A new parallel LU decomposition method
D.C. Yu, H. Wang · IEEE Transactions on Power Systems · 1990
A new method for parallel decomposition of a sparse matrix is presented. The architectural model is a multiprocessor hypercube. The development of this method is based on two concepts, namely, the data flow computer and the path graph. Also, a sparse-oriented operational sequence matrix C is used to store and manipulate the data flow. The C matrix presents the time units and the sequence of all divide and update operations in the LU decomposition. From the C matrix, the minimal completion time, the critical path, and the scheduling of the processors for the LU decomposition can be determined. The proposed method recognizes the fact that the operating times units among division, multiplication, and subtraction in the processor are not the same. Also, communication overhead is included. A number of power systems have been implemented and a number of conditions have been simulated to evaluate the performance of the proposed method. The results are presented and discussed.>