论文标题
关于使用能量分裂和扰动技术的非线性动力学的能源支付动量积分器的设计
On the design of energy-decaying momentum-conserving integrator for nonlinear dynamics using energy splitting and perturbation techniques
论文作者
论文摘要
这项工作提出了一套数值技术，以促进为非线性动力学设计结构的集成器的设计。著名的Labudde-Greenspan集成剂和各种能量摩托车方案在其算法力量定义中采用了差异商公式，随着分母接近零，由于数值不稳定。有必要在不调用商公式的情况下开发具有结构的集成器。在这项工作中，哈密顿系统的势能分为两个部分，并且特别开发的正交规则分别应用于它们。所得的集成剂可以被视为经典的一阶或二阶术语扰动的集成剂，并且能量拆分保证了数值残差中的耗散性质。同时，在设计中尊重不变的保护。对提出的集成商进行了完整的分析，并提供了代表性的数值示例来证明其性能。当检测到差异商中的数值不稳定时，它们可以独立用作非线性问题的能源销售和动量支持方案，或与保存的集成商（例如Labudde-Greenspan Integrator）一起使用的替代选择。
This work proposes a suite of numerical techniques to facilitate the design of structure-preserving integrators for nonlinear dynamics. The celebrated LaBudde-Greenspan integrator and various energy-momentum schemes adopt a difference quotient formula in their algorithmic force definitions, which suffers from numerical instability as the denominator gets close to zero. There is a need to develop structure-preserving integrators without invoking the quotient formula. In this work, the potential energy of a Hamiltonian system is split into two parts, and specially developed quadrature rules are applied separately to them. The resulting integrators can be regarded as classical ones perturbed with first- or second-order terms, and the energy split guarantees the dissipative nature in the numerical residual. In the meantime, the conservation of invariants is respected in the design. A complete analysis of the proposed integrators is given, with representative numerical examples provided to demonstrate their performance. They can be used either independently as energy-decaying and momentum-conserving schemes for nonlinear problems or as an alternate option with a conserving integrator, such as the LaBudde-Greenspan integrator, when the numerical instability in the difference quotient is detected.
