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Symmetric Galerkin boundary integral formulation for interface and multi‐zone problems
Author(s) -
Gray L. J.,
Paulino Glaucio H.
Publication year - 1997
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/(sici)1097-0207(19970830)40:16<3085::aid-nme194>3.0.co;2-u
Subject(s) - galerkin method , boundary (topology) , boundary value problem , singular boundary method , finite element method , boundary element method , boundary knot method , mathematics , interface (matter) , mathematical analysis , numerical analysis , matrix (chemical analysis) , symmetry (geometry) , geometry , physics , mechanics , structural engineering , engineering , materials science , composite material , bubble , maximum bubble pressure method
Domains containing an ‘internal boundary’, such as a bi‐material interface, arise in many applications, e.g. composite materials and geophysical simulations. This paper presents a symmetric Galerkin boundary integral method for this important class of problems. In this situation, the physical quantities are known to satisfy continuity conditions across the interface, but no boundary conditions are specified. The algorithm described herein achieves a symmetric matrix of reduced size. Moreover, the symmetry can also be invoked to lessen the numerical work involved in constructing the system of equations, and thus the method is computationally very efficient. A prototype numerical example, with several variations in the boundary conditions and material properties, is employed to validate the formulation and corresponding numerical procedure. The boundary element results are compared with analytical solutions and with numerical results obtained with the finite element method. © 1997 John Wiley & Sons, Ltd.