论文标题
一种新的变分离散技术，用于绕过管理方程的初始价值问题
A new variational discretization technique for initial value problems bypassing governing equations
论文作者
论文摘要
由于自然的经典和量子描述都取决于因果关系和变异原则，因此我们为经典初始价值问题（IVP）开发了一种新颖且高度的离散处方。它基于具有双倍自由度的优化（动作）功能，该功能是使用单个正规化列表（SBP）操作员离散化的。作为优化任务配制，它使我们能够获得经典的轨迹，而无需得出运动方程。我们在这种情况下开发的新颖正规化是受初始数据的弱点的启发，通常部署在IVP的现代处理中，并使用仿射坐标实施。我们从数值上证明了我们方法在具有经典运动方程式的系统中的稳定性，准确性和收敛性能，这些运动方程式具有一阶和二阶导数。我们在具有经典运动方程的系统中的方法属性属性，其及时具有一阶和二阶导数。
Motivated by the fact that both the classical and quantum description of nature rest on causality and a variational principle, we develop a novel and highly versatile discretization prescription for classical initial value problems (IVPs). It is based on an optimization (action) functional with doubled degrees of freedom, which is discretized using a single regularized summation-by-parts (SBP) operator. Formulated as optimization task it allows us to obtain classical trajectories without the need to derive an equation of motion. The novel regularization we develop in this context is inspired by the weak imposition of initial data, often deployed in the modern treatment of IVPs and is implemented using affine coordinates. We demonstrate numerically the stability, accuracy and convergence properties of our approach in systems with classical equations of motion featuring both first and second order derivatives in time. onvergence properties of our approach in systems with classical equations of motion featuring both first and second order derivatives in time.
