### Abstract

Parallel algebraic multigrid methods in gyrokinetic turbulence simulations are presented. Discretized equations of the elliptic operator -∇^{2}u+ αu=f (with both α = 0 and α ≠ 0) are ubiquitous in magnetically confined fusion plasma applications. When α is equal to zero a "pure" Laplacian or Poisson equation results and when α is greater than zero a so called Helmholtz equation is produced. Taking a gyrokinetic turbulence simulation model as a testbed, we investigate the performance characteristics of basic classes of linear solvers (direct, one-level iterative, and multilevel iterative methods) on 2D unstructured finite element method (FEM) problems for both the Poisson and the Helmholtz equations.

Original language | English |
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Pages (from-to) | 881-899 |

Number of pages | 19 |

Journal | Communications in Computational Physics |

Volume | 2 |

Issue number | 5 |

Publication status | Published - 2007 Oct |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

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## Cite this

*Communications in Computational Physics*,

*2*(5), 881-899.