Penalty Spring Stabilization of Singular Jacobians

Abstract

A limit-point treatment is presented which is a synthesis of two earlier techniques. To traverse limit points, Sharifi and Popov (1970) introduced fictitious stiffnesses in the form of rank-one updates but did not use auxiliary systems. Rheinboldt (1981) discussed the use of auxiliary systems in conjunction with the partition of the Jacobian matrix. The procedure presented in this paper avoids the need for partitioning and consequent special treatment of the elements in the ith row and column of K; only the diagonal entry is changed. It enjoys the added advantage that none of the auxiliary system right-hand sides requires access to elements of the K matrix.