Cray T3D numerical experience on block bordered nonlinear systems

The block-bordered class of nonlinear systems is typically related to the modeling of medium-to-large size problems, to which domain decomposition techniques are applied. Very frequently this is a preliminary phase of an iterative approach to the solution. The PICRN algorithm by Feng and Schnabel is an implicit, two-stage quasi-Newton method that takes advantage from the structure of the Jacobian system and is very suitable for distributed memory multiprocessor architectures. A Cray T3D experimentation carried out on a nonlinear, particularly ill-conditioned system, coming from a VLSI simulation, allows to study the algorithm behaviour and gives the reason for the needed improvements and theoretical extensions successively proposed.