Shape optimization of conductive-media interfaces using an IGA-BEM solver

Abstract

In this paper, we present a method that combines the Boundary Element Method (BEM) with IsoGeometric Analysis (IGA) for numerically solving the system of Boundary Integral Equations (BIE) arising in the context of a 2-D steady-state heat conduction problem across a periodic interface separating two conducting and conforming media. Our approach leads to a fast converging solver that achieves the same level of accuracy for fewer degrees of freedom, when compared with low-order BEM. Additionally, an optimization procedure is developed and test cases of interface's shape optimization, with the aim of heat transfer maximization under given constraints, are demonstrated.

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

“…Representative works of such studies can be found in Benzaken et al [Benzaken, Herrema, Hsu et al (2017)] and Herrema et al [Herrema, Wiese, Darling et al (2017)], where a surrogate model technique and a generalized pattern search algorithm, respectively, are adopted to optimize the wind turbine blades (see Fig. 6(c)) with complex geometries, Kostas et al [Kostas, Ginnis, Politis et al (2015)] where evolutionary algorithms are utilized to optimize ship-hull shape, Herath et al [Herath, Natarajan, Prusty et al (2015); Kostas, Ginnis, Politis et al (2017); Kostas, Fyrillas, Politis et al (2018)] with genetic algorithms, Lieu et al [Lieu, Lee, Lee et al (2018); Lieu and Lee (2019)] with an adaptive hybrid evolutionary firefly algorithm, Wang et al [Wang, Yu, Shao et al(2018)] with a chaotic particle swarm optimization method, and Zhang et al [Zhang, Li, Shen et al (2019)] with multi-island genetic algorithm and adaptive simulated annealing methods.…”

An Isogeometric Boundary Element Method for 3D lifting flows using T-splines

“…5) it is evident that, as long as the longitudinal coordinate x of P(x) is different from that of the trailing edge, α = 3π/2 at both the suction and the pressure edge of the wing-cap. Then, (23) gives:…”

“…The additional benefits of IGA, related to the smoothness of the basis in FEM, are well known and described in [17,18]. IGA-enhanced BEM approaches have also gained momentum in recent years with works in different fields, including hydrodynamics [19,20,21], structures [22], heat transfer [23], acoustics [24], etc. IGA applications, due to the nature of the approach, require a geometric representation that is adequately flexible for both modelling and analysis.…”

A shape optimisation with the isogeometric boundary element method and adjoint variable method for the three-dimensional Helmholtz equation

“…So far, shape optimisations based on the IGBEM have been investigated in terms of potential problems (or steady-state heat problems) [11][12][13][14][15], elastostatic problems [16][17][18][19][20][21], including 2D thermoelastic problem [22], and acoustic problems in concern [23][24][25][26][27][28][29]. In regard to 2D, Liu et al [23] performed a shape optimisation of a Γ-shaped sound barrier, where the direct differentiation method (DDM) was employed to compute the sensitivity of the objective function with respect to CPs.…”