Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling
Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling
复制标题
地震波场建模的优化体积点高阶三角谱元法
DOI：
10.1016/j.jcp.2017.01.069
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发表时间：
2017-05
影响因子：
4.1
通讯作者：
Badal Jose
中科院分区：
文献类型：
--
作者：
Liu Youshan;Teng Jiwen;Xu Tao;Badal Jose
质量集总法避免了质量矩阵求逆的代价，同时通过采用额外的内部积分点（称为立方点）来保持空间精度。迄今为止，这些点仅在张量域中解析已知，例如四边形或六面体单元。因此，非张量区域的对角质量矩阵谱元方法（SEM）总是依赖于数值计算的插值点或求积点。然而，只有1到6度的立方点是已知的，这就是为什么我们已经开发了基于ap范数的优化算法来获得高阶立方点的原因。通过这种方式，我们获得并列出了7到9度的具有所有正积分权重的新体积点。频散分析表明，从新的优化体积点确定的频散关系是可比的质量和刚度矩阵的精确积分。同时，新的优化体积点的Lebesgue常数表明其具有令人惊讶的良好插值性能。因此，这些点提供良好的插值特性和积分精度。的Courant-Friedrichs-Lewy（CFL）的数字制成表格，为传统的Fekete为基础的三角形光谱元件（TSEM），与精确积分的TSEM，和优化的立方为基础的TSEM（OTSEM）。一个补充的研究表明，光谱收敛的OTSEM。半空间模型的数值算例表明，OTSEM的精度提高了约一个数量级相比，传统的Fekete为基础的TSEM。特别地，7阶OTSEM的精度甚至高于基于14阶Fekete的TSEM的精度。此外，OTSEM产生的结果可以与四边形SEM（QSEM）在精度上竞争。OTSEM的高精度也与非平坦的地形模型进行了测试。在计算效率方面，OTSEM比基于Fekete的TSEM更有效，尽管当需要相当的数值精度时，它比QSEM稍微昂贵。
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known ascubaturepoints. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only thecubaturepoints for degrees 1 to 6 are known, which is the reason that we have developed ap-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational efficiency, the OTSEM is more efficient than the Fekete-based TSEM, although it is slightly costlier than the QSEM when a comparable numerical accuracy is required.
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影响因子：
3
作者：
D. Komatitsch;J. Vilotte
通讯作者：
D. Komatitsch;J. Vilotte
影响因子：
3.1
作者：
Dai, YH;Yuan, Y
通讯作者：
Yuan, Y
DOI：
10.2307/2153000
发表时间：
1991
期刊：
--
影响因子：
--
作者：
D. S. Watkins
通讯作者：
D. S. Watkins
影响因子：
3.3
作者：
Youshan Liu;J. Teng;Haiqiang Lan;Xiang Si;Xueying Ma
通讯作者：
Youshan Liu;J. Teng;Haiqiang Lan;Xiang Si;Xueying Ma
影响因子：
2.9
作者：
J. Hesthaven
通讯作者：
J. Hesthaven