Highly accurate fast solver for Helmholtz equations

Xian He Sun, Yu Zhuang

Research output: Contribution to conferencePaperpeer-review

2 Scopus citations


In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments, then, are introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.

Original languageEnglish
Number of pages8
StatePublished - 1997
EventProceedings of the 1997 International Conference on Supercomputing - Vienna, Austria
Duration: Jul 7 1997Jul 11 1997


ConferenceProceedings of the 1997 International Conference on Supercomputing
CityVienna, Austria


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