Iterative Solvers for Elliptic Problems with Arbitrary Anisotropy Strengths

Yang, Chang; Claustre, J; Deluzet, Fabrice

doi:10.1137/17m1113965

Cited by 8 publications

(10 citation statements)

References 28 publications

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“…This is a straightforward task for the Duality Based method. We refer to [41] for conclusive demonstrations of this last two statements. In this regard, the Two Field Iterated method offers a decisive advantage over the Micro Macro approach.…”

Section: A Comparison Of the Precision And Computational Efficiency Of The Different Methodsmentioning

confidence: 79%

“…This is indeed a crucial property to envision three dimensional computations. As emphasized in [41], the computational efficiency of sparse direct solvers (used for two dimensional computations either in [3,29] or in the present work), is poor for three dimensional computations. The scaling of both the memory requirements and computational costs increasing extremely non linearly with the number of unknowns.…”

Section: Introductionmentioning

confidence: 78%

“…Its numerical resolution is costless compared to that of the fluctuation φ ′ which is a two dimensional problem. This property has been harnessed in [41] to improve the computational efficiency of the Duality Based method and render its cost comparable to, or lower than, the resolution of an isotropic problem. Another advantage should be outlined here.…”

Section: Convergence Of the Fixed-point Iterationsmentioning

confidence: 99%

“…Similar problems have been investigated in precedent realizations (see [12,5,41] and [13,31]). These works are devoted to the derivation of Asymptotic-Preserving methods for anisotropic elliptic or diffusion equations.…”

Section: Introductionmentioning

confidence: 97%

“…It could also be transposed to coordinates aligned with the main (poloidal) component of the magnetic field which are routinely used (see [39]). The advantage of this approach is its high efficiency as outlined in [41]. The resolution of the anisotropic problems may therefore be much more computationally efficient than the resolution of the corresponding isotropic problem.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On the numerical resolution of anisotropic equations with high order differential operators arising in plasma physics

Yang

Deluzet

Narski

2019

Journal of Computational Physics

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In this paper, numerical schemes are introduced for the efficient resolution of anisotropic equations including high order differential operators. The model problem investigated in this paper, though simplified, is representative of the difficulties encountered in the modeling of Tokamak plasmas. The occurrence of high order differential operators introduces specific difficulties for the design of effective numerical methods. On the one hand, regular discretizations of the problem provide matrices characterized by a condition number that blows up with increasing anisotropy strength. On the other hand, matrices issued from Asymptotic-Preserving methods preserve a condition number bounded with respect to the anisotropy strength, nonetheless it scales very poorly as the mesh is refined. Both alternatives reveal to be inoperative in this specific framework to address the targeted values of anisotropy on refined meshes. We therefore introduce two successful methods offering the advantages of each approach: a condition number unrelated to the anisotropy strength and scaling as favorably as standard discretizations with the mesh refinement.

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Section: A Comparison Of the Precision And Computational Efficiency Of The Different Methodsmentioning

confidence: 79%