Comparative analysis of different variants of the Uzawa algorithm in problems of the theory of elasticity for incompressible materials

Abstract

Different variants of the Uzawa algorithm are compared with one another. The comparison is performed for the case in which this algorithm is applied to large-scale systems of linear algebraic equations. These systems arise in the finite-element solution of the problems of elasticity theory for incompressible materials. A modification of the Uzawa algorithm is proposed. Computational experiments show that this modification improves the convergence of the Uzawa algorithm for the problems of solid mechanics. The results of computational experiments show that each variant of the Uzawa algorithm considered has its advantages and disadvantages and may be convenient in one case or another.

Keywords

• Theory of elasticity
• Incompressible materials
• Finite-element method
• The Uzawa algorithm
• Iterative methods
• Systems of linear algebraic equations