@article{WOS:001014762300001,
title = {Solver comparison for Poisson-like equations on tokamak geometries},
author = {Emily Bourne and Philippe Leleux and Katharina Kormann and Carola Kruse and Virginie Grandgirard and Yaman Guclu and Martin J. Kuhn and Ulrich Rude and Eric Sonnendrucker and Edoardo Zoni},
doi = {10.1016/j.jcp.2023.112249},
issn = {0021-9991},
year = {2023},
date = {2023-09-01},
journal = {JOURNAL OF COMPUTATIONAL PHYSICS},
volume = {488},
publisher = {ACADEMIC PRESS INC ELSEVIER SCIENCE},
address = {525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA},
abstract = {The solution of Poisson-like equations defined on a complex geometry is
required for gyrokinetic simulations, which are important for the
modelling of plasma turbulence in nuclear fusion devices such as the
ITER tokamak. In this paper, we compare three existing solvers finely
tuned to solve this problem, in terms of the accuracy of the solution,
and their computational efficiency. We also consider practical
implementation aspects, including the parallel efficiency of the code,
potentially enabling an integration of the solvers in a state-of-the-art
first-principle gyrokinetic simulation framework. The first, the Spline
FEM solver, uses C1 polar splines to construct a finite elements method
which solves the equation on curvilinear coordinates. The resulting
linear system is solved using a conjugate gradient method. The second,
the GMGPolar solver, uses a symmetric finite difference method to
discretise the differential equation. The resulting linear system is
solved using a tailored geometric multigrid scheme, with a combination
of zebra circle and radial line smoothers, together with an implicit
extrapolation scheme. The third, the Embedded Boundary solver, uses a
finite volumes method on Cartesian coordinates with an embedded boundary
scheme. The resulting linear system is solved using a multigrid scheme.
The Spline FEM solver is shown to be the most accurate. The GMGPolar
solver is shown to use the least memory. The Embedded Boundary solver is
shown to be the fastest in most cases. All three solvers are shown to be
capable of solving the equation on a realistic non-analytical geometry.
The Embedded Boundary solver is additionally used to attempt to solve an
X-point geometry.(C) 2023 Elsevier Inc. All rights reserved.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}