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Multi-Physics Bi-directional Evolutionary Topology Optimization on GPU-architecture
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.D. J. Munk thanks the Australian government for their financial support through the Endeavour Fellowship scheme. The authors would like to acknowledge the UK Consortium on Mesoscale Engineering
Sciences (UKCOMES) EPSRC grant No EP/L00030X/1 for providing the HPC capabilities used in this article
Multiâphysics biâdirectional evolutionary topology optimization on GPUâarchitecture
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
Geodesic Convolutional Shape Optimization
Aerodynamic shape optimization has many industrial applications. Existing
methods, however, are so computationally demanding that typical engineering
practices are to either simply try a limited number of hand-designed shapes or
restrict oneself to shapes that can be parameterized using only few degrees of
freedom. In this work, we introduce a new way to optimize complex shapes fast
and accurately. To this end, we train Geodesic Convolutional Neural Networks to
emulate a fluidynamics simulator. The key to making this approach practical is
remeshing the original shape using a polycube map, which makes it possible to
perform the computations on GPUs instead of CPUs. The neural net is then used
to formulate an objective function that is differentiable with respect to the
shape parameters, which can then be optimized using a gradient-based technique.
This outperforms state- of-the-art methods by 5 to 20% for standard problems
and, even more importantly, our approach applies to cases that previous methods
cannot handle
A topology optimization method in rarefied gas flow problems using the Boltzmann equation
This paper presents a topology optimization method in rarefied gas flow problems to obtain the optimal structure of a flow channel as a configuration of gas and solid domains. In this paper, the kinetic equation, the governing equation of rarefied gas flows, is extended over the entire design domain including solid domains assuming the solid as an imaginary gas for implicitly handling the gas-solid interfaces in the optimization process. Based on the extended equation, a 2D flow channel design problem is formulated, and the design sensitivity is obtained based on the Lagrange multiplier method and adjoint variable method. Both the rarefied gas flow and the adjoint flow are computed by a deterministic method based on a finite discretization of the molecular velocity space, rather than the DSMC method. The validity and effectiveness of our proposed method are confirmed through several numerical examples
A "poor man's" approach to topology optimization of natural convection problems
Topology optimization of natural convection problems is computationally
expensive, due to the large number of degrees of freedom (DOFs) in the model
and its two-way coupled nature. Herein, a method is presented to reduce the
computational effort by use of a reduced-order model governed by simplified
physics. The proposed method models the fluid flow using a potential flow
model, which introduces an additional fluid property. This material property
currently requires tuning of the model by comparison to numerical Navier-Stokes
based solutions. Topology optimization based on the reduced-order model is
shown to provide qualitatively similar designs, as those obtained using a full
Navier-Stokes based model. The number of DOFs is reduced by 50% in two
dimensions and the computational complexity is evaluated to be approximately
12.5% of the full model. We further compare to optimized designs obtained
utilizing Newton's convection law.Comment: Preprint version. Please refer to final version in Structural
Multidisciplinary Optimization https://doi.org/10.1007/s00158-019-02215-
OpenLB User Guide: Associated with Release 1.6 of the Code
OpenLB is an object-oriented implementation of LBM. It is the first
implementation of a generic platform for LBM programming, which is shared with
the open source community (GPLv2). Since the first release in 2007, the code
has been continuously improved and extended which is documented by thirteen
releases as well as the corresponding release notes which are available on the
OpenLB website (https://www.openlb.net). The OpenLB code is written in C++ and
is used by application programmers as well as developers, with the ability to
implement custom models OpenLB supports complex data structures that allow
simulations in complex geometries and parallel execution using MPI, OpenMP and
CUDA on high-performance computers. The source code uses the concepts of
interfaces and templates, so that efficient, direct and intuitive
implementations of the LBM become possible. The efficiency and scalability has
been checked and proved by code reviews. This user manual and a source code
documentation by DoxyGen are available on the OpenLB project website
Topology Optimization of Two Fluid Heat Exchangers
A method for density-based topology optimization of heat exchangers with two
fluids is proposed. The goal of the optimization process is to maximize the
heat transfer from one fluid to the other, under maximum pressure drop
constraints for each of the fluid flows. A single design variable is used to
describe the physical fields. The solid interface and the fluid domains are
generated using an erosion-dilation based identification technique, which
guarantees well-separated fluids, as well as a minimum wall thickness between
them. Under the assumption of laminar steady flow, the two fluids are modelled
separately, but in the entire computational domain using the Brinkman
penalization technique for ensuring negligible velocities outside of the
respective fluid subdomains. The heat transfer is modelled using the
convection-diffusion equation, where the convection is driven by both fluid
flows. A stabilized finite element discretization is used to solve the
governing equations. Results are presented for two different problems: a
two-dimensional example illustrating and verifying the methodology; and a
three-dimensional example inspired by shell-and-tube heat exchangers. The
optimized designs for both cases show an improved heat transfer compared to the
baseline designs. For the shell-and-tube case, the full freedom topology
optimization approach is shown to yield performance improvements of up to 113%
under the same pressure drop
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