Optimal Parallel Solution of Sparse Triangular Systems

This paper describes a method for the parallel solution of tr/ans_lar sets of equations, appropriate when there are many rlght-hand sides. By preproceuing, the method can reduce the number of parsl/el steps required to solve Zz = b compared to parallel forward or backsolve. AppUcations are to iterative solvers with tzian_d&r preconditioners, to structural sns]ysds, or to power system= applications, where there may be many right-hand sides (not all available = p_o_. The inverse of £ is represented as a product of sparse trian_als_ factors. The problem considered in this paper is to find a factored representation of this inverse of L with the smsllest number of factors "This work was supported in part under NSF Contracts ECS-8822654 and ECS8907391. tThis work was supported by the NAS System= Division and/or DARPA via Cooperstire A_.ement NCC 2-387 between NASA and the University Space R_esrch Association (USR.A). Work was performed st the Research Institute for Advanced Computer Science (RIACS), NASA Ames Research Center, Moffett Field, CA 94035 and at CERFACS, 42 Ave. Gustave Coriolis, 31057 Toulouse Cedex, France. The assistance of CE_ACS and its staff during this author's visit in Au4just 1989 are gratefully acknowledged.