Volume 2, Issue 5
Parallel Algebraic Multigrid Methods in Gyrokinetic Turbulence Simulations

M. F. Adams & Y. Nishimura

DOI:

Commun. Comput. Phys., 2 (2007), pp. 881-899.

Published online: 2007-02

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  • Abstract

Parallel algebraic multigrid methods in gyrokinetic turbulence simulations are presented. Discretized equations of the elliptic operator −∇2u+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.

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@Article{CiCP-2-881, author = {}, title = {Parallel Algebraic Multigrid Methods in Gyrokinetic Turbulence Simulations}, journal = {Communications in Computational Physics}, year = {2007}, volume = {2}, number = {5}, pages = {881--899}, abstract = {

Parallel algebraic multigrid methods in gyrokinetic turbulence simulations are presented. Discretized equations of the elliptic operator −∇2u+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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7931.html} }
TY - JOUR T1 - Parallel Algebraic Multigrid Methods in Gyrokinetic Turbulence Simulations JO - Communications in Computational Physics VL - 5 SP - 881 EP - 899 PY - 2007 DA - 2007/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7931.html KW - AB -

Parallel algebraic multigrid methods in gyrokinetic turbulence simulations are presented. Discretized equations of the elliptic operator −∇2u+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.

M. F. Adams & Y. Nishimura. (2020). Parallel Algebraic Multigrid Methods in Gyrokinetic Turbulence Simulations. Communications in Computational Physics. 2 (5). 881-899. doi:
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