This paper on "An Experimental with Iterative Equation Solution" was presented at the 3rd International Conference on Quality Assurance and Standards in Finite Element Analysis - 10-12 September 1991, Stratford-upon-Avon, England.

Introduction to Paper

When FEGS first embarked on parallel work in the early 1980's the most obvious route towards major parallelism was via iterative algorithms.
However, an experiment carried out on the attractive-looking Conjugate Gradient method to confirm our hopeful estimates of its rate of convergence gave quite unexpected results: the solution stopped converging while still a long way from the true solution. Worse, changing the precision of the computation did not make any significant difference to the conclusion.
This paper describes in scientific detail the experiment which alerted us to the risks involved, and which led us to take the conventional (factorisation) solver route. IL discusses preconditioning issues.