Computationally Efficient Boundary Element Methods for High-Frequency Helmholtz Problems in Unbounded Domains

  • Timo Betcke
  • Elwin van ’t WoutEmail author
  • Pierre Gélat
Part of the Geosystems Mathematics book series (GSMA)


This chapter presents the application of the boundary element method to high-frequency Helmholtz problems in unbounded domains. Based on a standard combined integral equation approach for sound-hard scattering problems we discuss the discretization, preconditioning and fast evaluation of the involved operators. As engineering problem, the propagation of high-intensity focused ultrasound fields into the human rib cage will be considered. Throughout this chapter we present code snippets using the open-source Python boundary element software BEM++ to demonstrate the implementation.


Boundary Element Method HIFU Treatment Boundary Integral Operator Boundary Integral Formulation Helmholtz Problem 
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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Timo Betcke
    • 1
  • Elwin van ’t Wout
    • 2
    Email author
  • Pierre Gélat
    • 3
  1. 1.Department of MathematicsUniversity College LondonLondonUK
  2. 2.School of Engineering and Faculty of MathematicsPontificia Universidad Católica de ChileSantiagoChile
  3. 3.Department of Mechanical EngineeringUniversity College LondonLondonUK

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