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Parareal Methods for Highly Oscillatory Ordinary Differential Equations.
| 题名： | Parareal Methods for Highly Oscillatory Ordinary Differential Equations. |
| 作者： | Ariel, G.; Kim, S.; Tsai, R. |
| 关键词： | Oscillations, Dynamic systems, Algorithms, Hamiltonians, Numerical analysis, Differential equations, Parareal algorithms, Computational engineering |
| 摘要： | We introduce a new parallel in time (parareal) algorithm which couples multiscale integrators with fully resolved fine scale integration and computes highly oscillatory solutions for a class of ordinary differential equations in parallel. The algorithm computes a low-cost approximation of all slow variables in the system. Then, fast phase-like variables are obtained using the parareal iterative methodology and an alignment algorithm. The method may be used either to enhance the accuracy and range of applicability of the multiscale method in approximating only the slow variables, or to resolve all the state variables. The numerical scheme does not require that the system is split into slow and fast coordinates. Moreover, the dynamics may involve hidden slow variables, for example, due to resonances. Convergence of the parareal iterations is proved and demonstrated in numerical examples. |
| 总页数： | Ariel, G.; Kim, S.; Tsai, R. |
| 报告类型： | 科技报告 |
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