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Today's editor:  Craig Douglas (

Volume 2, Number 6 (June 19, 1992)

Today's topics:

     C++/OOP and (F)WEB question about multigrid
     Paper on effective field theories
     p method domain decomposition paper
     Parallel multigrid codes?
     Journal of Parallel Algorithms and Applications Call for Papers


From: Marcus Speh 
Subject: C++/OOP and (F)WEB question about multigrid

  I would like to know about references and/or people designing
MG algorithms in C++; I received U. Ruede's paper (thanks a lot !)
and he promised another one in the near future (following the SIAM workshop
on scientific C++ computing), but I would need something more basic and
cut to a question like: does it pay/ and why to code in an OOP language ?

 Does anybody know about .web versions, either with
Levy's CWEB, Knuth's type-it-in-by-hand WEB or Krommes' multilingual
FWEB (ratfor, C, C++, fortran) of multigrid algorithms or - packages ?
  I am just starting to use J. Krommes' FWEB for this purpose:
I find it exceptionally well suited for (scientific) visualization of
algorithms. I would appreciate any hint or information.

                                              Marcus Speh

    Editor's Note:  I know that Joe Pasciak ( and
    -------------   Parashkevov Rossen ( both write
                    their codes using fweb.


Date: Thu, 14 May 92 16:16:11 +0200
From: Marcus Speh 
Subject: Paper on multigrid methods for effective field theories


by G. Mack, T. Kalkreuter, G. Palma, M. Speh(*),
Univ. Hamburg, Germany

(with 7 PS figures included, 2 figures missing)

To appear in Springer Lecture Notes of Physics, 
Proc. of the 31. IUKT Schladming on Computational Physics 
eds. C.B. Lang, H. Gausterer

(*)comments, questions, please to:


Effective field theories encode the predictions of a quantum field theory at
low energy.  The effective theory has a fairly low ultraviolet cutoff.  As a
result, loop corrections are small, at least if the effective action contains
a term which is quadratic in the fields, and physical predictions can be read
straight from the effective Lagrangean.

Methods will be discussed how to compute an effective low energy action from a
given fundamental action, either analytically or numerically, or by a
combination of both methods.  Basically, the idea is to integrate out the high
frequency components of fields.  This requires the choice of a "blockspin,"
i.e., the specification of a low frequency field as a function of the
fundamental fields.  These blockspins will be the fields of the effective
field theory.  The blockspin need not be a field of the same type as one of
the fundamental fields, and it may be composite.  Special features of
blockspins in nonabelian gauge theories will be discussed in some detail.

In analytical work and in multigrid updating schemes one needs interpolation
kernels A from coarse to fine grid in addition to the averaging kernels C
which determines the blockspin.  A neural net strategy for finding optimal
kernels is presented.

Numerical methods are applicable to obtain actions of effective theories on
lattices of finite volume.  The special case of a "lattice" with a single
site (the constraint effective potential) is of particular interest.  In a
Higgs model, the effective action reduces in this case to the free energy,
considered as a function of a gauge covariant magnetization.  Its shape
determines the phase structure of the theory.  Its loop expansion with and
without gauge fields can be used to determine finite size corrections to
numerical data.

Keywords: Effective action, 
          lattice gauge theory,
          blockspin methods,
          multigrid updating schemes,
          neural multilevel algorithm.

Comments, questions, suggestions are very welcome. 
Please contact me.
Marcus Speh ( 


Date: Fri, 15 May 92
From: Jonathan M. Smith (
Subject: p method domain decomposition paper

Efficient Domain Decomposition Preconditioning for the p-version Finite Element
                          Method - The mass matrix.

                              Jonathan M. Smith

                             University of Durham
                     Department of Mathematical Sciences
                                Durham DH1 3LE


In recent years we have observed both the increased popularity of the
_p_-version finite element method and domain decomposition preconditioning
techniques.  Current work has given us theoretical and numerical results,
showing that we can reduce the condition number of the stiffness matrix from
polynomial to polynomial logarithmic in the number of degrees of freedom.

However in the _p_-version, we have an additional problem.  We observe that
heirachical bases, which while being very natural bases for the _p_-version
finite element method, are very unnatural bases for the mass matrix.  This can
be seen by noting the growth in the condition number is exponential in _p_,
the degree of the polynomial on each element.

