Shape optimization by conventional and extended isogeometric boundary element method with PSO for two-dimensional Helmholtz acoustic problems

Abstract

In this paper, a new approach is developed for applications of shape optimization on the two-dimensional time harmonic wave propagation (Helmholtz equation) in acoustic problems. The particle swarm optimization (PSO) algorithm - a gradient-free optimization method avoiding the sensitivity analysis - is coupled with two boundary element methods (BEM) and isogeometric analysis (IGA). The first method is the conventional isogeometric boundary element method (IGABEM). The second method is the eXtended IGABEM (XIBEM) enriched with the partition-of-unity expansion using a set of plane waves. In both methods, the computational domain is parameterized and the unknown solution is approximated using non-uniform rational B-splines basis functions (NURBS).In the optimization models, the advantage of IGA is the feature of representing the three models; i.e. shape design/analysis/optimization, using a set of control points, which also represent control variables and optimization parameters, making communication between the three models easy and straightforward.A numerical example is considered for the duct problem to validate the presented techniques against the analytical solution. Furthermore, two different applications for various frequencies are studied; the vertical noise barrier and the horn problems, and the obtained results are compared against previously published numerical methods using sensitivity analysis and genetic algorithms to verify the efficiency of the proposed approaches.