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A wideband fast multipole accelerated boundary integral equation method for time-harmonic elastodynamics in two dimensions


Toru Takahashi, Department of Mechanical Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan.



This article presents a wideband fast multipole method (FMM) to accelerate the boundary integral equation method for two-dimensional elastodynamics in frequency domain. The present wideband FMM is established by coupling the low-frequency FMM and the high-frequency FMM that are formulated on the ingenious decomposition of the elastodynamic fundamental solution developed by Nishimura's group. For each of the two FMMs, we estimated the approximation parameters, that is, the expansion order for the low-frequency FMM and the quadrature order for the high-frequency FMM according to the requested accuracy, considering the coexistence of the derivatives of the Helmholtz kernels for the longitudinal and transcendental waves in the Burton–Muller type boundary integral equation of interest. In the numerical tests, the error resulting from the fast multipole approximation was monotonically decreased as the requested accuracy level was raised. Also, the computational complexity of the present fast boundary integral equation method agreed with the theory, that is, Nlog N, where N is the number of boundary elements in a series of scattering problems. The present fast boundary integral equation method is promising for simulations of the elastic systems with subwavelength structures. As an example, the wave propagation along a waveguide fabricated in a finite-size phononic crystal was demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.

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