Abstract
An efficient algorithm is presented for solving optimization problem of geometrical domains in which elliptic boundary value problems are defined. The surface of the domain is implicitly described through a level set function and the moving boundary is determined by the time-dependent dynamic knots of the radial basis functions (RBFs). A method of Partition of Unity (POU) is leveraged to calculate the solution, which divides the domain into some smaller overlapping local sub-domains and reconstructs them into the global surface with less numerical cost. Apart from the convergence properties, numerical results are given and discussed.
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This research work is supported by the Research Grants Council of Hong Kong SAR (Project No. CUHK417309).
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Ho, H.S., Wang, M.Y. & Zhou, M. Parametric structural optimization with dynamic knot RBFs and partition of unity method. Struct Multidisc Optim 47, 353–365 (2013). https://doi.org/10.1007/s00158-012-0848-7
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DOI: https://doi.org/10.1007/s00158-012-0848-7