A new partitioned quasi-Newton solver for finite element analyses
by
Martin B Reed
Brunel University, Uxbridge, UK

Iterative solvers are routinely employed for the efficient solution of the global stiffness equations K u = f arising from large-scale finite element analyses. The most common algorithm is preconditioned conjugate gradients. An alternative is to use a partitioned quasi-Newton (QN) algorithm; in this, the QN matrix B_k which approximates K is assembled from element matrices in the same manner as K itself. Each iteration still requires the solution of a linear system B_k p_k = -g_k, however.

In this talk we present a new partitioned QN algorithm, in which it is the inverse of K which is approximated. As a consequence, each iteration involves only a global matrix-vector multiplication.

The efficiency of the new solver is demonstrated on elasticity and elasto-plasticity problems modelled using the FELIPE finite element package.

FELIPE finite element package

Date received: February 15, 2001