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A novel truly explicit time-marching procedure for simple and effective analyses of wave propagation models

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Abstract

In this paper, a novel explicit time-marching procedure is proposed for wave propagation analysis. The new method is extremely simple to implement and highly effective, providing a very attractive formulation. It considers staggered forward and backward finite difference expressions to approximate the derivative fields of the model, as well as it introduces adaptive corrections into the computations, improving the accuracy and the stability of the analysis. The novel approach is truly explicit (all force terms are treated explicitly), truly self-starting, and it enables adaptive algorithm dissipation. In fact, the proposed technique stands as a single-step approach that adapts itself (taking into account a highly straightforward algorithm) according to the computed responses, the physical properties of the model and the adopted temporal and spatial discretizations. Numerical results are presented at the end of the paper, illustrating the excellent performance of the novel formulation, considering different (linear and nonlinear) wave propagation models.

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Acknowledgements

The financial support by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) is greatly acknowledged.

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Correspondence to Delfim Soares Jr..

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Soares, D. A novel truly explicit time-marching procedure for simple and effective analyses of wave propagation models. Engineering with Computers 38 (Suppl 2), 1033–1051 (2022). https://doi.org/10.1007/s00366-020-01245-y

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