Implementation and comparison of different versions of the Uzawa algorithm in elasticity problems for incompressible materials
Abstract
Implementation and comparison of different versions of the Uzawa algorithm in elasticity problems for incompressible materials
Incoming article date: 14.05.20132-D and 3-D problems of the elasticity problems for incompressible materials are considered. Solving these problems using the finite-element method results in solving the linear algebraic equations system with sparse matrix. For incompressible materials this system is the system with a saddle point (i.e. the matrix eigen values have different signs). Thus, applying such solving methods as the conjugate gradient method and the generalized minimal residual method is impossible. Uzawa method is suggested to be used for such problems. It is an iterative process, and at each iteration it is necessary to solve the linear algebraic equations system, but this system is without a saddle point. The different variants of Uzawa algorithm are realized within CAE Fidesys software package, and their efficiency is compared in the article.
Keywords: theory of elasticity, incompressible materials, finite-element method, Uzawa algorithm, iteration methods for systems of linear algebraic equations