项目名称: 数值求解非线性方程组的预条件研究及其应用
项目编号: No.11471285
项目类型: 面上项目
立项/批准年度: 2015
项目学科: 数理科学和化学
项目作者: 黄正达
作者单位: 浙江大学
项目金额: 60万元
中文摘要: 针对非线性方程组(非线性偏微分方程的离散系统及非线性矩阵方程)的数值求解展开研究。研究非线性方程组的合理形变,以改善非线性方程组的性态,降低非线性迭代方法的计算复杂度;研究非线性迭代本身所具备的预处理功能,以提高迭代方法在偏微分方程数值求解中的效率;结合非线性方程组的构造特性,在关注非线性迭代法的内循环步中线性方程组的代数预处理技术的同时,研究如何进行有效的预处理以保持非线性迭代的收敛阶,提高计算效率。考虑上述内容在不可压缩流体及电磁问题计算中的应用。
中文关键词: 非线性;方程;预处理;迭代算法;计算效能
英文摘要: We focus on the study of the numerical solution to systems of nonlinear equations(arising from the discretion of nonlinear partial derivative equations or nonlinear matrix equations). We study on the suitable transformations of systems in order to improve the property for reducing the computational complexity of iterations used. We study on the preconditioning function of iterations used for systems of nonlinear equations themselves in order to improve the efficiency of iterations in the solution of nonlinear partial derivative equations. Combining with the construction of systems of nonlinear equations, we study on how to implement effectively the algebraic preconditioning in each inner loop in order to keep the convergent speed and boost the efficiency of an iteration we used, while we are considering this preconditioning for each step of the iteration. We consider applications to the computation of problems of incompressible fluid and electromagnetism.
英文关键词: nonlinear;equation;preconditioning;iterative method;computational efficiency