| Summary: | 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.
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