Advanced spectral boundary integral equation method for modeling wave propagation in elastic metamaterials with doubly periodic arrays of rectangular crack-like voids.

To investigate accurately unique and advanced wave properties in elastic metamaterials advanced and efficient numerical methods are needed. The paper presents an extended boundary integral equation method for simulating elastic wave scattering by doubly periodic arrays of rectangular crack-like voids. The convergence of the arising double series is proved and the convergence rate is carefully analyzed. Employing the results of the investigation of the convergence rate, an algorithm for fast numerical calculation of double series is proposed to reduce computational costs through preliminary analytical evaluation and the proposed summation strategy. The efficiency of the extended boundary integral equation method is demonstrated and examples of the calculated transmission coefficients exhibiting the influence of the introduction of the doubly periodic array are given. [ABSTRACT FROM AUTHOR]