Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow

IF 3.8 2区 物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Maria Vasilyeva , Golo Wimmer , Ben S. Southworth
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引用次数: 0

Abstract

We consider anis heat flow with extreme anisotropy, as arises in magnetized plasmas for fusion applications. Such problems pose significant challenges in both obtaining an accurate approximation as well in the construction of an efficient solver. In both cases, the underlying difficulty is in forming an accurate approximation of temperature fields that follow the direction of complex, non-grid-aligned magnetic fields. In this work, we construct a highly accurate coarse grid approximation using spectral multiscale basis functions based on local anisotropic normalized Laplacians. We show that the local generalized spectral problems yield local modes that align with magnetic fields, and provide an excellent coarse-grid approximation of the problem. We then utilize this spectral coarse space as an approximation in itself, and as the coarse-grid in a two-level spectral preconditioner. Numerical results are presented for several magnetic field distributions and anisotropy ratios up to 1012, showing highly accurate results with a large system size reduction, and two-grid preconditioning that converges in O(1) iterations, independent of anisotropy. Aptara
极端各向异性热流的多尺度逼近和双网格预调节器
我们考虑具有极端各向异性的热流,如在聚变应用的磁化等离子体中出现的热流。这些问题在获得精确的近似和构造有效的求解器方面都提出了重大的挑战。在这两种情况下,潜在的困难是形成一个精确的温度场近似值,它遵循复杂的、非网格排列的磁场的方向。在这项工作中,我们基于局部各向异性归一化拉普拉斯算子,利用谱多尺度基函数构建了高精度的粗网格近似。我们证明了局部广义谱问题产生了与磁场对齐的局部模式,并提供了问题的一个很好的粗网格近似。然后,我们利用这个谱粗空间作为其本身的近似,并作为两级谱预调节器中的粗网格。给出了几种磁场分布和各向异性比高达1012的数值结果,显示出高精度的结果,系统尺寸大幅减小,两网格预处理在O(1)次迭代中收敛,与各向异性无关。Aptara
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来源期刊
Journal of Computational Physics
Journal of Computational Physics 物理-计算机:跨学科应用
CiteScore
7.60
自引率
14.60%
发文量
763
审稿时长
5.8 months
期刊介绍: Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries. The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.
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