### Abstract

A new finite element Poisson solver is developed and applied to a global gyrokinetic toroidal code (GTC) which employs the field aligned mesh and thus a logically non-rectangular grid in a general geometry. Employing test cases where the analytical solutions are known, the finite element solver has been verified. The CPU time scaling versus the matrix size employing portable, extensible toolkit for scientific computation (PETSc) to solve the sparse matrix is promising. Taking the ion temperature gradient modes (ITG) as an example, the solution from the new finite element solver has been compared to the solution from the original GTC's iterative solver which is only efficient for adiabatic electrons. Linear and nonlinear simulation results from the two different forms of the gyrokinetic Poisson equation (integral form and the differential form) coincide each other. The new finite element solver enables the implementation of advanced kinetic electron models for global electromagnetic simulations.

Original language | English |
---|---|

Pages (from-to) | 657-671 |

Number of pages | 15 |

Journal | Journal of Computational Physics |

Volume | 214 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 May 20 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Numerical Analysis
- Modelling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics

### Cite this

*Journal of Computational Physics*,

*214*(2), 657-671. https://doi.org/10.1016/j.jcp.2005.10.011

}

*Journal of Computational Physics*, vol. 214, no. 2, pp. 657-671. https://doi.org/10.1016/j.jcp.2005.10.011

**A finite element Poisson solver for gyrokinetic particle simulations in a global field aligned mesh.** / Nishimura, Yasutaro; Lin, Z.; Lewandowski, J. L.V.; Ethier, S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A finite element Poisson solver for gyrokinetic particle simulations in a global field aligned mesh

AU - Nishimura, Yasutaro

AU - Lin, Z.

AU - Lewandowski, J. L.V.

AU - Ethier, S.

PY - 2006/5/20

Y1 - 2006/5/20

N2 - A new finite element Poisson solver is developed and applied to a global gyrokinetic toroidal code (GTC) which employs the field aligned mesh and thus a logically non-rectangular grid in a general geometry. Employing test cases where the analytical solutions are known, the finite element solver has been verified. The CPU time scaling versus the matrix size employing portable, extensible toolkit for scientific computation (PETSc) to solve the sparse matrix is promising. Taking the ion temperature gradient modes (ITG) as an example, the solution from the new finite element solver has been compared to the solution from the original GTC's iterative solver which is only efficient for adiabatic electrons. Linear and nonlinear simulation results from the two different forms of the gyrokinetic Poisson equation (integral form and the differential form) coincide each other. The new finite element solver enables the implementation of advanced kinetic electron models for global electromagnetic simulations.

AB - A new finite element Poisson solver is developed and applied to a global gyrokinetic toroidal code (GTC) which employs the field aligned mesh and thus a logically non-rectangular grid in a general geometry. Employing test cases where the analytical solutions are known, the finite element solver has been verified. The CPU time scaling versus the matrix size employing portable, extensible toolkit for scientific computation (PETSc) to solve the sparse matrix is promising. Taking the ion temperature gradient modes (ITG) as an example, the solution from the new finite element solver has been compared to the solution from the original GTC's iterative solver which is only efficient for adiabatic electrons. Linear and nonlinear simulation results from the two different forms of the gyrokinetic Poisson equation (integral form and the differential form) coincide each other. The new finite element solver enables the implementation of advanced kinetic electron models for global electromagnetic simulations.

UR - http://www.scopus.com/inward/record.url?scp=33644957068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644957068&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2005.10.011

DO - 10.1016/j.jcp.2005.10.011

M3 - Article

VL - 214

SP - 657

EP - 671

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 2

ER -