具有平移动力学的分段光滑系统的保守积分器
Conservative Integrators for Piecewise Smooth Systems with Transversal Dynamics
摘要：
我们引入了具有横向动力学和分段光滑守恒量的分段光滑系统的长期积分的守恒积分器。本质上，对于分段定义的守恒量的分段动力系统，使其轨迹横向交叉到其界面，我们结合Mannshardt的过渡方案和离散乘子方法，以获得保守的积分器能够保持守恒量的机器精度和精度顺序。证明了余维为1个守恒量的情形下，守恒积分的精度阶在穿过界面后保持不变。数值例子说明了整个接口的精度顺序和守恒量的保存。
英文摘要：
We introduce conservative integrators for long term integration of piecewise smooth systems with transversal dynamics and piecewise smooth conserved quantities. In essence, for a piecewise dynamical system with piecewise defined conserved quantities such that its trajectories cross transversally to its interface, we combine Mannshardt's transition scheme and the Discrete Multiplier Method to obtain conservative integrators capable of preserving conserved quantities up to machine precision and accuracy order. We prove that the order of accuracy of the conservative integrators is preserved after crossing the interface in the case of codimension one number of conserved quantities. Numerical examples illustrate the preservation of accuracy order and conserved quantities across the interface.
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