9 Parallel Me ~ thods for Solving Nonlinear Block Bordered Systems of Equationsl

We discuss a group of parallel algorithms, and their implementation, for solving a special class of large sparse nonlinear equations. The type of sparsity occurring in these problems, which arise in VLSI design, structural engineering and many other areas, is called a block bordered structure. We describe an explicit method and several implicit methods for solving block bordered nonlinear problems, and make a mathematical analysis and computational comparisons of the two types of methods. Several variations and globally convergent modifications of the implicit method are also presented. We describe parallel algorithms for solving block bordered nonlinear equations, and present experimental results on the Intel hypercube that show the effectiveness of the parallel implicit algorithms. These experiments include a fairly large circuit simulation that leads to a multi-level block bordered system of nonlinear equations. Accession For ITIS GRA&I DTIC TAB 3 Unannounced 00 Justif jostleDlstrJ~ut1m/ Availability Codes Avail and/or Dist Speolal