Recursive Sweeping Preconditioner for the 3D Helmholtz Equation

2015/02/25 by Fei Liu, Lexing Ying, Liu, Fei +1 · 1 citation
Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1502.07266

openalex publication_date 2015/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces the recursive sweeping preconditioner for the numerical solution of the Helmholtz equation in 3D. This is based on the earlier work of the sweeping preconditioner with the moving perfectly matched layers (PMLs). The key idea is to apply the sweeping preconditioner recursively to the quasi-2D auxiliary problems introduced in the 3D sweeping preconditioner. Compared to the non-recursive 3D sweeping preconditioner, the setup cost of this new approach drops from O(N^4/3) to O(N), the application cost per iteration drops from O(Nlog N) to O(N), and the iteration count only increases mildly when combined with the standard GMRES solver. Several numerical examples are tested and the results are compared with the non-recursive sweeping preconditioner to demonstrate the efficiency of the new approach.

Citations

• Notes on Perfectly Matched Layers (PMLs)

Cited by

• A diagonal sweeping domain decomposition method with source transfer for the Helmholtz equation

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