Smith's Vertex Algorithm for Elliptic Problems with Large Jump Coefficients in Two Dimensions

• Main Authors: Li, Jia-yi, 李佳育
• Other Authors: Hsuanseng Cheng
• Format: Others
• Language: zh-TW
• Published: 1997
• Online Access: http://ndltd.ncl.edu.tw/handle/58443678068043752246

碩士 === 國立清華大學 === 數學系 === 85 === In this theis, we carry out some numerical experiments in two dimensionsabout Smith's vertex algorithm for elliptic finite element problem which comefrom the discretizations of second order, positive definite and symmetric elliptic partial equations with large jump coefficients. The correspondinglinear systems are solved by preconditioned conjugate gradient method with respect to some special inner product. It is well-known that smith's algorithm has a uniform convergence rate which is independent of all mesh-size parameters if the variation in coefficients of original differential equation is notlarge. However, if we allow very large variations in coefficients, its convergence behavior is not clear until now. From our numerical data, condition numbers are not always uniformlly bounded with respect to thesejumps in coefficients. We will establish some conjuctures about how its condition numbers varies with all mesh-size parameters in the general case.We remark that these conjectures are different from those about two levelSchwarz methods problems with large-jump coefficients.