This book is an introduction to the fast multipole boundary element method (BEM), which has emerged in recent years as a powerful and practical numerical tool for solving large-scale engineering problems based on the boundary integral equation (BIE) formulations. The book integrates the classical results in BIE formulations, the conventional BEM approaches applied in solving these BIEs, and the recent fast multipole BEM approaches for solving large-scale BEM models. The topics covered in this book include potential, elasticity, Stokes flow, and acoustic wave problems in both two-dimensional (2D) and three-dimensional (3D) domains.

The book can be used as a textbook for a graduate course in engineering and by researchers in the field of applied mechanics and engineers from industries who would like to further develop or apply the fast multipole BEM to solve large-scale engineering problems in their own field. This book is based on the lecture notes developed by the author over the years for a graduate course on the BEM in the Department of Mechanical Engineering at the University of Cincinnati. Many of the results are also from the research work of the author's group at Cincinnati and from the collaborative research conducted by the author with other researchers during the last 20 years.

The book is divided into six chapters. Chapter 1 is a brief introduction to the BEM and the fast multipole method. Discussions on the advantages of the BEM are highlighted.