Commun. Comput. Phys., 2 (2007), pp. 881-899. Parallel Algebraic Multigrid Methods in Gyrokinetic Turbulence Simulations M. F. Adams 1, Y. Nishimura 2*1 Columbia University, APAM, 500 W.~120th St.~Rm 200, MC 4701, New York, NY 10027, USA. 2 Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575, USA. Received 13 September 2006; Accepted (in revised version) 20 January 2007 Communicated by Zhihong Lin Available online 20 March 2007 Abstract Parallel algebraic multigrid methods in gyrokinetic turbulence simulations are presented. Discretized equations of the elliptic operator $-\nabla^2 u + \alpha u = f$ (with both $\alpha=0$ and $\alpha \not= 0$) are ubiquitous in magnetically confined fusion plasma applications. When $\alpha$ is equal to zero a pure'' Laplacian or Poisson equation results and when $\alpha$ 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. Notice: Undefined variable: ams in /var/www/html/issue/abstract/readabs.php on line 163 PACS: 52.30.Gz, 52.35.Ra, 52.65.Rr Key words: Algebraic multigrid, gyrokinetic Poisson equation, particle in cell simulation. *Corresponding author. Email: adams@pppl.gov (M. F. Adams), nishimuy@uci.edu (Y. Nishimura)