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Mathematics > Numerical Analysis

arXiv:1408.1578 (math)
[Submitted on 7 Aug 2014 (v1), last revised 16 Sep 2014 (this version, v2)]

Title:Directional Preconditioner for High Frequency Obstacle Scattering

Authors:Lexing Ying
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Abstract:The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the boundary integral method. This new preconditioner builds a data-sparse approximation of the integral operator, transforms it into a sparse linear system, and computes an approximate inverse with efficient sparse and hierarchical linear algebra algorithms. This preconditioner is efficient and results in small and almost frequency-independent iteration counts when combined with standard iterative solvers. Numerical results are provided to demonstrate the effectiveness of the new preconditioner.
Comments: 17 pages
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1408.1578 [math.NA]
  (or arXiv:1408.1578v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1408.1578

Submission history

From: Lexing Ying [view email]
[v1] Thu, 7 Aug 2014 13:14:56 UTC (136 KB)
[v2] Tue, 16 Sep 2014 19:54:18 UTC (137 KB)
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