Boundary Element Methods [Hardcover]

This work presents a thorough treatment of boundary element methods (BEM) for solving strongly elliptic boundary integral equations obtained from boundary reduction of elliptic boundary value problems? in $\mathbb{R}^3$. The book is self-contained, the prerequisites on elliptic partial differential and integral equations being presented in Chapters 2 and 3. The main focus is on the development, analysis, and implementation of Galerkin boundary element methods, which is one of the most flexible and robust numerical discretization methods for integral equations. For the efficient realization of the Galerkin BEM, it is essential to replace time-consuming steps in the numerical solution process with fast algorithms. In Chapters 5-9 these methods are developed, analyzed, and formulated in an algorithmic way.Preface.- Introduction.- Elliptic Differential Equations.- Elliptic Boundary Integral Equations.- Boundary Element Methods.- Generating the Matrix Coefficients.- Solution of Linear Systems of Equations.- Cluster Methods.- Parametric Surface Approximation.- A Posteriori Error Estimation.- Bibliography.- Index of Symbols.- Index.

From the reviews:

The books main focus is the systematic development of numerical methods to determine the Galerkin solution of boundary integral equations (BIEs) in the context of three-dimensional elliptic boundary value problems (BVPs). & There are separate studies of transmission problems, screen problems, and exterior BVPs for the Helmholtz equation. & In summary, this is a well-written book on the numerical analysis of Galerkin methods for the solution of boundary integral equations. (Paul Andrew Martin, Mathematical Reviews, Issue 2011 i)

This book is & the most comprehensive and self-contained book on BEMs of the ones that exist & . The book is written rigorously and is an important scholarly contribution to the area of boundary elements. & this book is an excellent mathematical monograpl3%