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SGBEM with Lagrange multipliers applied to elastic domain decomposition problems with curved interfaces using non‐matching meshes
Author(s) -
Vodička R.,
Mantič V.,
París F.
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2832
Subject(s) - lagrange multiplier , polygon mesh , domain decomposition methods , mortar methods , constraint algorithm , robustness (evolution) , mathematics , finite element method , saddle point , mathematical analysis , mathematical optimization , geometry , structural engineering , biochemistry , chemistry , engineering , gene
An original approach to the solution of linear elastic domain decomposition problems by the symmetric Galerkin boundary element method is developed. The approach is based on searching for the saddle‐point of a new potential energy functional with Lagrange multipliers. The interfaces can be either straight or curved, open or closed. The two coupling conditions, equilibrium and compatibility, along an interface are fulfilled in a weak sense by means of Lagrange multipliers (interface displacements and tractions), which enables non‐matching meshes to be used at both sides of interfaces between subdomains. The accuracy and robustness of the method is tested by several numerical examples, where the numerical results are compared with the analytical solution of the solved problems, and the convergence rates of two error norms are evaluated for h ‐refinements of matching and non‐matching boundary element meshes. Copyright © 2010 John Wiley & Sons, Ltd.