Multi-physics bi-directional evolutionary topology optimization on GPU-architecture

Abstract

Topology optimization has proven to be viable for use in the preliminary phases of real world design problems. Ultimately, the restricting factor is the computational expense since a multitude of designs need to be considered. This is especially imperative in such fields as aerospace, automotive and biomedical, where the problems involve multiple physical models, typically fluids and structures, requiring excessive computational calculations. One possible solution to this is to implement codes on massively parallel computer architectures, such as Graphics Processing Units (GPUs). The present work investigates the feasibility of a GPU-implemented Lattice Boltzmann method for multi-physics topology optimization for the first time. Noticeable differences between the GPU implementation and a Central Processing Unit (CPU) version of the code are observed and the challenges associated with finding feasible solutions in a computational efficient manner are discussed and solved here, for the first time on a multi-physics topology optimization problem. The main goal of this paper is to speed up the topology optimization process for multi-physics problems without restricting the design domain, or sacrificing considerable performance in the objectives. Examples are compared with both standard CPU and various levels of numerical precision GPU codes to better illustrate the advantages and disadvantages of this implementation. A structural and fluid objective topology optimization problem is solved to vary the dependence of the algorithm on the GPU, extending on the previous literature that has only considered structural objectives of non-design dependent load problems. The results of this work indicate some discrepancies between GPU and CPU implementations that have not been seen before in the literature and are imperative to the speed-up of multi-physics topology optimization algorithms using GPUs.

A Review of Topology Optimisation for Fluid-Based Problems

“…Munk et al [172] compared the previous formulation [168] to level set and density-based methods for the case of minimising the compliance of a fluid-loaded baffle plate. Subsequently, Munk et al [173] ported the work to graphics processing unit (GPU) architecture in order to reduce the high computational time for the LBM model. Feppon et al [174] used a level set-based framework to explicitly track and advance the interface using the Hamilton-Jacobi equation.…”

“…Of these 31 papers, 11 use an Ersatz-material, 11 use an adapted approach and only nine use a surface-capturing discretisation method. Lastly, the rest of the papers are distributed as follows: 5 using BESO [168,169,172,173,177]; 2 using phase field [42,59]; 1 using a discrete surface representation [63]; 1 using a geometry-projection method [138]; and 2 utilising the topological gradient [46,74]. Figure 6 shows the distribution of papers in these overall methods.…”

“…It is clear that FEM is the most widely used discretisation method with 134 papers or 76%. The next most used method is LBM at 28 papers [14,20,22,24,26,[36][37][38]44,55,65,69,75,77,78,84,97,108,113,118,119,126,131,163,168,172,173,186] or 16%. PM is the least used method with only a single paper [79].…”

“…For conjugate heat transfer, there are eight in forced convection [110,117,119,122,126,129,132,135] and six in natural convection [150,151,[153][154][155]160]. The fluid-structure interaction category counts four papers [164,168,172,173], but it must be noted that, common for all, the three-dimensional design freedom is severely limited, as the design domain is restricted in the third dimension. Finally, a very large share of the three-dimensional results belong in the category of microstructure and porous media problems with 14 papers [175][176][177][179][180][181][182][183][184][187][188][189]191,192].…”

“…The efforts within wet topology optimisation of FSI problems only cover 15 papers [161,[163][164][165][166][167][168][169][170][171][172][173][174], and these all remain restricted to small deformations and steady-state. Thus, the solution of the problems in the deformed state is either negligible or of minor importance to the optimisation procedure, at least if the design objective is minimum compliance.…”