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T. Airaksinen, E. Heikkola, A. Pennanen and J. Toivanen, “An Algebraic Multigrid based Shifted-Laplacian P[econditioner for the Helmholtz Equation,” Journal of Computational Physics, Vol. 226, No. 1, 2007, pp. 1196-1210.doi:10.1016/j.jcp.2007.05.013

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• TITLE: Frequency-domain Elastic wave Simulation Based on the Nonoverlapping Domain Decomposition Method

  AUTHORS: Wensheng Zhang, Yinyun Dai

  KEYWORDS: Finite Difference; Nonoverlapping DDM; Elastic wave Equation; Wave Simulation; Preconditioner; Absorbing Boundary Conditions

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.3B, October 25, 2013

  ABSTRACT: A new wave simulation technique for the elastic wave equation in the frequency domain based on a no overlapping domain decomposition algorithm is investigated. The boundary conditions and the finite difference discrimination of the elastic wave equation are derived. The algorithm of no overlapping domain decomposition method is given. The method solves the elastic wave equation by iteratively solving sub problems defined on smaller sub domains. Numerical computations both for homogeneous and inhomogeneous media show the effectiveness of the proposed method. This method can be used in the full-waveform inversion.