An iterative technique for the finite element analysis of near-incompressible materials

A new preconditioner for the conjugate gradient method applicable to the fi nite element analysis of near-incompressible finite elasticity is presented . The boundary value problem is discretized with a displacement/pressure mi xed formulation. The pressure degrees of freedom are eliminated at the elem ent level. The problem is linearized using a Newton-Raphson technique. Each linear system is solved using the preconditioned conjugate gradient. The n ew preconditioner is based on projections onto a subspace associated with t he bulk modes of deformation. The condition number of the preconditioned st iffness matrix and consequently the rate of convergence of the precondition ed conjugate gradient are totally insensitive to increasing bulk modulus. T he method has been applied to model problems in linear and nonlinear 2D and 3D using a near-incompressible hyperelastic material model. The performanc e of the iterative method compares favorable with direct solvers as well as with conjugate gradient methods for indefinite systems, in terms of storag e requirements, operation count and CPU time. (C) 1999 Published by Elsevie r Science S.A. All rights reserved.