On the generalization of wavelet diagonal preconditioning to the Helmholtz equation

2010/10/22 by Christiaan C. Stolk, Stolk, Christiaan C.
Computer Science · Earth and Planetary Sciences · Physics and Astronomy · #65N22 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA) #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.1010.4764

openalex publication_date 2010/10/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

We present a preconditioning method for the multi-dimensional Helmholtz equation with smoothly varying coefficient. The method is based on a frame of functions, that approximately separates components associated with different singular values of the operator. For the small singular values, corresponding to propagating waves, the frame functions are constructed using ray theory. A series of 2-D numerical experiments demonstrates that the number of iterations required for convergence is small and independent of the frequency. In this sense the method is optimal.

Citations

• Sweeping Preconditioner for the Helmholtz Equation: Hierarchical Matrix Representation
• Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers

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