Numerical methods for constrained optimization in 2D and 3D biomechanics

This paper formulates, analyses and discusses 2D and 3D static and dynamic model problems in the orthopaedic practice. Finite element approximations, algorithms and iterative methods for constrained optimization are discussed . Since the conjugate gradient method is one of the most effective methods for both unconstrained and constrained optimization, it can be applied with out or with preconditioning for solving the basic step of the discretized p roblem. A comparison of several preconditioned conjugate gradient methods i s discussed. The problems discussed are applied to analyses of real patient s. Finally, the numerical results are discussed. Copyright (C) 1999 John Wi ley & Sons, Ltd.