[ont.events] Can A Direct Method Be Optimal? Can Schwarz Splitting Be Preconditioned? Solutions From Templator Operators.

ylfink@water.waterloo.edu (ylfink) (02/05/88)

DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES

SCIENTIFIC COMPUTATION SEMINAR

                    - Thursday, February 11, 1988

Dr.  Wei  Pai  Tang,  a member of this department, will
speak on ``Can A Direct Method Be Optimal?  Can Schwarz
Splitting  Be Preconditioned?  Solutions From Templator
Operators''.

TIME:                4:30 PM

ROOM:              MC 5097

ABSTRACT

Template  operator  is  a  new structure for the linear
operator  in  finite dimensional space.  It removes the
artificial   sequential   constraint   in   the  matrix
structure,  and  maintains the topological frame of the
original   continuous   problem  from  which  a  finite
dimensional linear operator is derived.  In particular,
for  a  sparse  linear  operator,  the proximity of the
variables  and  the  locality  of the operator are well
maintained.

In  this  talk,  we  show  the exponential decay of the
inverse   for   a   sparse  template  operator  can  be
successfully used to obtain an efficient implementation
of  Schwarz Splitting.  More specifically, a guide line
for   a   good   splitting   is   discussed   and  some
preconditioned   Schwarz   Splitting   techniques   are
studied.

Template  operator  is  also a good tool for developing
new  parallel  algorithms.  The ``fastest'' fast solver
for the model problem is proposed here.  The complexity
of  this  algorithm is 10N.  This algorithm can also be
generated  to  the model problem on an irregular region
or in three dimensional space.