The Boundary Element Method

The boundary element method (BEM) has established itself as a powerful numerical analysis tool. The distinct feature of BEM is that it reduces the problem dimensionality by one. This implies that two- and three-dimensional problems can be solved in one and two dimensions, respectively. For this reason, BEM offers particular advantages in comparison with domain methods, such as the finite element method. BEM is a global technique, which is based on the superposition of the free-field Green's functions and as such, does not easily lend itself to the development of algebraic eigenvalue formulation. In the past two decades, research activities in this area have increased rapidly, which has resulted in a wealth of literature on BE eigenanalysis.In The Boundary Element Method, a chronological review of all BE eigenvalue methods that have been proposed to date is provided. Subjects treated range from an outline of the non-algebraic BE eigenvalue analysis technique, such as the Determinant Search Method, to in-depth consideration of more elegant BE algebraic eigenvalue formulations, such as the Dual and Multiple Reciprocity, Particular Integral, Fictitious Function and Series Expansion Methods. The fundamentals of BEM are also provided in the book. In order to illustrate application of the methods presented, numerous examples are included. In addition, advantages and disadvantages of each eigenformulation are discussed and recommendations are given to increase the robustness and reliability of BE eigenvalue analyses through future research in this evolving area.This book is intended for researchers and professionals in the field of engineering and BE code development. It provides comprehensive information on BEM and numerous ideas for future research. Moreover it would serve as a valuable textbook for the education of graduate engineering students.