Stokes问题的多尺度小波Galerkin方法  

A Multi-scale Wavelet Galerkin Method for Solving Boundary Integral Equations of Stokes Problems

作　　者：谭蔼美[1] 吴伟芬[1] 黄晓园[1] 

机构地区：[1]广西师范学院数学科学学院

出　　处：《广西师范学院学报（自然科学版）》2012年第3期15-20,共6页Journal of Guangxi Teachers Education University(Natural Science Edition)

摘　　要：用多尺度小波Galerkin快速算法求解Stokes问题.首先,根据位势理论将Stokes问题转化为第一类边界积分方程.其次,构造具有高阶消失矩的多尺度小波基,并用多尺度小波Galerkin方法求解Stokes方程得到稠密矩阵.最后提出相应的矩阵截断策略,对稠密矩阵进行压缩成为稀疏阵.在保持收敛阶前提下,大大减少了计算量.We develop in this paper a fast multi-scale wavelet Galerkin method for solving Stokes problems.Firstly,we transfer the Stokes problem to boundary integral equations of the first kind according to potential theory.Secondly,we structure multi-scale wavelet basis with disappearing moment of high order,and acquire dense matrices by using multi-scale wavelet Galerkin methods to solve Stokes equation.At last,we propose matrix truncation strategy and compress dense matrices into sparse matrices.This method leads to reducing the amount of computation under preservation of the convergence order.

关 键 词：STOKES问题 多尺度小波空间 GALERKIN方法 矩阵截断策略 

分 类 号：O175[理学—数学]