Scale separation in fast hierarchical solvers for discontinuous Galerkin methods
Scale separation in fast hierarchical solvers for discontinuous Galerkin methods
复制标题
不连续伽辽金方法的快速分层求解器中的尺度分离
DOI：
10.1016/j.amc.2015.05.047
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
L. Korous
中科院分区：
文献类型：
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作者：
V. Aizinger;D. Kuzmin;L. Korous
本文给出了由不连续伽辽金近似引起的线性系统的一种求解方法。该两级算法基于层次尺度分离方案（HSS），使得线性系统仅对代表DG解的粗尺度的单元平均值进行全局求解。该问题的系统矩阵与胞心有限体积法完全相同。解的高阶分量（细尺度）通过求解小的局部问题作为修正来计算。这种技术对于采用层次基的DG方案特别有效，并导致平稳和时变双曲型和抛物型问题的无条件稳定方法。与多重网格方案不同，对于任意阶的DG近似，只使用两个级别。该方法概念简单，易于实现。在我们的数值实验中，它具有较好的顶多重网格性能。数值实验验证了该算法的准确性和鲁棒性。
We present a method for solution of linear systems resulting from discontinuous Galerkin (DG) approximations. The two-level algorithm is based on a hierarchical scale separation scheme (HSS) such that the linear system is solved globally only for the cell mean values which represent the coarse scales of the DG solution. The system matrix of this coarse-scale problem is exactly the same as in the cell-centered finite volume method. The higher order components of the solution (fine scales) are computed as corrections by solving small local problems. This technique is particularly efficient for DG schemes that employ hierarchical bases and leads to an unconditionally stable method for stationary and time-dependent hyperbolic and parabolic problems. Unlikep-multigrid schemes, only two levels are used for DG approximations of any order. The proposed method is conceptually simple and easy to implement. It compares favorably top-multigrid in our numerical experiments. Numerical tests confirm the accuracy and robustness of the proposed algorithm.
DOI：
10.1007/11666806_8
发表时间：
2005
期刊：
Computers & Fluids
影响因子：
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作者：
P. Bochev;T. Hughes;G. Scovazzi
通讯作者：
G. Scovazzi