Parametric structural optimization with dynamic knot RBFs and partition of unity method

Authors:
Hon Shan Ho;Michael Yu Wang;Mingdong Zhou
Affiliations:
Department of Electrical Engineering, The Hong Kong Polytechnic University, Hunghom, Hong Kong;Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong;Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong
Venue:
Structural and Multidisciplinary Optimization
Year:
2013

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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.