Using methods based on those for the stiffness matrix, derived by Babuska,
Craig, Mandel and Pitkaranta in 1988-89, it is possible to control this
ill-conditioning; resulting in a bound on the relative condition independent
of _p_, for relatively little work.  In this paper we shall present present
empirical results for both triangular and quadrilateral quasi-uniform meshes,
and analytical bounds for quadrilateral meshes.


Date: Mon, 15 Jun 92 06:05:57 PDT
From: lamb@research.CS.ORST.EDU (Ben Lam)
To: douglas@CS.YALE.EDU
Subject: MADPACK

   I am using your MADPACK and wonder whether there is a parallel version
of it.  Do you know of other parallel multigrid and conjugate gradient


--Ben Lam

    Editor's Note:  The parallel version of version 2 of madpack is something
    -------------   I would not want to perpetrate on the world since it is
                    just too hard to use.  There is a new version of madpack,
                    which contains an abstract solver (DAMG) and a 2D/3D
                    Poisson solver (DPMG).  DAMG has 4 multigrid schemes, 11
                    solvers and 5 preconditioners (and can be different per
                    level), handles non PDE problems, any PDE that can be
                    discretized, and optionally will call back your own change
                    level, smoother, or preconditioner subroutines, can be
                    restarted after adding levels (coarser or finer), and will
                    feed your cat when you are on vacation.  DPMG is tailored
                    for 3 different machine architectures, has a variety of
                    projection and interpolation operators, handles uniform or
                    tensor product grids and not completely trivial boundary
                    I am talking to some people about doing a parallel version
                    of DPMG and possibly DAMG that is usable.  Anyone
                    interested in this should contact me directly through Yale

                    FURTHER, I would be very interested in adding parallel
                    multigrid and/or domain decomposition solvers to the code
                    repository, so if you have something, please contribute
                    it.  Research codes are welcome; they do not have to be
                    product quality.


From: PAA Editorial Board
Subject: Journal of Parallel Algorithms and Applications Call for Papers

Journal of
Algorithms and

Editor in Chief:
Professor David J. Evans, Director, Parallel Algorithms Research Centre,
Loughborough University of Technology, Loughborough, Leics. LE11 3TU, U.K.

Editorial Review Board:
      Akl, S.G. (Canada)                  Loizou, G. (UK)
      Boglaev, Y.P. (Russia)              Margaritis, K.G. (Greece)
      Clint, M. (UK)                      Petkov, N. (Netherlands)
      Das, S.K. (USA)                     Quinn, M.J. (USA)
      Dehne, F. (Canada)                  Raymond-Smith, V. (UK)
      Douglas, C.C. (USA)                 Thune, M. (Sweden)
      Jeong, C.S. (Korea)                 Tollenaire, T. (Belguim)
      Lee, R.C.T. (R.O. China)            Vajtersic, M. (Czechoslavakia)
                                          Zenos, S.A. (USA)

Editorial Policy:

      Parallel Algorithms and Applications will publish papers which relate to
      Parallel and Multiprocessor computer systems covering the following

      Parallel Algorithms:  Design, Analysis and Usage in Numerical Analysis,
      Discrete Mathematics, Non-numerical, Geometric, Graphics, Genetic,
      Optimisation, Pattern Recognition, Simulation, Signal/Image Processing
      and Systolic Algorithms.

      Parallel Applications:  Usage in the areas of Artificial Intelligence,
      Systems Software and Compilers, CAD/CAM, Databases, Expert Systems,
      Information Retrieval, Neural Networks, Industrial, Scientific and
      Commercial Applications for Pipelined, Vector, Array, Parallel, and
      Distributed Computers.


Date: Mon, 1 Jun 1992 10:42:10 GMT
Subject: bib directory

  author =      "P. M. De{~Z}eeuw",
  title =       "Matrix--dependent prolongations and restrictions
                 in a blackbox multigrid solver",
  journal =     "J. Comput. Appl. Math.",
  volume =      "33",
  year =        "1990",
  pages =       "1--27"
  author =      "P. M. De{~Z}eeuw",
  title =       "Nonlinear multigrid applied to a one--dimensional
                 stationary semiconductor model",
  journal =     "SIAM J. Sci. Stat. Comput.",
  volume =      "13",
  year =        "1992",
  pages =       "512--530"


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