On comparison of multigrid cycles for poisson solver in polar plane coordinates

Masthurah, Nurhayati; Ni'mah, Iftitahu; Muttaqien, Furqon Hensan; Sadikin, Rifki

doi:10.1109/tssa.2015.7440445

Cited by 1 publication

(2 citation statements)

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“…Multigrid methods are among the most efficient solvers for elliptic model problems such as (1.1); see, e.g., [6,35]. Multigrid methods for meshes in polar coordinates were considered in, e.g., [1,3,23,33,35] but are, however, less studied. In the following sections, we will develop special multigrid components for the model problem in curvilinear coordinates such as the generalized polar coordinates proposed in (2.2).…”

Section: Geometric Multigrid For Curvilinear Coordinatesmentioning

confidence: 99%

“…However, multigrid methods for curvilinear (e.g., polar) meshes are less commonly studied topics; cf. [1,3,23,33,35] for some results. When additional difficulties arise, such as generalized polar coordinates, varying coefficients, and locally refined, anisotropic meshes, then the multigrid components must be suitably modified and adapted to maintain excellent convergence rates at low cost per iteration.…”

Section: Introductionmentioning

confidence: 99%

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Implicitly Extrapolated Geometric Multigrid on Disk-Like Domains for the Gyrokinetic Poisson Equation from Fusion Plasma Applications

2022

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The gyrokinetic Poisson equation arises as a subproblem of Tokamak fusion reactor simulations. It is often posed on disk-like cross sections of the Tokamak that are represented in generalized polar coordinates. On the resulting curvilinear anisotropic meshes, we discretize the differential equation by finite differences or low order finite elements. Using an implicit extrapolation technique similar to multigrid $$\tau $$ τ -extrapolation, the approximation order can be increased. This technique can be naturally integrated in a matrix-free geometric multigrid algorithm. Special smoothers are developed to deal with the mesh anisotropy arising from the curvilinear coordinate system and mesh grading.

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Section: Geometric Multigrid For Curvilinear Coordinatesmentioning

confidence: 99%