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	基于八阶NAD算子的保辛分部Runge-Kutta方法及其波场模拟(英文)
	张朝元 ; 马啸 ; 杨磊 ; 宋国杰 ; Zhang Chao-Yuan ; Ma Xiao ; Yang Lei ; Song Guo-Jie
	2016-03-30 ; 2016-03-30
关键词	保辛分部Runge-Kutta方法 近似解析离散化算子 数值频散 波场模拟 Symplectic partitioned Runge–Kutta method Nearly analytic discrete operator Numerical dispersion Wavefield simulation P631.4
其他题名	Symplectic partitioned Runge–Kutta method based on the eighth-order nearly analytic discrete operator and its wavefield simulations
中文摘要	基于声波方程扩充的哈密尔顿系统,本文给出了空间精度为八阶的近似解析离散化(NAD)保辛分部Runge-Kutta方法,简称八阶NSPRK方法。该方法采用八阶精度的近似解析离散算子近似空间高阶偏微分算子,并使用二阶精度的辛分部Runge-Kutta方法进行时间离散。我们从理论和数值计算两个方面研究了八阶NSPRK方法的稳定性条件和数值频散关系,并同四阶NSPRK方法、八阶Lax-Wendroff(LWC)方法和八阶交错网格(SG)方法进行了比较。结果表明八阶NSPRK方法压制数值频散的能力显著优于传统数值计算方法。与四阶NSPRK方法和传统四阶辛格式(SPRK)方法相比,八阶NSPRK方法具有最小的数值误差和最高的计算效率:在达到同样消除数值频散的前提下,八阶NSPRK方法的计算速度约为四阶NSPRK方法的2.5倍、为四阶SPRK方法的3.4倍;八阶NSPRK方法的存储量仅为四阶NSPRK方法的47.17%、为四阶SPRK方法的49.41%。在双层介质、非均匀介质和Marmousi等复杂速度模型中,八阶NSPRK方法模拟得到的波场快照非常清晰,无可见数值频散。这些结果表明,八阶NSPRK方法在粗网格条件下能有效地压制数值频散,从而能够极大地节省计算内存,提高计算速度。总体而言,八阶NSPRK方法是一种在地震探测领域和地震学研究中有着巨大应用潜力的数值计算方法。; We propose a symplectic partitioned Runge–Kutta(SPRK) method with eighthorder spatial accuracy based on the extended Hamiltonian system of the acoustic wave equation. Known as the eighth-order NSPRK method, this technique uses an eighth-order accurate nearly analytic discrete(NAD) operator to discretize high-order spatial differential operators and employs a second-order SPRK method to discretize temporal derivatives. The stability criteria and numerical dispersion relations of the eighth-order NSPRK method are given by a semi-analytical method and are tested by numerical experiments. We also show the differences of the numerical dispersions between the eighth-order NSPRK method and conventional numerical methods such as the fourth-order NSPRK method, the eighthorder Lax–Wendroff correction(LWC) method and the eighth-order staggered-grid(SG) method. The result shows that the ability of the eighth-order NSPRK method to suppress the numerical dispersion is obviously superior to that of the conventional numerical methods. In the same computational environment, to eliminate visible numerical dispersions, the eighthorder NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 times faster than the fourth-order SPRK, and the memory requirement is only approximately 47.17% of the fourth-order NSPRK method and 49.41 % of the fourth-order SPRK method, which indicates the highest computational efficiency. Modeling examples for the two-layer models such as the heterogeneous and Marmousi models show that the wavefields generated by the eighth-order NSPRK method are very clear with no visible numerical dispersion. These numerical experiments illustrate that the eighth-order NSPRK method can effectively suppress numerical dispersion when coarse grids are adopted. Therefore, this method can greatly decrease computer memory requirement and accelerate the forward modeling productivity. In general, the eighth-order NSPRK method has tremendous potential value for seismic exploration and seismology research.
语种	英语 ; 英语
内容类型	期刊论文
源URL	[http://ir.lib.tsinghua.edu.cn/ir/item.do?handle=123456789/145987]
专题	清华大学
推荐引用方式 GB/T 7714	张朝元,马啸,杨磊,等. 基于八阶NAD算子的保辛分部Runge-Kutta方法及其波场模拟(英文)[J],2016, 2016.
APA	张朝元.,马啸.,杨磊.,宋国杰.,Zhang Chao-Yuan.,...&Song Guo-Jie.(2016).基于八阶NAD算子的保辛分部Runge-Kutta方法及其波场模拟(英文)..
MLA	张朝元,et al."基于八阶NAD算子的保辛分部Runge-Kutta方法及其波场模拟(英文)".(2016).

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