## An O(n log n) Solution Algorithm for Spectral Element Methods

Title | An O(n log n) Solution Algorithm for Spectral Element Methods |

Publication Type | Report |

Year of Publication | 2003 |

Authors | Lee, I, Raghavan, P, Fischer, PF |

Date Published | 04/2003 |

Other Numbers | ANL/MCS-P1041-0403 |

Abstract | Many three-dimensional flow problems in science and engineering feature geometries that are homogeneous in at least one flow direction. Two examples are the high-aspect-ratio domains in Fig. 1, which shows spectral element (SE) meshes currently being used for simulations of Rayleigh-Benard convection (a) and reactor core cooling (b). In these cases, the numerical simulation costs can often be reduced by recasting the original problem (or subproblem) in terms of eigenvectors of the (discrete) one-dimensional operators to yield a set of decoupled problems of lower dimension. Here, we consider application of this approach to reduce three-dimensional problems to independent two-dimensional subproblems. The costs of performing the transformations and solving the subproblems is addressed, and we show that it is possible to achieve O(n log n) complexity for n-gridpoint problems in R3. |

http://www.mcs.anl.gov/papers/P1041.pdf |