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International Journal of Frontiers in Engineering Technology, 2021, 3(5); doi: 10.25236/IJFET.2021.030510.

A Parallel Preconditioned Solver for the 3D Helmholtz Equation


Dongsheng Cheng, Jiaxi Lin, Kaicheng Lan and Yuexin Zheng

Corresponding Author:
Dongsheng Cheng

School of Software Engineering, Shenzhen Institute of Information Technology, Shenzhen, China


Discretization of the 3D Helmholtz equation leads to a linear system of a large size. The resulting linear system is difficult to be solved by a sequential method. In this paper, we propose a parallel preconditioned Bi-CGSTAB method for solving the system based on MPI(Message Passing Interface). We precondition the 3D Helmholtz equation by the complex shifted-Laplacian preconditioner, and employ the Krylov subspace method Bi-CGSTAB combined with the multi-grid to solve the resulting system. Numerical experiments are presented to illustrate the efficiency of the parallel Preconditioned solver.


Helmholtz equation, Preconditioner, Parallel, Bi-CGSTAB, Multigrid

Cite This Paper

Dongsheng Cheng, Jiaxi Lin, Kaicheng Lan and Yuexin Zheng. A Parallel Preconditioned Solver for the 3D Helmholtz Equation. International Journal of Frontiers in Engineering Technology (2021), Vol. 3, Issue 5: 84-90. https://doi.org/10.25236/IJFET.2021.030510.


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