OPTIMALLY BLENDED SPECTRAL-FINITE ELEMENT SCHEME FOR WAVE PROPAGATION AND NONSTANDARD REDUCED INTEGRATION
OPTIMALLY BLENDED SPECTRAL-FINITE ELEMENT SCHEME FOR WAVE PROPAGATION AND NONSTANDARD REDUCED INTEGRATION
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DOI：
10.1137/090754017
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发表时间：
2010-01-01
影响因子：
2.9
通讯作者：
Wajid, Hafiz Abdul
中科院分区：
文献类型：
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作者：
Ainsworth, Mark;Wajid, Hafiz Abdul
对于小波数极限，我们研究了一致(有限元)质量矩阵和集中(谱单元)质量矩阵加权平均所得到的数值格式的色散和耗散。我们发现并证明了对于最佳混合，所得到的格式(A)为pth阶格式提供了2p+4阶的精度(与有限元和谱元格式相比，精度提高了两个数量级)；(B)其绝对精度分别是纯有限元和谱元格式的O(p(-3))和O(p(-2))倍；(C)容易表现出相位滞后。此外，我们还证明，只要用新的非标准求积规则来代替通常用于组装质量和刚度矩阵的高斯求积规则，就可以有效地实现最优混合方案。
We study the dispersion and dissipation of the numerical scheme obtained by taking a weighted averaging of the consistent (finite element) mass matrix and lumped (spectral element) mass matrix for the small wave number limit. We find and prove that for the optimum blending the resulting scheme (a) provides 2p + 4 order accuracy for pth order method (two orders more accurate compared with finite and spectral element schemes); (b) has an absolute accuracy which is O(p(-3)) and O(p(-2)) times better than that of the pure finite and spectral element schemes, respectively; (c) tends to exhibit phase lag. Moreover, we show that the optimally blended scheme can be efficiently implemented merely by replacing the usual Gaussian quadrature rule used to assemble the mass and stiffness matrices by novel nonstandard quadrature rules which are also derived.