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2015•ESAIM Mathematical Modelling and Numerical AnalysisOpen access

Domain decomposition method for crack problems with nonpenetration condition

E. M. Rudoy

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Abstract

The work deals with an iteration method for numerical solving the equilibrium problem of two-dimensional elastic body with a crack under the nonpenetration condition. The method is based on the domain decomposition and Uzawa’s algorithm. To construct an algorithm, the domain is partitioned into two subdomains whose common boundary contains the crack. In each subdomain the linear problems are solved. We use Lagrangian multipliers to couple the solutions and provide the nonpenetration condition on the crack.

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What this paper is about

The work deals with an iteration method for numerical solving the equilibrium problem of two-dimensional elastic body with a crack under the nonpenetration condition. The method is based on the domain decomposition and Uzawa’s algorithm. To construct an algorithm, the domain is partitioned into two subdomains whose common boundary contains the crack. In each subdomain the linear problems are solved. We use Lagrangian multipliers to couple the solutions and provide the nonpenetration condition on the crack.

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Available abstract

The work deals with an iteration method for numerical solving the equilibrium problem of two-dimensional elastic body with a crack under the nonpenetration condition. The method is based on the domain decomposition and Uzawa’s algorithm. To construct an algorithm, the domain is partitioned into two subdomains whose common boundary contains the crack. In each subdomain the linear problems are solved. We use Lagrangian multipliers to couple the solutions and provide the nonpenetration condition on the crack.

Key concepts: Domain decomposition methods, Mathematics, Fictitious domain method, Domain (mathematical analysis), Mortar methods, Decomposition method (queueing theory), Numerical analysis, Lagrange multiplier

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