## Abstract

A multilevel Cartesian non-uniform grid time domain algorithm (CNGTDA) is introduced to rapidly compute transient wave fields radiated by time dependent three-dimensional source constellations. CNGTDA leverages the observation that transient wave fields generated by temporally bandlimited and spatially confined source constellations can be recovered via interpolation from appropriately delay- and amplitude-compensated field samples. This property is used in conjunction with a multilevel scheme, in which the computational domain is hierarchically decomposed into subdomains with sparse non-uniform grids used to obtain the fields. For both surface and volumetric source distributions, the computational cost of CNGTDA to compute the transient field at N_{s} observation locations from N_{s} collocated sources for N_{t} discrete time instances scales as O(N_{t}N_{s}logN_{s}) and O(N_{t}N_{s}log^{2}N_{s}) in the low- and high-frequency regimes, respectively. Coupled with marching-on-in-time (MOT) time domain integral equations, CNGTDA can facilitate efficient analysis of large scale time domain electromagnetic and acoustic problems.

Original language | English |
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Pages (from-to) | 8430-8444 |

Number of pages | 15 |

Journal | Journal of Computational Physics |

Volume | 229 |

Issue number | 22 |

DOIs | |

State | Published - Nov 2010 |

## Keywords

- Computational electromagnetics
- Fast methods
- Fast multipole method
- Integral equations
- Method of moments
- Time domain