Title: Domain decomposition algorithms for three-dimensional elasticity problems
Abstract: In this work, we develop domain decomposition algorithms for three dimensional elasticity problems. The material parameters in our model problem can be highly heterogeneous and geometry of our model problem may have joints and contacts. For discretization of such a complicated model, mortar finite element methods are used [1,9] . The resulting linear system in the mortar discretization is very large and very ill-condit ioned. In order to find a fast and reliable solution we apply an iterative method with a preconditioner to the resulting linear system. The preconditioner is built by decomposing the original linear system into one global coarse problem and many smaller local problems, which are obtained by using domain decomposition methods. We develop the preconditioners by using BDDC (Balancing Domain Decomposition by Constraints) and FETI-DP (Dual-Primal Finite Element Tearing and Interconnecting) methods, which are known to be the most scalable domain decomposition methods for second and fourth order elliptic problems, see [4,5,2,8]. Using these preconditioners, we prove that the condition number of the preconditioned linear system is bounded by C(1 + log(H/h)) 2 , where H/h denotes the size of each local problems and C is a constant independent of the number of subdomains in the partition and the jump of the material parameters. This bound is known to be optimal for standard conforming finite element discret ization of elasticity problems [7] and we extend the result to the case with mortar finite element discretization, i.e., nonconforming finite element discretization. We also present numerica l experiments of our methods for the models with discontinuous material parameters and for nonconforming subdomain partitions. Our methods can be extended to incompressible elasticity problems [3,6]
Publication Year: 2011
Publication Date: 2011-11-01
Language: en
Type: article
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