© 2015

The Helmholtz Equation Least Squares Method

For Reconstructing and Predicting Acoustic Radiation


Part of the Modern Acoustics and Signal Processing book series (MASP)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Sean F. Wu
    Pages 1-10
  3. Sean F. Wu
    Pages 11-26
  4. Sean F. Wu
    Pages 63-79
  5. Sean F. Wu
    Pages 81-99
  6. Sean F. Wu
    Pages 129-144
  7. Sean F. Wu
    Pages 145-162
  8. Sean F. Wu
    Pages 163-193
  9. Back Matter
    Pages 221-233

About this book


This book gives a comprehensive introduction to the Helmholtz Equation Least Squares (HELS) method and its use in diagnosing noise and vibration problems. In contrast to the traditional NAH technologies, the HELS method does not seek an exact solution to the acoustic field produced by an arbitrarily shaped structure. Rather, it attempts to obtain the best approximation of an acoustic field through the expansion of certain basis functions. Therefore, it significantly simplifies the complexities of the reconstruction process, yet still enables one to acquire an understanding of the root causes of different noise and vibration problems that involve arbitrarily shaped surfaces in non-free space using far fewer measurement points than either Fourier acoustics or BEM based NAH. The examples given in this book illustrate that the HELS method may potentially become a practical and versatile tool for engineers to tackle a variety of complex noise and vibration issues in engineering applications.


Helmholtz Least Squares Method implementation non-spherical nearfield acoustic holography predicting acoustic fields reconstructing acoustic fields solving NVH issues transient nearfield acoustical holography

Authors and affiliations

  1. 1.Department of Mechanical EngineeringWayne State UniversityDetroitUSA

About the authors

Sean F. Wu received his Ph.D. from Georgia Institute of Technology, U.S.A. in 1987. He joined the Mechanical Engineering Department at Wayne State University as an Assistant Professor in 1988, was promoted to Associate Professor in 1995 and Professor in 1999, was selected in an unanimous vote as the Charles DeVlieg Professor in 2002 and appointed by the Board of Governors to the rank of University Distinguished Professor in 2005.

Dr. Wu holds the rank of Fellow in the American Society of Mechanical Engineers and the Acoustical Society of America, and serves as an Associate Editor and Express Letter Editor for the Journal of the Acoustical Society of America and Co-Editor-In-Chief for Journal of Computational Acoustics.

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