refraction n and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. Such problems can be solved numerically by first truncating the given unbounded domain, imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization (for example, using a finite element method). In practical applications, the mesh size h and the wave number K are not independent but are constrained by the accuracy of the desired computation. It will be shown that the number of points per wavelength, measured by (Kh)^{-1}, is not sufficient to determine the accuracy of a given discretization. For example, the quantity K^{3}h^{2} is shown to determine the accuracy in the L^{2} norm for a second-order discretization method applied to several propagation models.

Original language | English (US) |
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Pages (from-to) | 396-404 |

Number of pages | 9 |

Journal | Journal of Computational Physics |

Volume | 59 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1985 |

## ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics