Symmetric galerkin boundary integral formulation for interface and multi-zone problems

L. J. Gray, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

86 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)3085-3101
Number of pages17
JournalInternational Journal for Numerical Methods in Engineering
Issue number16
StatePublished - 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


  • Boundary integral method
  • Composite materials
  • Interfaces
  • Multi-zone boundary element analysis
  • Symmetric-Galerkin approximation


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