CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:   A Neumann-Neumann Domain Decomposition Algorithm for Solving Plate 
         and Shell Problems 

SPEAKER: Jan Mandel, Department of Mathematics, UCD
         (Based on joint work with Patrick Le Tallec and Marina Vidrascu, 
          INRIA, Le Chesnay, France)

DATE:    Wednesday, September 6, 1995

PLACE:   Math Conference Room - Suite 540
         UCD Building, 1250 14th St., Denver

TIME:    2:30 pm (Refreshments served at 2:15 pm)



ABSTRACT

This talk is concerned with a new Neumann-Neumann type preconditioner
of large scale linear systems arising from plate and shell problems.
The advantage of the new method is a smaller coarse space than earlier
method of the authors, which improves parallel scalability. A new
abstract framework for Neumann-Neumann preconditioners is used to prove
optimal convergence properties of the method. The convergence estimates
are independent of the number of subdomains, coefficient jumps between
subdomains, and depend only polylogarithmically on the number of
elements per subdomain.

We formulate and prove an approximate parametric variational principle
for Reissner-Mindlin elements as the plate thickness approaches zero,
which  makes the results applicable to a large class of non-locking
elements in everyday engineering use.  The theoretical results are
confirmed by computational experiments on model problems as well as
examples from real world engineering practice.