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N. Umetani, S. P. Maclachlan and C. W. Oosterlee, “A Multigrid-Based Shifted Laplacian Preconditioner for a Fourth-Order Helmholtz Discretization,” Numerical Linear Algebra with Applications, Vol. 16, No. 8, 2009, pp. 603-626. http://dx.doi.org/10.1002/nla.634

has been cited by the following article:

• TITLE: Finite-Difference Solution of the Helmholtz Equation Based on Two Domain Decomposition Algorithms

  AUTHORS: Wensheng Zhang, Yunyin Dai

  KEYWORDS: Finite Difference; Domain Decomposition; Nonoverlapping; Overlapping; Helmholtz Equation; Preconditioner

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.1 No.4, November 6, 2013

  ABSTRACT: In this paper, wave simulation with the finite difference method for the Helmholtz equation based on the domain decomposition method is investigated. The method solves the problem by iteratively solving subproblems defined on smaller subdomains. Two domain decomposition algorithms both for nonoverlapping and overlapping methods are described. More numerical computations including the benchmark Marmousi model show the effectiveness of the proposed algorithms. This method can be expected to be used in the full-waveform inversion in the future.