Shape optimization of conductive-media interfaces using an IGA-BEM solver. (English) Zbl 1440.74334
Summary: 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 solver with high convergence rate when compared with low-order BEM. Additionally, an optimization framework comprising a parametric model for the interface’s shape, our IGA-BEM solver, and evolutionary and gradient-based optimization algorithms is developed and tested. The optimization examples demonstrate the efficiency of the framework in generating optimum interfaces for maximizing heat transfer under various geometric constraints.
MSC:
| 74P20 | Geometrical methods for optimization problems in solid mechanics |
| 74S15 | Boundary element methods applied to problems in solid mechanics |
| 65D07 | Numerical computation using splines |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
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