From: rick@cs.arizona.edu (Rick Schlichting)
Newsgroups: comp.research.japan
Subject: Kahaner Report: Preconditioned Conjugate Gradient Symp., Keio U, 2/92
Date: 27 Sep 92 03:39:06 GMT


  [Dr. David Kahaner is a numerical analyst on sabbatical to the 
   Office of Naval Research-Asia (ONR Asia) in Tokyo from NIST.  The 
   following is the professional opinion of David Kahaner and in no 
   way has the blessing of the US Government or any agency of it.  All 
   information is dated and of limited life time.  This disclaimer should 
   be noted on ANY attribution.]

  [Copies of previous reports written by Kahaner can be obtained using
   anonymous FTP from host cs.arizona.edu, directory japan/kahaner.reports.]

To: Distribution
From: 
 David K. Kahaner
 US Office of Naval Research Asia
 (From outside US):  23-17, 7-chome, Roppongi, Minato-ku, Tokyo 106 Japan
 (From within  US):  Unit 45002, APO AP 96337-0007
  Tel: +81 3 3401-8924, Fax: +81 3 3403-9670
  Email: kahaner@cs.titech.ac.jp
Re: Preconditioned Conjugate Gradient Symposium, Keio U, 2/92
21 Sept 1992
This file is named "keio8pcg.92"

ABSTRACT. Abstracts of papers presented at the 8th Preconditioned
Conjugate Gradient Symposium, 28 Feb 1992, at Keio University, Yokohama
Japan are presented. 

This symposium was the eighth in a series focusing on computational
linear algebra. These are small one day meetings, with ten or fewer
papers presented, mostly in Japanese. The organizers are 

     Prof. Takashi Nodera
     Dept of Mathematics
     Keio University
     3-14-1 Hiyoshi Kohoku
     Yokohama 223 Japan
      Tel: +81 44-63-1141 ext 3762
      Email: NODERA@MATH.KEIO.AC.JP

and Dr. Makoto Natori (University of Tsukuba). The full text of the
papers presented at the symposium is given in the Keio University
publication, "Advances in Numerical Methods for Large Sparse Sets of
Linear Equations No. 8, 1992", edited by Natori and Nodera. Contact
either Nodera or me for copies or further information.

Parallel Processing for Scientific Computing (Keio Univ)

Finite element analysis of natural convection in concentric horizontal annuli
using simultaneous relaxation of velocity and Bernoulli function
     Y. Kato and T. Tanihashi (Dept. of Mech. Eng., Fac. of Sci. and Tech.,
     Keio Univ., Japan) (Paper in Japanese)

     Abstract
          In previous research, a simple finite-element method using 
     simultaneous relaxation of velocity and the Bernoulli function was 
     presented to simulate three-dimensional flow problems.  In the 
     present paper, this scheme is expanded to consider heat convection 
     problems.  In order to reduce the computational storage, coefficient 
     matrices are calculated by simple integration formulas for an eight-
     node isoparametric element.  Natural convection in horizontal 
     concentric annuli is calculated to certify the scheme.  The present 
     method is stable in heat convection analysis and the numerical 
     results agree well with the experimental results.  

Preconditioned conjugate gradients and domain decomposition methods
     Peter Bjorstad (Universitetet I Bergen) (Paper not printed)

     Abstract
          We describe and discuss the conjugate gradient method used to 
     accelerate the convergence of the linear systems arising from 
     elliptic partial differential equations.  In particular, we consider 
     the class of domain decomposition methods.  Both iterative 
     substructuring methods (non-overlapping) as well as overlapping 
     methods (Schwarz methods) will be covered.  These methods are very 
     promising when used in parallel computing environments.  The talk 
     will consider both MIMD parallel implementations as well as 
     massively parallel SIMD algorithms.  Examples will be given from 
     elliptic equations with discontinuous coefficients as well as from 
     the equations of elasticity used by structural engineers.  

Implementation and evaluation of ILU-preconditioned iterative methods on Cenju
parallel computer (Paper in Japanese)
     T. Washio (C&C Info. Lab., NEC), et al.

     Abstract
          The Implementations of parallel processings of ILU 
     preconditioning by PB(m) ordering (1991 S. Doi) and red/black 
     ordering (popular parallel ordering) on Cenju parallel computer, 
     composed of 64 processor elements, are introduced.  By using 64 
     processor elements, these implementations lead to speedups of 53 and 
     55, compared with using one processor elements, by PB(m) and 
     red/black respectively, for a cofficient matrix of the system of 
     linear equation, which arises from 5-point discretization of 2D 
     convection-diffusion equation, with 384x384 grids.  And, CPU time of 
     each preconditioning is almost equal each other.  Finally, it is 
     shown by numerical experiments using ICCG and Bi-CGSTAB that the 
     iteration counts and also CPU time of the whole iteration process by 
     PB(m) are about half of those by red/black.  

