Symplectic partitioned Runge-Kutta method based onthe eighth-order nearly analytic discrete operator and its wavefield simulations

We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order 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 thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% 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-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.

A Nearly Analytic Discrete Method for One-dimensional Unsteady Convection-dominated Diffusion Equations

In this paper, a nearly analytic discretization method for one-dimensional linear unsteady convection-dominated diffusion equations and viscous Burgers’ equation as one of the nonlinear equation is considered. In the case of linear equations, we find the local truncation error of the scheme is O(τ 2 + h4) and consider the stability analysis of the method on the basis of the classical von Neumann’s theory. In addition, the nearly analytic discretization method for the one-dimensional viscous Burgers’ equation is also constructed. The numerical experiments are performed for several benchmark problems presented in some literatures to illustrate the theoretical results. Theoretical and numerical results show that our method is to be higher accurate and nonoscillatory and might be helpful particularly in computations for the unsteady convection-dominated diffusion problems.

A nearly analytic exponential time difference method for solving 2D seismic wave equations

In this paper, we propose a nearly analytic exponential time difference （NETD） method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations （ODEs）. Then, the converted ODE system is solved by the exponential time difference （ETD） method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in mul- tilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Mar- mousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods.

黏滞声波地震波场模拟的SG-ONADM混合方法

交错网格方法(SG)和最优近似解析离散化方法(ONADM)是两类典型的地震波场数值模拟方法.两类方法各有其优势,相对于ONADM方法,SG方法在单个时间层内的计算更为简单;相对于SG方法,ONADM方法可以在较大空间步长条件下有效压制数值频散.结合两种方法的优势,本文提出了一种新的地震波场模拟方法(SGONADM).该方法对控制方程中的一阶偏导数采用SG方法给出的一阶偏导数近似公式,高阶偏导数采用ONADM方法给出的高阶偏导数逼近公式.理论分析及数值算例表明,SG-ONADM方法保留了两种方法的优势,不仅能在较大空间步长条件下有效压制数值频散,同时具有较低的内存需求量;在对同一计算区域进行波场模拟时,SG-ONADM方法的计算效率要高于SG方法和ONADM方法.最后,我们使用SG-ONADM方法进行黏滞声波波场模拟,研究了黏滞声波在复杂介质中的传播.

A modified nearly analytic discrete method and wavefield simulations in transversely isotropic media

Nearly analytic discrete method (NADM) is a higher accurate method for elastic wave equation that can suppress effectively numerical dispersion caused by discretizing the wave equation. In this paper we investigate the efficient implementation of NADM and present a refinement of the original NADM. Our theoretical analyses show that the modified NADM can improve significantly over the original one in numerous perspectives including numerical errors, storage spaces, and computational costs. Three-component synthetic VSP seismograms in 3-layered transversely isotropic (TI) media generated by the modified NADM are also reported. Theoretical analyses and numerical results show that the modified NADM can reduce storage space about 53 percent and computational costs about 30 percent compared with the original NADM. Moreover the accuracy of the modified NADM in time increases from 2-order of the original NADM to 4-order. Numerical results suggest that the modified NADM is more suitable to large-scale modeling because the modified method has little numerical dispersions even when too-coarse grids are used.

Design of Near-optimal Earth Escape Orbits for Solar Sail Spacecraft

With the increase of the interest in solar sailing, it is required to provide a basis for future detailed planetary escape mission analysis by drawing together prior work, clarifying and explaining previously anomalies. In this paper, a technique for escaping the Earth by using a solar sail is developed and numerically simulated. The spacecraft is initially in a geosynchronous transfer orbit (GTO). Blended solar sail analytical control law, explicitly independent of time, are then presented, which provide near-optimal escape trajectories and maintain a safe minimum altitude and which are suitable as a potential autonomous onboard controller. This control law is investigated from a range of initial conditions and is shown to maintain the optimality previously demonstrated by the use of a single-energy gain control law but without the risk of planetary collision. Finally, it is shown that the blending solar sail analytical control law is suitable for solar sail on-board autonomously control system.

基于改进的层次分析法和接近理想点法的桥梁施工方案风险评价研究

桥梁工程建设具有施工周期长、施工环境差、系统调配复杂、资金流动量大的特点,需要准备大量的施工原料、机械、人力资源。因此,在桥梁施工过程中会面临自然环境、安全施工等多种风险的影响。为保证施工的顺利进行,本文建立了基于改造的层次分析法(Analytic Hierarchy Process,AHP)和接近理想点法(Technique for Order Preference by Similarity to an Ideal Solution,TOPSIS)的桥梁施工方案风险评价模型,通过对风险进行评价研究,提出最优施工方案,以减少施工风险,提高施工效率。