Iterative Methods for Large Sparse Linear Systems Arising from Partial Differential Equations

这项研究的目的是开发、测试和分析计算由椭圆型偏微分方程离散化而产生的大型稀疏线性方程组的解的迭代方法。研究的重点是双周期问题的部分消元技术、由非自伴问题衍生的非对称系统的迭代格式、预条件子和并行计算。对基准问题的分析研究，包括来自三维模型的系统，将与使用串行和并行计算机的数值实验相结合。

The purpose of this investigation is to develop, test, and analyze iterative methods for computing the solutions of large, sparse linear systems arising from the discretization of elliptic partial differential equations. The focus of the research is on partial elimination techniques for two-cycle problems, iteration schemes for nonsymmetric systems derived from non-self-adjoint problems, preconditioners, and parallel computations. An analytic study on benchmark problems, including systems from three-dimensional models, will be combined with numerical experimentation using both serial and parallel computers.