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.