CSAR Seminar
SPEAKER: Kenn K. Q. Zhang,
University of Illinois at Chicago
TITLE:
A Discrete Operator Splitting Superposition-Based Parallel Finite
Element Method for Incompressible Flows
DATE: Wednesday, March 26, 2008
TIME: 12:00 Noon
PLACE: 2240 DCL
1304 W. Springfield Ave., Urbana, IL
ABSTRACT
The popular juxtaposition-based domain decomposition is intuitive, but
it involves complicated pre-processing and sometimes communications of
excessive quantities, is less adapted for continuous numerical methods
and restricted to field problems, and requires the inter-subdomain
boundary treatments which is different from the inter-element
treatments, and is method dependent and sometimes problem dependent.
In this presentation a superposition-based domain decomposition is
proposed, which employs element-by-element construction,
processor-level assembling, and condensed random data structure.
Superposition-based parallelization shows great flexibility in
partitioning the computational domains, communicates more consolidated
data, and can be applied beyond field problems. Moreover,
superposition-based parallelization can, as an option, follow the same
numerical process as its serial counterpart to produce digit-by-digit
the same result, which makes code development and debugging much
easier. Solving large scale indefinite systems continues to pose as a
challenging issue for incompressible flows and may lead to a way to
solve compressible and incompressible flows in a unified approach. In
this presentation, the discrete operator splitting (DOS) technique is
proposed to break the original ill-natured large indefinite system into
two smaller well-natured definite systems coupled through source
terms. The underpinning idea of the technique is to seamlessly combine
the splitting and iterations together. These two techniques (the
parallelization and the DOS) are implemented with a continuous finite
element method and applied to several incompressible Navier-Stokes
benchmark flows. The algorithm for the logical parallelization,
an upgrade from the superposition-based parallelization, will also be
detailed.