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The use of periodic structures as noise abatement devices has already been the object of considerable research seeking to understand its efficiency and see to what extent they can provide a functional solution in mitigating noise from different sources. The specific case of sonic crystals consisting of different materials has received special attention in studying the influence of different variables on its acoustic performance. The present work seeks to contribute to a better understanding of the behavior of these structures by implementing an approach based on the numerical method of fundamental solutions (MFS) to model the acoustic behavior of two-dimensional sonic crystals. The MFS formulation proposed here is used to evaluate the performance of crystals composed of circular elements, studying the effect of varying dimensions and spacing of the crystal elements as well as their acoustic absorption in the sound attenuation provided by the global structure, in what concerns typical traffic noise sources, and establishing some broad indications for the use of those structures.

Abstract. In this paper we present a variant of the Accelerated Overrelaxation iterative method (AOR), denoted by modified AOR-like method (MAORlike method) for solving the augmented systems, i.e., the AOR-like method with three real parameters ω, r and α. For special values of ω, r and α we get the MSOR-like method, the AOR-like method and the SOR-like method. An equation relating the involved parameters and the eigenvalues of the iteration matrix of the MAOR-like method is obtained. Furthermore, some convergence conditions for the MAOR-like method are derived. This paper generalizes the main results of Li, Li (2007). Numerical examples are presented to show that, for a suitable choice of the involved parameters, the MAOR-like method is superior when compared to the above iterative methods and to the SSOR-like method presented by Zheng, Wang, and Wu (2009).

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