Convergence Behavior of Non-Linear Equation Solvers in Fuel Performance Analysis Codes

Abstract

Algorithms for fuel perfomance analysis codes involve solution of simultaneous non linear equations at every data point of analysis with total permanent strains or strain increments as unknowns. Solution of these unknowns involves major part of the total code run time. Hence substantial part of the code development effort is directed towards the implementation of a reliable convergence scheme. As non linear equations can have multiple roots there is always a possibility of converging to a point other than the desired one, rno.ce so in case of improper initial guess.In computer code COMTA convergence has oeen ensured by incorporating elaborate guess subroutines and two independent classes of convergence schemes. First convergence scheme is based on Newton-Raphson algorithm and the other is based on optimization technique.In this paper the above schemes are compared in terms of total number of itereations, total run time, effect of allowable error in solution, mode of progress towards convergence point, effect of improper guess etc.