Solução de equações de redes de energia eletrica em computadores multiprocessadores

AUTOR(ES)

Antonio Padilha Feltrin

DATA DE PUBLICAÇÃO

1991

RESUMO

This thesis describes a methodology for decomposing the repeat solution process of the equation Ax = b into independent tasks to be done in parallel, based on the matrix inverse factors (W-matrix) with partitions. It is a matter of fact that low-cost multiprocessor computers are now available featuring supercomputer-like performances. The partitioningscheme proposed in this thesis consists of breaking up the W-matrix according the depths of the factorization path tree. In this scheme, all the information needed to generate the partitions can be obtained straightforward from the network factorization path tree. The partitioning algorithm is simple and ease to implement. The elements of Wj matrices, except the last partition, can be obtained directly from L-matrix elements, not requiring extra work. The proposed scheme guarantees that additionaJ fills will be only created in the last partition. The forward and backward solutions are performed by rows, and the strategy proposed is to schedule on each processor the operations corresponding to a row of each partition. It should be kept in mind that the multiprocessor environments are equipped with powerful unit processors and then it seems a sound strategy to perform the . mult-add elementary operations inside the hardware in order to exploit its computing efficiency. This strategy seeks to match the parallel algorithm to the paralleJ architecture. The precedent relations - that give rise to delays - are replaced by mult-add operations performed inside the processor node without external communication. In the last partition, the forward, diagonal and backward solutions may be gathered, and so all the operations can be expressed as the product of matrix W1pby the updated components of vector b. The performance results show that the potentiaJ speedup of the solution time is essentially bounded by the floating point operation capability of each processor, denoting that the methodology is a suitable way to exploit the growing power of the computing technology.

ASSUNTO(S)

sistemas de energia eletrica - automação

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