Dongsheng Cheng, Jiaxi Lin, Kaicheng Lan and Yuexin Zheng
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
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