تقرير
Parareal algorithm via Chebyshev-Gauss spectral collocation method
العنوان: | Parareal algorithm via Chebyshev-Gauss spectral collocation method |
---|---|
المؤلفون: | Zhou, Quan, Liu, Yicheng, Wu, Shu-Lin |
سنة النشر: | 2023 |
المجموعة: | Computer Science Mathematics |
مصطلحات موضوعية: | Mathematics - Numerical Analysis |
الوصف: | We present the Parareal-CG algorithm for time-dependent differential equations in this work. The algorithm is a parallel in time iteration algorithm utilizes Chebyshev-Gauss spectral collocation method for fine propagator F and backward Euler method for coarse propagator G. As far as we know, this is the first time that the spectral method used as the F propagator of the parareal algorithm. By constructing the stable function of the Chebyshev-Gauss spectral collocation method for the symmetric positive definite (SPD) problem, we find out that the Parareal-CG algorithm and the Parareal-TR algorithm, whose F propagator is chosen to be a trapezoidal ruler, converge similarly, i.e., the Parareal-CG algorithm converge as fast as Parareal-Euler algorithm with sufficient Chebyhsev-Gauss points in every coarse grid. Numerical examples including ordinary differential equations and time-dependent partial differential equations are given to illustrate the high efficiency and accuracy of the proposed algorithm. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2304.10152 |
رقم الأكسشن: | edsarx.2304.10152 |
قاعدة البيانات: | arXiv |
الوصف غير متاح. |