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FAST MULITPOLE METHODS FOR HELMHOLTZ EQUATION IN 3 DIMENSIONS
Nail Gumerov, Ramani Duraiswami
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.
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.