A Two Field Iterated Asymptotic-Preserving Method for Highly Anisotropic Elliptic Equations

Deluzet, Fabrice; Narski, Jacek

doi:10.1137/17m115205x

Cited by 10 publications

(16 citation statements)

References 21 publications

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“…To this end, the targeted anisotropy strength (ε = 10 −8 ) is selected and refined meshes will be used to proceed with the comparisons of the different methods. The Duality Based formulation (8)(9), the Micro Macro formulation (16) and the Two Field Iterated formulation (13)(14) are compared against the discretized Singular Perturbation problem. The precision of the approximation carried out by the different methods is plotted on Fig.…”

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

confidence: 99%

“…The computational times are given relative to those of the Singular Perturbation problem. The Duality Based scheme is less than twice as expensive as the discretized Singular Perturbation scheme (8)(9), the Micro Macro method (16) and the Two Field Iterated scheme (13)(14). The computation time is relative to that of the SP problem resolution.…”

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

confidence: 99%

“…For any (φ (0) , q (0) ) ∈ V × V, the sequence (φ (k) , q (k) ) k>0 defined by the iterative method (13)(14) converges to a fixed point (φ, q). The component φ of the stationary point solves uniquely the initial singular problem (4) for ε > 0 and the limit problem (5) when ε = 0.…”

Section: The Two Field Iterated Formulationmentioning

confidence: 99%

“…) the approximation of q(x i , y j ) for (i, j) ∈ I × J . The Two Field Iterated system (13)(14) is discretized thanks to the linear systems…”

Section: A Finite Difference Space Discretizationmentioning

confidence: 99%

“…The second method proposed herein is a two field iterated method in the spirit of [14]. This method can address arbitrary field geometries with non adapted coordinates and meshes.…”

Section: Introductionmentioning

confidence: 99%

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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: 99%

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

confidence: 99%

Section: The Two Field Iterated Formulationmentioning

confidence: 99%

“…) the approximation of q(x i , y j ) for (i, j) ∈ I × J . The Two Field Iterated system (13)(14) is discretized thanks to the linear systems…”

Section: A Finite Difference Space Discretizationmentioning

confidence: 99%

“…The second method proposed herein is a two field iterated method in the spirit of [14]. This method can address arbitrary field geometries with non adapted coordinates and meshes.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations