Automatic transition from simulation to one‐shot shape optimization with Navier‐Stokes equations

Özkaya, Emre; Gauger, Nicolas R.

doi:10.1002/gamm.201010011

Cited by 20 publications

(5 citation statements)

References 13 publications

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“…AD has repeatedly proven its value in scientific computing, especially for large simulation codes where symbolic derivatives are not feasible and finite differences produce numerically unstable and unreliable results. Areas of application include discrete adjoint solvers [32,1], shape optimization [11,24], inverse problems [2], and machine learning [13]. A comprehensive introduction to AD is given in [12].…”

Section: Introductionmentioning

confidence: 99%

Event-Based Automatic Differentiation of OpenMP with OpDiLib

Blühdorn,

Sagebaum,

Gauger

2021

Preprint

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We present the new software OpDiLib, a universal add-on for classical operator overloading AD tools that enables the automatic differentiation (AD) of OpenMP parallelized code. With it, we establish support for OpenMP features in a reverse mode operator overloading AD tool to an extent that was previously only reported on in source transformation tools. We achieve this with an event-based implementation ansatz that is unprecedented in AD. Combined with modern OpenMP features around OMPT, we demonstrate how it can be used to achieve differentiation without any additional modifications of the source code; neither do we impose a priori restrictions on the data access patterns, which makes OpDiLib highly applicable. For further performance optimizations, restrictions like atomic updates on the adjoint variables can be lifted in a fine-grained manner for any parts of the code. OpDiLib can also be applied in a semi-automatic fashion via a macro interface, which supports compilers that do not implement OMPT. In a detailed performance study, we demonstrate the applicability of OpDiLib for a pure operator overloading approach in a hybrid parallel environment. We quantify the cost of atomic updates on the adjoint vector and showcase the speedup and scaling that can be achieved with the different configurations of OpDiLib in both the forward and the reverse pass.

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Section: Introductionmentioning

confidence: 99%

Event-Based Automatic Differentiation of OpenMP with OpDiLib

Blühdorn,

Sagebaum,

Gauger

2021

Preprint

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“…Within the context of simultaneous analysis and design (SAND), we deal with intermediate flow and adjoint solutions, resulting in approximated values for the objective function and the gradient. This is also called One Shot optimization [14,15]. The presented methodology, incorporating an analytic approximation of the Hessian, is expected to be superior in comparison to other approximations of the Hessian, as it does not suffer from noise, when the Hessian is constructed from inexact gradients, as it would happen in Quasi-Newton methods.…”

Section: Introductionmentioning

confidence: 99%

Combining Sobolev Smoothing with Parameterized Shape Optimization

Schmidt¹,

Gauger²

2021

Preprint

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On the one hand Sobolev gradient smoothing can considerably improve the performance of aerodynamic shape optimization and prevent issues with regularity. On the other hand Sobolev smoothing can also be interpreted as an approximation for the shape Hessian. This paper demonstrates, how Sobolev smoothing, interpreted as a shape Hessian approximation, offers considerable benefits, although the parameterization is smooth in itself already. Such an approach is especially beneficially in the context of simultaneous analysis and design, where we deal with inexact flow and adjoint solutions, also called One Shot optimization. Furthermore, the incorporation of the parameterization allows for direct application to engineering test cases, where shapes are always described by a CAD model. The new methodology presented in this paper is used for reference test cases from aerodynamic shape optimization and performance improvements in comparison to a classical Quasi-Newton scheme are shown.

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“…Hence we discuss briefly several techniques to reduce the huge consumption of memory here. First of all, memory-reduced methods such as one shot (also called Simultaneous Analysis and Design (SAND)) [30] and checkpointing [31,32] are widely used in the implementation of time-dependent optimization problems. The SAND approach might work well in engineering applications, especially when the forward problem is slowly varying in time.…”

Section: Introductionmentioning

confidence: 99%

Discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice Boltzmann method

Geier

Liu

et al. 2014

Computers & Mathematics with Applications

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a b s t r a c tA discrete adjoint sensitivity analysis for fluid flow topology optimization based on the lattice Boltzmann method (LBM) with multiple-relaxation-times (MRT) is developed. The lattice Boltzmann fluid solver is supplemented by a porosity model using a Darcy force. The continuous transition from fluid to solid facilitates a gradient based optimization process of the design topology of fluidic channels. The adjoint LBM equation, which is used to compute the gradient of the optimization objective with respect to the design variables, is derived in moment space and found to be as simple as the original LBM. The moment based spatial momentum derivatives used to express the discrete objective functional (cost function) have the advantage that the local stress tensor is a local quantity avoiding the numerical computation of gradients of the discrete velocity field. This is particularly useful if dissipation is a design criterion as demonstrated in this paper. The method is validated by a detailed comparison with results obtained by Borrvall et al. for Stokes flow. While their approach is only valid for Stokes flow (i.e. very low Reynolds numbers) our approach in its present form can in principle be applied for flows of different Reynolds numbers just like the Navier-Stokes equation based approaches. This point is demonstrated with a bending pipe example for various Reynolds numbers.

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Automatic transition from simulation to one‐shot shape optimization with Navier‐Stokes equations

Cited by 20 publications

References 13 publications

Event-Based Automatic Differentiation of OpenMP with OpDiLib

Event-Based Automatic Differentiation of OpenMP with OpDiLib

Combining Sobolev Smoothing with Parameterized Shape Optimization

Discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice Boltzmann method

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