Dependency-based algorithms for vector processing of sparse matrix forward/backward substitutions [power system stability analysis]

Recent efforts to improve the execution speed of steady-state and transient analysis of power systems are focused on exploiting parallel and vector processing. In this paper, two algorithms for forward/backward substitutions and their implementation on vector computers are considered. A dependency-based substitution algorithm (DBSA) is proposed and compared with the well known W-matrix method. According to DBSA, the nonzero entries of the factor matrices are rearranged in groups of elements (slices) leading to independent operations. In the implementation of the W-matrix method, the nonzero elements of the inverse factors are grouped in sets (pseudocolumns) to overcome the problem of dependency between addition operations. Test cases, performed on a CRAY X-MP2/216 and a CRAY Y-MP8/464 vector computer, are taken from real-life power system problems and consist in the solution of linear systems with up to 12000 equations. The maximum speed-ups achieved (with respect to a code based on standard sparsity programming) are near to 7 for complex arithmetic and to 11 for real arithmetic.