Symmetric Galerkin Boundary Element Method (PDF)

Symmetric Galerkin Boundary Element Method presents an introduction as well as recent developments of this accurate, powerful, and versatile method. The formulation possesses the attractive feature of producing a symmetric coefficient matrix. In addition, the Galerkin approximation allows standard continuous elements to be used for evaluation of hypersingular integrals.

FEATURES
. Written in a form suitable for a graduate level textbook as well as a self-learning tutorial in the field.
. Covers applications in two-dimensional and three-dimensional problems of potential theory and elasticity. Additional basic topics involve axisymmetry, multi-zone and interface formulations. More advanced topics include fluid flow (wave breaking over a sloping beach), non-homogeneous media, functionally graded materials (FGMs), anisotropic elasticity, error estimation, adaptivity, and fracture mechanics.
. Presents integral equations as a basis for the formulation of general symmetric Galerkin boundary element methods and their corresponding numerical implementation.
. Designed to convey effective unified procedures for the treatment of singular and hypersingular integrals that naturally arise in the method. Symbolic codes using Maple® for singular-type integrations are provided and discussed in detail.
. The user-friendly adaptive computer code BEAN (Boundary Element ANalysis), fully written in Matlab®, is available as a companion to the text. The complete source code, including the graphical user-interface (GUI), can be downloaded from the web site http://www.ghpaulino.com/SGBEM_book. The source code can be used as the basis for building new applications, and should also function as an effective teaching tool. To facilitate the use of BEAN, a video tutorial and a library of practical examples are provided.