Iterative Solvers
Sparse direct solvers, which have been for a long time the main
workhorses of commercial finite element software,
continue to play an important role in these simulation codes.
However, with the pressing need for higher-fidelity three-dimensional
finite element structural models with millions of degrees of freedom, and
the demands placed by direct solvers on computer resources for such
large problems, a large segment of the computational mechanics community
is increasingly leaning towards iterative solvers.
The significant progress achieved during the last decade in the
development of fast and robust iterative algorithms for the solution
of solid mechanics, plate and shell, and acoustic scattering problems,
and the advent of commercial parallel hardware, are other key
factors for this change in directions.
These factors are interrelated because iterative methods are more
amenable to parallel processing than direct algorithms.
Their development has benefited
and continue to flourish under research programs such as the
National Science Foundation's HPCC (High Performance Computing &
Communications) and the Department of Energy's ASCI (Accelerated
Strategic Computing Initiative), which have emphasized
challenging applications of parallel computation.
-L.L.Thompson
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