国際応用数理評議会（ICIAM  Board Meeting）出席のため来日される海外の数値解
析および応用数学の研究者による下記のセミナーを開催いたします。奮ってご参加くだ
さい。またご興味のある方々に、下記案内を回して下さると幸いです。来聴歓迎、入場
無料。


数値解析と応用数学に関するセミナー

開催日： 2002年5月23日（木）、24日（金）、27日（月）
場所： 学術総合センター（東京、竹橋）　12階　1212−1213会議室
　　　　（ご案内・地図： http://www.nii.ac.jp/help-j.html ）
主催：　日本応用数理学会、国立情報学研究所
入場：　無料
組織委員：　三井 斌友（名古屋大学）、速水　謙（国立情報学研究所）
問い合わせ：三井 斌友（mitsui@malt.math.human.nagoya-u.ac.jp）
速水　謙（hayami@nii.ac.jp  tel. 03-4212-2553)

日程

5月23日（木）

1:30-1:40 pm オープニング（三井 斌友 教授）

1:40 - 2:40 pm
 Professsor Olavi Nevanlinna (Helsinki University of Technology)
   Meromorphic Resolvents and Iterative Methods.

2:50 - 3:50 pm
Ian H. Sloan (The University of New South Wales)
Numerical Integration with Many, Many Variables.

4:00 - 5:00 pm
 Professor Alain Damlamian (University of Paris, )
   Multi-Scale Homogenization and Periodic Unfolding.


5月24日（金）

2:00 - 3:00 pm
Professor Reinhard Mennicken  (University of Regensburg)
   Spectral Theory for Systems of Differential Operators of Mixed Order
and Applications

3:10 - 4:10 pm
Professor Rolf Jeltsch (ETH Zuerich)
The Method of Transport for Systems of Hyperbolic Conservation Laws.


5月27日（月）

2:00 - 3:00 pm                                            　
Professor Bob Russel (Simon Fraser University)
Adaptive Algorithms for Solving Time-Dependent PDEs.

3:10 - 4:10 pm
Professor Robert O’Malley (University of Washington):
Shock Motion for Singularly Perturbed Partial Differential Equations.


講演概要:

Professsor Olavi Nevanlinna (Helsinki University of Technology)
Meromorphic Resolvents and Iterative Methods.

   Scalar meromorphic functions can have Picard special values, that is,
values which are not taken at all.  More generally, certain values can be
defective but the sum of all defects is bounded.
   We have studied operator valued meromorphic functions, developed a
perturbation theory for them (Ann. Acad. Sci.Fenn. Mathematica 2000, Vol 25,
3-30), which can be used to  show for example that growth of  resolvents as
meromorphic functions is robust under small rank perturbations.   We have
published earlier that the growth  of resolvent can be linked to speed of
iterations  (together with Saara Hyv"onen, BIT, 2000, vol 40, 267-290).
   In this talk we  link  the  Picard defect values to  "nonnormality",  by
showing that if the operator is normal and the growth  of the resolvent is
of finite order, then  the resolvent is  not defective in the sense  of
value distribution.
   We also  give a result of the following general nature. Suppose  f(z)  is
a scalar meromorphic function and  A is a bounded operator  with a
meromorphic resolvent, then  f(zA) is an operator valued meromorphic
function and its growth   is  is on the level of the maximum of the that of
f and the resolvent.
   The new results are intended to appear  in a  monograph   in the AMS
Fields Institute monograph series.


Ian H. Sloan (The University of New South Wales)
Numerical Integration with Many, Many Variables.

Nowadays integration problems with very large numbers of variables arise in
many applications, including mathematical finance.  While Monte Carlo
methods are available for problems with any number of integration variables,
increasingly attention has turned to quasi-Monte Carlo methods.  These have
the appearance of Monte Carlo methods, but with the integration points
chosen deterministically instead of randomly.  This talk will review the
history of quasi-Monte Carlo methods, finishing with recent step-by-step
constructions of shifted lattice rules with very large numbers of points and
hundreds of variables.


Professor Alain Damlamian (University of Paris, )
Multi-Scale Homogenization and Periodic Unfolding.

   We present the method of periodic unfolding and its applications to
periodic homogenization, including the  multi-scale case.  This sheds new
light on the so called two-scale convergence but is much more elementary and
straightforward.  It also applies to cases which  two-scale convergence has
not been able to handle.  Some examples will be also given.


Professor Reinhard Mennicken  (University of Regensburg)
Spectral Theory for Systems of Differential Operators of Mixed Order and
Applications

(Abstract to be announced.)


Professor Rolf Jeltsch (ETH Zuerich):
The Method of Transport for Systems of Hyperbolic Conservation Laws.

   In 1992 M. Fey introduced the method of transport for the Euler equations
of gas dynamics.  We shall derive this method for the Euler equations using
the advection form.  In this form one sees more easily the characteristic
propagation directions inherent in the differential equation.  A
straightforward decomposition and linearisation of this advection form leads
to a genuinely multi-dimensional method. This method is robust, but of first
order only.  It is indicated how one can obtain a second order scheme.  It
is then shown that the method can be applied not only to the Euler equations
of gas dynamics but also to the shallow water equation, MHD, Navier-Stokes
and equations to model elasto-plastic waves in solids.  We discuss briefly
the treatment of boundary conditions and mesh adaptations as well as
parallelisations for MIMD computers.


Professor Bob Russel (Simon Fraser University)
Adaptive Algorithms for Solving Time-Dependent PDEs.

Of fundamental concern in the development of numerical algorithms for
solving time dependent PDEs is the construction of the numerical grid.  It
must adjust to extreme features of the physical solution while conforming to
boundary behaviour and maintaining smoothness.  This problem has proven to
be extremely challenging and has motivated extensive mathematical analysis
(e.g., for harmonic maps) and numerical
experimentation.
    We shall review recent progress in the development of moving grid
algorithms and outline some of the outstanding problems which remain.
Numerical software will be illustrated for a variety of challenging
problems.


Professor Robert O'Malley (University of Washington):
Shock Motion for Singularly Perturbed Partial Differential Equations.

   We consider the solution of some special initial boundary value problems
for parabolic PDEs in a bounded spatial domain and show how shocks can move
on very long time intervals.  Results follow from an analysis of the tail
behavior for the appropriate shock profile function.