A wavelet method for reducing the computational cost of BE-based homogenization analysis |
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| Affiliation: | 1. Department of Mathematics, Iran University of Science and Technology, Tehran, Iran;2. Department of Mathematics, Ilam University, PO Box 69315516, Ilam, Iran;1. Department of Electrical Engineering, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran;2. Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran;1. Department of Mechanical Engineering, Eindhoven University of Technology, Den Dolech 2, 5612 AZ Eindhoven, The Netherlands;2. Materials Innovation Institute, Mekelweg 2, 2628 CD Delft, The Netherlands;1. School of Mechanical Engineering, State Key Lab. for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China;2. School of Mechantronic Engineering, Guilin University of Electronic Technology, Guilin 541004, PR China;1. McConnell Brain Imaging Centre, Montreal Neurological Institute, McGill University 3801, University Street, Montreal, Canada H3A 2B4;2. Department of Neurology & Neurosurgery, McGill University, Canada;3. Instituto de Aplicaciones de las Tecnologı´as de la Información y de las Comunicaciones Avanzadas (ITACA), Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain |
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| Abstract: | A wavelet BEM is applied to the evaluation of the effective elastic moduli of unidirectional composites, based on the homogenization theory. This attempt is devoted to the reduction of computational cost for the BE-based homogenization analysis. Truncation for matrix compression is carried out by the Beylkin-type algorithm. A thresholding value for the truncation is set such that the discretization error of BE solution is comparable to its truncation error. Besides, rearrangement of the BE equations is proposed to attain rapid convergence of iterative solutions. Through investigation of asymptotical convergence of the effective moduli, it is found that the BE-based homogenization analysis ensures the same rate of convergence for effective moduli as for characteristic functions. By applying the wavelet BEM to heterogeneous media which have microstructures with many voids, the effective moduli with agreement of 2–4 digits can be evaluated using 20–50% memory requirements of conventional BE approaches. |
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