论文标题
一维弹性动力学的优化方法
Optimization Methods for One Dimensional Elastodynamics
论文作者
论文摘要
我们提出了一种解决保护法系统的新方法，该方法接受了时间限制形式的各种表述，并涵盖了P系统或弹性动力学系统。该方法包括使用受约束的梯度下降来求解具有变化公式的隐式方案，而不连续的盖尔金有限元方法用于空间离散化。最终的优化方案表现良好，它在冲击附近处理振荡方面具有优势，并且计算成本的劣势可以通过在优化方法中使用步骤选择的技术来部分缓解。
We propose a new approach for solving systems of conservation laws that admit a variational formulation of the time-discretized form, and encompasses the p-system or the system of elastodynamics. The approach consists of using constrained gradient descent for solving an implicit scheme with variational formulation, while discontinuous Galerkin finite element methods is used for the spatial discretization. The resulting optimization scheme performs well, it has an advantage on how it handles oscillations near shocks, and a disadvantage in computational cost, which can be partly alleviated by using techniques on step selection from optimization methods.
