求解半线性椭圆型方程组的并行算法

Parallel Algorithms for Solving Semi Linear Elliptic Equations

本文结合区域分裂技术、多重网格方法、加速Ｓｃｈｗａｒｚ收敛方法、高低解方法、非线性Ｊａｃｏｂｉ迭代方法和Ｎｅｗｔｏｎ线性化迭代方法，设计了三种求解半线性椭圆型方程（组）的并行算法：并行Ｎｅｗｔｏｎ多重网格算法、并行非线性多重网格算法和并行加速Ｓｃｈｗａｒｚ收敛算法。数值试验说明这三种算法的并行计算是可行的。

Three types of parallel algorithms for sloving semi linear elliptic equations are designed based on domain decomposition,multigrid,accelerated Schwarz,monotone(upper and lower solutions),nonlinear Jacobi iteration and Newton iteration.They are known as the parallel Newton multigrid method,the parallel nonlinear multigrid method and the parallel accelerated Schwarz convergence method.The numerical experiments show that parallel computing of the three algorithms are feasible.