>13:30 - 15:00
 SMARTからSMAへー台湾におけるサブミリ波干渉計への取り組みー


>17:00 - 18:30
 A General Theory of Local Preconditioning



COE学術講演会のお知らせ

ミシガン大航空工学科の西川さんに数値計算法について講演して頂きます。
西川さんはROE法で知られる、P.L.Roeの御弟子さんでCFD（数値流体力学）の
基礎研究をされています。皆様お誘い合わせの上是非御参加ください。

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日時：２００４年２月２３日（月）
      １７：００〜１８：３０
場所：自然科学３号館６階セミナー室（６０９）
講演者：西川裕章
ミシガン大学航空工学科
Title:
           A General Theory of Local Preconditioning

Abstract:

Local preconditioning, in the numerical solution of PDEs, 
is the attempt to accelerate convergence to the steady-state 
by altering the transient behavior of the PDEs. The technique
has a particular aim of accelerating the error propagation 
associated with the physical wavespeeds of the PDEs. If these
wavespeeds are very different, there will be error modes that
take many more iterations than others to reach the boundary
and expelled. The idea of local preconditioning is to multiply
the time derivative in the PDE by a matrix (local preconditioning
matrix) such that we equalize, as much as possible, the wavespeeds
of the PDE to make all error modes propagate at the same rate,
thereby accelerating the convergence. Although several such 
preconditioners have already been found for the Euler and the
Navier-Stokes equations, none of them extends easily to other
types of PDEs. Only recently, has a systematic way to derive
optimal preconditioners for any two-dimensional PDEs been
developed in the CFD group at the University of Michigan, based
on elliptic/hyperbolic decomposition. This theory has made it
possible to derive preconditioners for complex systems such as
the magnetohydrodynamic(MHD) equations for which a preconditioner
had not been available before. This talk will give an introduction
to local preconditioning, describe the general theory, discuss its
application to the MHD equations, and end with remark on further
development to come.