General spline filters for discontinuous Galerkin solutions.
General spline filters for discontinuous Galerkin solutions.
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DOI：
10.1016/j.camwa.2015.06.034
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发表时间：
2015-09-01
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影响因子：
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通讯作者：
Peters J
中科院分区：
文献类型：
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作者：
Peters J
不连续Galerkin（dG）方法输出多项式片段的序列。通过平滑增加精度保持（SIAC）卷积对序列进行后处理不仅增加了序列的平滑度，而且还可以提高其精度并产生超收敛。如果SIAC核以d次B样条的线性组合的形式再现2d次多项式，则SIAC卷积被认为是最优的。本文推导了计算非均匀结点的一般情况下的最优SIAC样条系数的简单公式。
The discontinuous Galerkin (dG) method outputs a sequence of polynomial pieces. Post-processing the sequence by Smoothness-Increasing Accuracy-Conserving (SIAC) convolution not only increases the smoothness of the sequence but can also improve its accuracy and yield superconvergence. SIAC convolution is considered optimal if the SIAC kernels, in the form of a linear combination of B-splines of degree d, reproduce polynomials of degree 2d. This paper derives simple formulas for computing the optimal SIAC spline coefficients for the general case including non-uniform knots.