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.