This volume in the Elsevier Series in Electromagnetism presents a detailed, in-depth and self-contained treatment of the Fast Multipole Method and its applications to the solution of the Helmholtz equation in three dimensions. The Fast Multipole Method was pioneered by Rokhlin and Greengard in 1987 and has enjoyed a dramatic development and recognition during the past two decades. This method has been described as one of the best 10 algorithms of the 20th century. Thus, it is becoming increasingly important to give a detailed exposition of the Fast Multipole Method that will be accessible to a broad audience of researchers. This is exactly what the authors of this book have accomplished.

For this reason, it will be a valuable reference for a broad audience of engineers, physicists and applied mathematicians.

Key Features

  • The Only book that provides comprehensive coverage of this topic in one location
  • Presents a review of the basic theory of expansions of the Helmholtz equation solutions
  • Comprehensive description of both mathematical and practical aspects of the fast multipole method and it's applications to issues described by the Helmholtz equation


Researchers and postgraduate students in electrical engineering, acoustics, mechanical engineering and quantum mechanics

Table of Contents

Introduction; elementary factored solutions; structure of FMM algorithms; new results on recurrence relations; translation coefficients; transforms of the Helmhlotz equation; properties and representations of translation operators; applications of multipole methods.


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© 2005
Elsevier Science
eBook ISBN:
Print ISBN:
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About the authors

Nail Gumerov

Affiliations and Expertise

Institute of Advanced Computer Studies, University of Maryland, USA

Ramani Duraiswami

Affiliations and Expertise

Institute of Advanced Computer Studies, University of Maryland, USA