The FEniCS Project Version 1.5

Alnæs, Martin Sandve; Blechta, Jan; Hake, Johan; Johansson, August; Kehlet, Benjamin; Logg, Anders; Richardson, Chris; Ring, Johannes; Rognes, Marie E.; Wells, Garth N.

doi:10.11588/ans.2015.100.20553

Cited by 487 publications

(203 citation statements)

References 12 publications

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“…and ω ∈ (0, 1) with ω < 3−3σ 1 3−2σ 1 . Let J (Σ) be bounded from below, and let L > 0 be a constant such that…”

Section: Algorithmmentioning

confidence: 99%

“…To generate the initial mesh we subdivide the domain into 32 equally large slices along both axes, which yields 1024 equally sized squares. Each square is then subdivided into four triangles along both of its diagonals, yielding a triangle mesh with 4096 cells, each of which has an area of 1 4096 and is contained within a ball of radius 1 64 , centered on the middle of its longest side. If we denote each cell of this initial mesh by T…”

Section: Source Inversion For the Poisson Equationmentioning

confidence: 99%

“…and the final objective function J of Problem (1) is J (U ) := J (χ U ). We develop our theory for the abstract problem (1). However, this more concrete example may aid the reader's understanding.…”

Section: Introductionmentioning

confidence: 99%

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Binary optimal control by trust-region steepest descent

Leyffer

Säger

2022

Math. Program.

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We present a trust-region steepest descent method for dynamic optimal control problems with binary-valued integrable control functions. Our method interprets the control function as an indicator function of a measurable set and makes set-valued adjustments derived from the sublevel sets of a topological gradient function. By combining this type of update with a trust-region framework, we are able to show by theoretical argument that our method achieves asymptotic stationarity despite possible discretization errors and truncation errors during step determination. To demonstrate the practical applicability of our method, we solve two optimal control problems constrained by ordinary and partial differential equations, respectively, and one topological optimization problem.

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“…and ω ∈ (0, 1) with ω < 3−3σ 1 3−2σ 1 . Let J (Σ) be bounded from below, and let L > 0 be a constant such that…”

Section: Algorithmmentioning

confidence: 99%

Section: Source Inversion For the Poisson Equationmentioning

confidence: 99%

See 1 more Smart Citation

Binary optimal control by trust-region steepest descent

Leyffer

Säger

2022

Math. Program.

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“…A shift-and-invert spectral transformation is used in order to enhance convergence of eigenvalues in the neighborhood of a given value. The code is written using the open source computing platform FEniCS [26,27]. The mesh is generated by way of a Delaunay triangulation using Gmsh [28].…”

Section: N(ω)pmentioning

confidence: 99%

“…We pre-multiply (27a) by p † * , which is the complex conjugate of the adjoint pressure eigenfunction, and integrate over the domain. Then we add (26). This is equivalent to writing the shape derivative of the Lagrangian, L = ω − p † , N (ω) p , where p † is the Lagrange multiplier.…”

Section: Shape Derivativesmentioning

confidence: 99%

Shape Optimization of Thermoacoustic Systems Using a Two-Dimensional Adjoint Helmholtz Solver

Falco

Juniper

2021

Journal of Engineering for Gas Turbines and Power

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Thermoacoustic instabilities, which arise due to the interaction between flames and acoustics, are sensitive to small changes to the system parameters. In this paper, we apply adjoint-based shape optimization to a 2D finite element Helmholtz solver to find accurately and inexpensively the shape changes that most stabilise a 2D thermoacoustic system in the linear regime. We examine two cases: a Rijke tube and a turbulent swirl combustor. Both systems exhibit an unstable longitudinal mode and we suppress the instability by slightly modifying the geometry. In the case of the turbulent swirl combustor, the sensitivities are higher in the plenum and in the burner than in the combustion chamber, mainly due to the effect of the mean temperature. In the cooler regions, the local wavelength is shorter, which means that geometry changes of a given distance have more influence than they do where the local wavelength is longer. This is the first time adjoint-based shape optimization is applied to 2D Helmholtz solvers in thermoacoustics, after being previously applied to low-order thermoacoustic networks. But Helmholtz solvers have an intrinsic advantage: they can handle complex geometries. The easy scalability of this method to complex 3D geometries make this tool a strong candidate for the iterative design of thermoacoustically stable combustors.

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Effect of the tiger stripes on the deformation of Saturn's moon Enceladus

Souček

Hron

Běhounková

et al. 2016

Geophysical Research Letters

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Enceladus is a small icy moon of Saturn with active jets of water emanating from fractures around the south pole, informally called tiger stripes, which might be connected to a subsurface water ocean. The effect of these features on periodic tidal deformation of the moon has so far been neglected because of the difficulties associated with implementation of faults in continuum mechanics models. Here we estimate the maximum possible impact of the tiger stripes on tidal deformation and heat production within Enceladus's ice shell by representing them as narrow zones with negligible frictional and bulk resistance passing vertically through the whole ice shell. Assuming a uniform ice shell thickness of 25 km, consistent with the recent estimate of libration, we demonstrate that the faults can dramatically change the distribution of stress and strain in Enceladus's south polar region, leading to a significant increase of the heat production in this area.

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The FEniCS Project Version 1.5

Cited by 487 publications

References 12 publications

Binary optimal control by trust-region steepest descent

Binary optimal control by trust-region steepest descent

Shape Optimization of Thermoacoustic Systems Using a Two-Dimensional Adjoint Helmholtz Solver

Effect of the tiger stripes on the deformation of Saturn's moon Enceladus

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