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

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.