摘要
一维抛物型偏微分方程可以用精细积分方法精确求解。当精细积分中的矩阵指数函数用Pad 逼近来代替时 ,可以得到一系列由简到繁、精度由低到高的差分格式 ,因而便于根据实际需要进行选取。常见的求解抛物型方程的差分格式如古典显式格式、隐式格式及六点差分格式为其中的特例。Pad 逼近格式主要包括矩阵运算和线性方程组求解。本文利用 Pad 逼近格式对应的方程组系数矩阵为带状矩阵的特点 ,把原来在整个区域上求解的问题转化为分区域求解 ,在 TRANSPUTER并行机上实现了该问题的并行算法 ,并对该并行算法的时间复杂度进行了分析。算例结果表明 Pad 逼近并行算法有很好的计算效果和并行效率。
HT5SS]The one\|dimensional partial parabolic equations can be solved by the highprecision integration method. A series of finite difference schemes, which are from simple to complex in forms, and from low order to high in accurate,can be provided as the exponential matrix function is approximated via the Pade approximants. The traditional explicit method, implicit method and six\|point difference method are examples of the Pade approximants. The solutions of the Pade approximants are mainly concerned about the calculation of matrix and linear equations. Take advantge of the narrow band's property of the equations' coefficient matrix, the problem can be solved in sub\|domain instead of the whole domain. A parallel algorithm based on these methods is presented and evaluated in this paper. The numerical examples given in this paper show that the finite difference scheme via Pade approximants are effective and their parallel computing are efficient.
出处
《计算力学学报》
CAS
CSCD
2000年第4期428-434,共7页
Chinese Journal of Computational Mechanics
