An Effective Semi-analytic Algorithm for Solving Helmholtz Equation in 1-D

  • Chunhui ZhuEmail author
  • Lijun LiuEmail author
  • Yanhui Liu
  • Zhen Yu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9714)


An efficient and accurate algorithm for solving Helmholtz equation in 1-D is presented in this paper. The key point of this work is to derive the analytic form for the convolution of the Green’s function and a complex exponential function with a finite support domain. A linear subtraction skill is introduced to improve the sampling efficiency. Therefore, the convolution of any function with the Green’s function is given in a semi-analytic form, which can be computed in a fast way with the help of FFT or NUFFT.


Helmholtz equation Analytic convolution FFT NUFFT Linear subtraction 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Electronic ScienceXiamen UniversityXiamenPeople’s Republic of China
  2. 2.Department of AutomationXiamen UniversityXiamenPeople’s Republic of China

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