dolfin-adjoint 2018.1: automated adjoints for FEniCS and Firedrake

Mitusch, Sebastian K.; Funke, Simon W.; Dokken, Jørgen S.

doi:10.21105/joss.01292

Cited by 158 publications

(107 citation statements)

References 4 publications

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“…We use a reduced space optimization formulation to solve Problem (18) and calculate the cost and constraint functions J(ν C ), G 1 (ν C ) and G 2 (ν C ) and their sensitivities DJ(ν C ), DG 1 (ν C ) and DG 2 (ν C ) using Firedrake [75,67,57] and the adjoint method with pyadjoint [68]. For the sensitivity computations, we consider the dependency of u C , p C , u H , p H and T on the design ν C so that, e.g.,…”

Section: Volume Fraction Methodsmentioning

confidence: 99%

“…Our choice is to calculate the shape derivatives DJ(D C ), DG 1 (D C ) and DG 2 (D C ) using the differentiate-discretize approach. This choice allows us to take advantage of the automatic shape derivative calculation in the Unified Form Language (UFL) [55] within the pyadjoint library [41], [68]. As in the volume-fraction method, we also use a reduced space formulation and hence we consider the dependency of the primal variables u C , p C , u H , p H and T on the design D C so that, e.g.…”

Section: Shape Derivativesmentioning

confidence: 99%

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Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

Troya¹,

Tortorelli²,

Beck³

2021

14th WCCM-ECCOMAS Congress

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We design heat exchangers using two topology optimization approaches: the density, i.e. volume fraction and level set methods. Our goal is to maximize the heat exchange between two fluids in separate channels while constraining the pressure drop across each channel. The heat exchanger is modeled with a coupled thermal-flow formulation. The flow is governed by an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation with high Peclet number. We solve one set of Stokes-Brinkman equations per fluid. Each Brinkman term in the flow equation serves to model the other phase as a solid, thereby preventing mixing. We first represent the solid and fluid phases using a volume fraction variable and apply a SIMP-like penalization in the Brinkman term to drive the optimization to a discrete design. The cost and constraint function derivatives are automatically calculated with the library pyadjoint and the optimization is performed by the Method of Moving Asymptotes. In a second optimization formulation, we use the level set approach to define the interface that separates the two fluids. Pyadjoint calculates the shape derivatives of the cost and constraint functions and the Hamilton-Jacobi advects the interface, allowing for topological changes. We present results in two dimensions and discuss the advantages and disadvantages of each approach.

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Section: Volume Fraction Methodsmentioning

confidence: 99%

Section: Shape Derivativesmentioning

confidence: 99%

Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

Troya¹,

Tortorelli²,

Beck³

2021

14th WCCM-ECCOMAS Congress

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“…The Lagrangian approach to compute derivatives of PDE-constrained functionals is well established (Ito and Kunisch 2008), and its steps can be replicated by symbolic computation software. Probably, the biggest success in this direction is the pyadjoint project (Farrell et al 2013;Mitusch et al 2019), which derives "the adjoint and tangent-linear equations and solves them using the existing solver methods in FEniCS/Firedrake" (Mitusch et al 2019). Thanks to the shape differentiation capabilities of UFL introduced in Ham et al (2019), pyadjoint is also capable of shape differentiating PDE-constrained functionals along directions discretized by finite elements (Dokken et al 2020).…”

Section: Shape Optimization and Shape Calculusmentioning

confidence: 99%

Fireshape: a shape optimization toolbox for Firedrake

Paganini

Wechsung

2021

Struct Multidisc Optim

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“…The number of degrees of freedom used to represent the model inputs can therefore be suitably large to represent a field which varies in both space and time, without impacting the computational cost. For models implemented within the Firedrake framework, the adjoint model can be generated algorithmically via the Python package pyadjoint (Mitusch et al, 2019); this package is utilised within this work to generate the Thetis adjoint model.…”

Section: Adjoint Modelmentioning

confidence: 99%

Adjoint-based sensitivity analysis for a numerical storm surge model

2021

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Numerical storm surge models are essential to forecasting coastal flood hazard and informing the design of coastal defences. However, such models rely on a variety of inputs, many of which will carry uncertainty, and an awareness and understanding of the sensitivity of the model outputs with respect to those uncertain inputs is necessary when interpreting model results. Here, we use an unstructured-mesh numerical coastal ocean model, Thetis, and its adjoint, to perform a sensitivity analysis for a hindcast of the 5 th /6 th December 2013 North Sea surge event, with respect to the bottom friction coefficient, bathymetry and wind stress forcing. The results reveal spatial and temporal patterns of sensitivity, providing physical insight into the mechanisms of surge generation and propagation, and can also be used to estimate the uncertainty in skew surge model predictions due to uncertainty in each model input. Our results demonstrate the power of adjoint methods to gain relevant insight into a storm surge model, providing information complementary to traditional ensemble uncertainty quantification methods.

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dolfin-adjoint 2018.1: automated adjoints for FEniCS and Firedrake

Cited by 158 publications

References 4 publications

Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

Fireshape: a shape optimization toolbox for Firedrake

Adjoint-based sensitivity analysis for a numerical storm surge model

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