排序方式： 共有27条查询结果，搜索用时 562 毫秒
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均匀介质、复杂各向同性介质和各向异性介质中的地震波传播过程,可用统一形式的标量声波方程描述.考虑到在无损耗条件下,地震波方程描述了地震波场这一个无穷维的哈密顿体系随时间的演化过程,该过程为一个单参数连续辛变换,因而可以在其哈密顿形式表述下导出其辛格式.与显式辛算法相比,隐式辛格式对应的隐式辛几何算法具有无条件稳定的特点,可以允许较大的计算步长.但是由于隐式算法不可避免地面临高阶矩阵的求逆,其每一步的计算速度较慢.为实现矩阵快速求逆,文中采用了螺旋边界条件下谱因式分解的方法.在螺旋边界条件下,需要求逆的矩阵化为带状矩阵,而且其各列非零元素的位置和大小具有非常好的相似性,因而可以采用谱因式分解的方法实现快速LU分解.文中采用二阶精度的隐式蛙跳辛格式和谱因式分解方法,计算了常速度、层状介质和Marmousi模型中的波场.计算表明,隐式辛算法不失为波场计算的一种好方法. 相似文献
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Taeyoung Lee Melvin Leok N. Harris McClamroch 《Celestial Mechanics and Dynamical Astronomy》2007,98(2):121-144
Equations of motion, referred to as full body models, are developed to describe the dynamics of rigid bodies acting under
their mutual gravitational potential. Continuous equations of motion and discrete equations of motion are derived using Hamilton’s
principle. These equations are expressed in an inertial frame and in relative coordinates. The discrete equations of motion,
referred to as a Lie group variational integrator, provide a geometrically exact and numerically efficient computational method
for simulating full body dynamics in orbital mechanics; they are symplectic and momentum preserving, and they exhibit good
energy behavior for exponentially long time periods. They are also efficient in only requiring a single evaluation of the
gravity forces and moments per time step. The Lie group variational integrator also preserves the group structure without
the use of local charts, reprojection, or constraints. Computational results are given for the dynamics of two rigid dumbbell
bodies acting under their mutual gravity; these computational results demonstrate the superiority of the Lie group variational
integrator compared with integrators that are not symplectic or do not preserve the Lie group structure. 相似文献
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射线追踪是地震波走时层析成像的基础,射线空间位置的准确性及射线走时的精度决定了层析成像的可靠性.本文根据哈密尔顿系统可以有效提高程函方程解稳定性的特性,采用辛几何算法（SAM-Symplectic Algorithm Method）及二维三次卷积插值技术进行地震波射线追踪.由于采用了SAM算法,保证了地震波波前精度,提高了射线空间位置的准确性.数值模拟结果表明SAM既能保证哈密尔顿系统的稳定性又具有运算速度快的特点,提高了射线追踪的计算精度. 相似文献
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A new algorithm is developed for long-term integrations of the N-body problem. The method uses symplectic integrations of the Hamiltonian equations of motion for each body. This allows one
to employ individual adaptive time-steps in computations. The efficiency of this technique is demonstrated by several tests
performed for typical problems of Solar System dynamics. 相似文献
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Brett Gladman Martin Duncan Jeff Candy 《Celestial Mechanics and Dynamical Astronomy》1991,52(3):221-240
We discuss the use of symplectic integration algorithms in long-term integrations in the field of celestial mechanics. The methods' advantages and disadvantages (with respect to more common integration methods) are discussed. The numerical performance of the algorithms is evaluated using the 2-body and circular restricted 3-body problems. Symplectic integration methods have the advantages of linear phase error growth in the 2-body problem (unlike most other methods), good conservation of the integrals of the motion, good performance for moderately eccentric orbits, and ease of use. Its disadvantages include a relatively large number of force evaluations and an inability to continuously vary the step size. 相似文献
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面向油气勘探开发提升地震偏移及属性刻划水平 总被引：20，自引：14，他引：6
针对复杂地质条件油气勘探开发的需求,仅就运用地震资料提取地质属性及构建油储模型所可能面临的难点,阐明必需提升地震波传播及成像研究水平的基础理论命题和数值计算的关键环节。文中着重于用形象的数值图像结果,说明开展此类研究的必要性。对我国而言,前新生代海相碳酸盐岩勘探和今后相当时期内对国志经济仍起支撑作用的东部老油田外围及深部油气的勘探开发,这两类研究对象尽管其地质演化年代及过程各异,但对地球物理偏移成像技术进步及油储建模而言,对提升探测的理论所提出的要求,都属于近代的难题,文中还阐明这类研究已是刻不容缓的原因所在。 相似文献
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将声波方程变换至Hamiltion体系,构造了适用于高效声波模拟的二阶显式辛Runge-Kutta-Nyström（RKN）格式,运用根数理论得到此格式的阶条件方程组. 针对两个自由度的辛条件方程组,根据三次项截断误差最小原理得到一种误差最小辛格式;通过分析声波的时间演进方程的稳定性,选择不同的辛系数使演进方程更稳定,并得到了另一种更为稳定辛格式;在频散关系分析中,选择使数值频散最小的辛系数,得到第三种最小频散辛格式. 在理论分析中,这组辛RKN格式相比常见格式在精度控制、数值频散压制以及稳定性提升等方面均具有明显优势;在数值实验中,通过具体算例验证了理论分析的正确性. 相似文献
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