On fast preconditioners for time-harmonic high-frequency wave equations
- Solving time-harmonic wave equations in high frequency regime is an important yet numerically challenging problem. This dissertation presents three fast preconditioners for time-harmonic high frequency wave equations under different problem settings. The first preconditioner adopts a recursive approach from the moving PML sweeping preconditioner for the 3D Helmholtz equation, which reduces both the setup and the application costs to linear while maintaining the iteration number to be frequency insensitive. The second one is an enhancement of the sparsifying preconditioner for periodic structures by taking the local potential information into account, which improves the accuracy of the preconditioner and reduces the iteration number to be essentially independent of the problem size. The third one assembles the key ideas from the first two works, which results in a highly efficient preconditioner for the Lippmann-Schwinger equation, where both the setup and the application costs are linear. Moreover, numerical results show that the iteration number grows only logarithmically as the frequency increases. To the best of our knowledge, this is the first method that achieves near-linear cost to solve the Lippmann-Schwinger equation in 3D high frequency regime.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Institute for Computational and Mathematical Engineering.
|Statement of responsibility
|Submitted to the Institute for Computational and Mathematical Engineering.
|Thesis (Ph.D.)--Stanford University, 2018.
- © 2018 by Fei Liu
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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