New decomposition methods for parallel computations of large systems
Dragoslav D. Šiljak, Aleksandar I. Zečević · 1993
The main objective of this thesis will be to present a new and general decomposition method for large systems which can take advantage of their special structural properties and produce a wide range of partitions, leading to an optimal solution to the problem of load balancing vs. inter-processor communications. A unique feature of the method is its applicability to dense and sparse matrices alike, as well as to mixtures of these two types of structures. This versatility is achieved by fusing epsilon decomposition, developed recently for identification of weakly coupled (possibly overlapping) subsystems, with our new version of bordered block diagonal decomposition for partitioning sparse systems. A particularly interesting property is the potential of the new scheme to accommodate asynchronous as well as multi-rate computations; applications to power system load-flow problems will be provided to illustrate the flexibility and speed-ups that have been achieved so far using the Intel iPSC/860 parallel processing system. We will also develop general methods for the parallel solution of large systems of linear and nonlinear equations, and discuss their use in transient stability analysis, equivalencing and other circuit related problems.