二维双曲型方程初边值问题的块三对角可扩展并行求解算法

A Scalable Parallel Algorithm of Block Tridiagonal Systemsfor the 2D-Hyperbolic Equation Initial Boundary Value Problem

对二维双曲型方程带Dirichlet边界条件初边值问题的离散系统使用块三对角可扩展并行算法求解.提出了保证精度和最优并行效率的分治策略.使用此方法在上海大学超级计算机"自强3000"上进行了数值实验,实验的结果与理论分析一致.在保证精度的前提下,得到线性加速比,并行效率达到90%以上.

A scalable parallel algorithm of block tridiagonal systems for solving the initial boundary value problem of 2D- hyperbolic equation with the Dirichlet boundary condition is discussed. The divided-and-conquer strategy to ensure the accuracy and best parallel efficiency are developed. The method proposed in this paper has been implemented on the super computer ＂ZiQiang 3000＂ of Shanghai University, and the numerical results match closely with theoretical analysis. With the given accuracy, the line speedup is obtained, and the parallel implementation efficiency over 90 % is reached.