Abstract:
The numerical simulation of many technical and scientific problems leads to the solution
of extremely large and sparse linear systems. Advanced computer architectures - vector
and parallel computers – and state-of-the-art algorithms have to be used in order to
solve these systems with a sufficient accuracy in a reasonable time. Importantly, the
simulation of many problems is only possible by the combination of technical and
algorithmic progress.
Classical solvers for symmetric and positive definite matrices will be reviewed. From this
starting point it will be shown that modern solvers rely on the same principles. With
this knowlege the methods can be easily classified despite of their confusing variety.
Morever, it will be shown how to parallelize modern solvers. Thus, the efficient use of
advanced computer architectures is combined with modern algorithms to achieve a high
perfomance.