论文标题
线性隐式多步骤方法以进行时间集成
Linearly Implicit Multistep Methods for Time Integration
论文作者
论文摘要
解决初始价值问题的时间整合方法是许多科学和工程模拟的重要组成部分。隐式时间积分器对于它们的稳定性属性是可取的，对时间步长的限制显着放松。但是，隐式方法需要每个时间步中一个或多个非线性方程系统的解决方案，对于大型模拟而言，这可能非常昂贵。本文介绍了一个线性隐式多步法方法（LIMM）的新家族，该家族仅需要每个时间步中一个线性系统的解决方案。提出了这些方法的顺序条件和稳定理论，以及设计和实施考虑。与广泛使用的BDF方法相比，开发了具有相似误差系数但有改善的稳定性区域的实用订购方法。新的LIMM方法的自动启动变量的数值测试和变量订单实现显示了相似的BDF实现的可测量性能改进。
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing restrictions on timestep size. However, implicit methods require solutions to one or more systems of nonlinear equations at each timestep, which for large simulations can be prohibitively expensive. This paper introduces a new family of linearly implicit multistep methods (LIMM), which only requires the solution of one linear system per timestep. Order conditions and stability theory for these methods are presented, as well as design and implementation considerations. Practical methods of order up to five are developed that have similar error coefficients, but improved stability regions, when compared to the widely used BDF methods. Numerical testing of a self-starting variable stepsize and variable order implementation of the new LIMM methods shows measurable performance improvement over a similar BDF implementation.
