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JCPHY

2011

2011

In this paper, we consider the numerical solution of the Helmholtz equation, arising from the study of the wave equation in the frequency domain. The approach proposed here diﬀers from those recently considered in the literature, in that it is based on a decomposition that is exact when considered analytically, so the only degradation in computational performance is due to discretization and roundoﬀ errors. In particular, we make use of a multiplicative decomposition of the solution of the Helmholtz equation into an analytical plane wave and a multiplier, which is the solution of a complexvalued advection-diﬀusion-reaction equation. The use of fast multigrid methods for the solution of this equation is investigated. Numerical results show that this is an eﬃcient solution algorithm for a reasonable range of frequencies.

Related Content

Added |
15 Sep 2011 |

Updated |
15 Sep 2011 |

Type |
Journal |

Year |
2011 |

Where |
JCPHY |

Authors |
Eldad Haber, Scott MacLachlan |

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