Parallel computational experience and dynamic scaling for a class of nonlinear systems

This work deals with computational and theoretical aspects of a particular class of algebraic nonlinear systems, known as block bordered. The domain decomposition techniques applied to the modeling of many real world problems give frequently nonlinear systems of this kind and iterative, Newton-like approaches to the solution are widely used. The PICRN algorithm of Feng and Schnabel is an implicit, two stage quasi-Newton method that takes advantage from the structure of the Jacobian system and is very well parallelizable on distributed memory multiprocessors architectures. Here we give the results of an experimentation carried on a nonlinear, particularly ill-conditioned system coming from VLSI simulation, performed on a Cray T3D using the Cray MPP Fortran in virtual shared memory environment. This numerical experience allows to study the algorithm behaviour and gives the reason for the dynamic scaling successively proposed and analyzed.