Inverse iteration method with a complex parameter
     Toshio Suzuki (Dept. of Mathematics, Yamanashi Univ.) (Paper in English)

     Abstract
          An improved method for inverse iteration is proposed.  
     Introducing a complex parameter, the inverse iteration for a 
     symmetric matrix is improved with more accurate error estimates for 
     the eigenvector than the traditional one.  Some numerical examples 
     are also shown.  

Implicit RK formula for parallel computers
     Akira Goto (School of Engineering, Nagoya Univ.), et al. (Paper in
       English)

     Abstract
          We propose a new A-stable 3-stage fourth order implicit Runge-
     Kutta (RK) formula which can be carried out in parallel.  Our 
     parallel algorithms can be applied to large-scale linear ordinary 
     differential equations such as Y'=Ly or y'-L(t)y+g(t).  An actual 
     implementation on parallel computers with 3 CPU's and shared memory 
     shows that our algorithm attains 2.9 times speed-up for the 
     equations of y'=Ly.  However the performance for the variable 
     coefficient equations y"=L(t)y+g(t) is worse than Gear's method 
     because of the feature of our formula.  
          Moreover, we introduce k_{IRK} as the product of the minimum 
     eigenvalue of the formula parameter matrix A and the stability 
     factor R(infinity)^2.  This index can be seen to represent the 
     degree of accuracy in the solution of the parallelized implicit RK 
     method through some numerical experiments.  

L^2-stability analysis for the convection diffusion difference problems
     S. Nagoya (Dept. of Computer Science & Information Mathematics, The 
     Univ.  of Electro-Communications), et al.  (Paper in Japanese)

     Abstract
          This paper concerns the characterization of the von Neumann 
     condition for a family of convection diffusion difference schemes.  
     Our consideration is restricted to the schemes which employ the 
     difference operators with equi-distance five points as the 
     approximations of the spacial first order and second order 
     differential operators.  As for the time discretization, the forward 
     difference is employed.  In this paper we say that the scheme 
     satisties the von Neumann condition if the maximum of the absolute 
     value of the amplification coefficient of the scheme is less than or 
     equal to 1.  
          The aim of this paper is to find mathematically rigorously the 
     characterization of the von Neumann condition for some difference 
     schemes, which include the 4th order schemes, with the aid of 
     computing faicilities.  

Stiff equations derived from diffusion-convection equations
     Kayoko Yamaguchi (Graduate Student, Doctoral Program in Engineering,
     Univ. of Tsukuba) (Paper in Japanese)

     Abstract
          This report investigates eigenvalues of coefficient matrices in 
     stiff equations which lie in the right half plane.  Some numerical 
     results for simple models to heat equation show that the eigenvalues 
     depend on the ratio of the diffusion term to the convection term.  

Visualization of convergence behavior of Bi-CG STB method, Part 2
     S. Fujino (Keisan Ryutai Rikigaku Lab.), et al. (Paper in Japanese)

     Abstract
          Convergence behavior of CGS and Bi-CG STAB methods is shown 
     using visualization technique.  This technique enables us to 
     observe, in particular, local convergence of the approximate 
     solutions at the iterative steps.  In this contribution we make 
     clear why the oscilations of the approximate solutions occur in the 
     physical domain by reconstructing of the approximate solutions with 
     the residual polynomials Rk(lambda), Qk(lambda).  

Some attempts of direct QR method for diagonalization of real-dense-symmetric
        matrix
     Y. Beppu (Shotoku Gakuen Womens' College, Uzura, Gifu, 500, Japan), 
     et al.  (Paper in Japanese)

     Abstract
          The nature of QR method was investigated by using some 
     different type Direct QR routines on four typical matrices.  After a 
     few QR iterations: QR decomposition and RQ reconstruction of a 
     matrix, the reconstructed matrix approximately becomes tri-diagonal 
     form.  
          Origin shift plays an important role for rapid convergence of 
     QR iterations.  Regularity of matrix is sometimes lost when origin 
     shift is applied to QR iteration.  Development of a stable QR 
     decomposition algorithms seems to be quite important.  



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