EXPLICIT LEAST-DEGREE BOUNDARY FILTERS FOR DISCONTINUOUS GALERKIN.
EXPLICIT LEAST-DEGREE BOUNDARY FILTERS FOR DISCONTINUOUS GALERKIN.
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适用于不连续 Galerkin 的显式最低阶边界滤波器。
DOI：
10.1137/17m1114016
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Peters,Jörg
中科院分区：
文献类型：
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作者：
Nguyen,Dang-Manh;Peters,Jörg
利用样条滤波器对间断Galerkin（DG）计算的输出进行卷积，可以提高输出的光滑度和精度。在域边界，这些过滤器必须是单侧的非周期性边界条件。最近，位置相关的平滑度增加精度保持（PSIAC）滤波器被证明是众所周知的单侧RLKV和SRV滤波器的超集。由于PSIAC滤波器可以用符号表示，因此PSIAC滤波相当于形成具有本地DG输出的线性产品，因此提供了更稳定、更高效的实施。本文介绍了一类新的PSIAC滤波器，NP，有小的支持和分段常数。对正则双曲检验方程的数值实验表明，NP滤波器的性能优于更复杂的已知边界滤波器。NP滤波器典型地减小了边界区域中的误差，该误差低于应用相同支撑的最优超收敛对称滤波器的内部的误差。NP滤波可以实现为形成具有短有理权重的数据的线性组合。对于DG度1、2和3，显式列出了有理滤波器矩阵。卷积输出的精确导数很容易计算。
Convolving the output of discontinuous Galerkin (DG) computations using spline filters can improve both smoothness and accuracy of the output. At domain boundaries, these filters have to be one-sided for nonperiodic boundary conditions. Recently, position-dependent smoothness-increasing accuracy-conserving (PSIAC) filters were shown to be a superset of the well-known one-sided RLKV and SRV filters. Since PSIAC filters can be formulated symbolically, PSIAC filtering amounts to forming linear products with local DG output and so offers a more stable and efficient implementation. The paper introduces a new class of PSIAC filters, NP, that have small support and are piecewise constant. Extensive numerical experiments for the canonical hyperbolic test equation show NPfilters outperform the more complex known boundary filters. NPfilters typically reduce theerror in the boundary region below that of the interior where optimally superconvergent symmetric filters of the same support are applied. NPfiltering can be implemented as forming linear combinations of the data with short rational weights. The rational filter matrices are explicitly listed for DG degree 1, 2, and 3. Exact derivatives of the convolved output are easy to compute.