TY - JOUR

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

AU - Nishimura, Y.

AU - Lin, Z.

AU - Lewandowski, J. L.V.

AU - Ethier, S.

N1 - Funding Information:
The authors thank Dr. Wei-li Lee, for numerous advices and his encouragement throughout the course of this work. The authors also thank Dr. J. Breslau, Dr. J. Chen, Dr. L. Chen, Dr. T. Hahm, Dr. S. Klasky, Dr. J. Manickam, Dr. G. Rewoldt, Dr. W. Tang, and Dr. W. Wang for various useful comments. Y.N. thanks Professor D. Keyes of Columbia University, Dr. M. Knepley, and Dr. B. Smith at Mathematics and Computer Science Division of Argonne National Laboratory, for their kind assistance in the usage of PETSc. This work is supported by Department of Energy (DOE) Grant DE-FG02-03ER54724, Cooperative Agreement No. DE-FC02-04ER54796 (UCI), DOE Contract No. DE-AC02-76CH03073 (PPPL), and in part by SciDAC Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas.

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.

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U2 - 10.1016/j.jcp.2005.10.011

DO - 10.1016/j.jcp.2005.10.011

M3 - Article

AN - SCOPUS:33644957068

VL - 214

SP - 657

EP - 671

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 2

ER -