deal.II—A general-purpose object-oriented finite element library

Bangerth, Wolfgang; Hartmann, Ralf; Kanschat, Guido

doi:10.1145/1268776.1268779

Cited by 1,150 publications

(1,023 citation statements)

References 25 publications

(24 reference statements)

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“…This research program is co-financed by Shell Global Solutions International B.V. The numerical examples presented in this paper are implemented using deal.II [20], an open-source C++ package for adaptive finite elements. We would like to thank the developers of this software.…”

Section: Acknowledgementsmentioning

confidence: 99%

Bounds for decoupled design and analysis discretizations in topology optimization

Gupta

Veen

Aragón

et al. 2017

Numerical Meth Engineering

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SUMMARYTopology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non-unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing nonuniqueness.

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Section: Acknowledgementsmentioning

confidence: 99%

Bounds for decoupled design and analysis discretizations in topology optimization

Gupta

Veen

Aragón

et al. 2017

Numerical Meth Engineering

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“…This setting ensures stable solution of the given problem. The resulting IPDG finite element algorithm has been coded using the C++ library deal.II [5,6].…”

Section: The Interior Penalty Discontinuous Galerkin Methodmentioning

confidence: 99%

A spatial model of cellular molecular trafficking including active transport along microtubules

Cangiani

Natalini

2010

Journal of Theoretical Biology

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To cite this version:A. Cangiani, R. Natalini. A spatial model of cellular molecular trafficking including active transport along microtubules. Journal of Theoretical Biology, Elsevier, 2010, 267 (4) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A SPATIAL MODEL OF CELLULAR MOLECULAR TRAFFICKING INCLUDING ACTIVE TRANSPORT ALONG MICROTUBULESA. CANGIANI * , R. NATALINI † Abstract. We consider models of Ran-driven nuclear transport of molecules such as proteins in living cells. The mathematical model presented is the first to take into account for the active transport of molecules along the cytoplasmic microtubules. All parameters entering the models are thoroughly discussed. The model is tested by numerical simulations based on Discontinuous Galerkin finite element methods. The numerical experiments are compared to the behavior observed experimentally.

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“…Using (20), the viscosities µ Stab,n+1 and µ Stab,n+ 1 2 are defined to be equal to µ Stab (Φ (1) , u n+1 ) and µ Stab (Φ (2) , u n+ 1 2 ), respectively, where the residual R Ent in the definition (18) of µ Ent is evaluated as follows:…”

Section: Approximation In Timementioning

confidence: 99%

Numerical simulations of bouncing jets

Bonito

Guermond

Lee

2015

Numerical Methods in Fluids

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Bouncing jets are fascinating phenomenons occurring under certain conditions when a jet impinges on a free surface. This effect is observed when the fluid is Newtonian and the jet falls in a bath undergoing a solid motion. It occurs also for non-Newtonian fluids when the jets falls in a vessel at rest containing the same fluid. We investigate numerically the impact of the experimental setting and the rheological properties of the fluid on the onset of the bouncing phenomenon. Our investigations show that the occurrence of a thin lubricating layer of air separating the jet and the rest of the liquid is a key factor for the bouncing of the jet to happen. The numerical technique that is used consists of a projection method for the Navier-Stokes system coupled with a level set formulation for the representation of the interface. The space approximation is done with adaptive finite elements. Adaptive refinement is shown to be very important to capture the thin layer of air that is responsible for the bouncing.

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deal.II—A general-purpose object-oriented finite element library

Cited by 1,150 publications

References 25 publications

Bounds for decoupled design and analysis discretizations in topology optimization

Bounds for decoupled design and analysis discretizations in topology optimization

A spatial model of cellular molecular trafficking including active transport along microtubules

Numerical simulations of bouncing jets

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