ROMAN VODICKA and VLADISLAV MANTIC
On variational formulations for elastic domain decomposition problems solved by SGBEM enforcing coupling conditions in a weak form
Received: 31 August 2010
Accepted: 23 December 2010
Mathematics Subject Classification (2000): 65N55, 74S15, 65N22.
Keywords: Domain decomposition, variational principles, saddle point, min-max principle, symmetric Galerkin boundary element method, boundary integral equations, non-matching meshes, non-conforming discretization.
Abstract: The solution of Domain Decomposition Boundary Value Problems of linear elasticity is considered. The proposed approach can be deduced either from a potential energy functional expressed in terms of subdomain displacement fields or from a min-max principle of boundary energy functional expressed in terms of unknown boundary displacement and traction fields. The coupling conditions between two subdomains adjacent to an interface are enforced in a weak form. Two novel features of both functionals are: a distinct role of subdomains lying on the opposite sides of an interface and no requirement of Lagrange multipliers enforcing the coupling conditions. The weak formulation of coupling conditions leads to an easy implementation of SGBEM codes allowing for non-matching meshes along interfaces between subdomains. The presented numerical results confirm an excellent accuracy and convergence behaviour of the numerical solutions, including the cases with non-matching (non-conforming) discretizations of curved interfaces and also with dissimilar materials in subdomains adjacent to an interface.