Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

By Anders Logg, K A Mardal, Garth N. Wells. 2012

3,110 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2a1cbae44b4a2b6896f7e6b0fd2fcbc427138f45

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In Mechanics of Materials

Citations in the corpus

Phase-field modeling of anisotropic brittle fracture including several damage mechanisms (2018, positive): “Finite element discretization and numerical aspects The finite element discretization relies on the FEniCS finite element library [53, 54], linear interpolation has been chosen for the displacement and damage fields.”
Firedrake (2015, methodology): “The FEniCS project provides the FEniCS Form Compiler (FFC), which takes variational forms speciﬁed in UFL and generates optimised C++ kernel functions conforming to the UFC interface [Logg et al. 2012a].”
Undercut and overhang angle control in topology optimization: A density gradient based integral approach (2017, methodology): “Logg A, Mardal KA, Wells G. Automated solution of differential equations by the finite element method: The FEniCS book, Vol. 84.”
Optimization of wind plant layouts using an adjoint approach (2017, methodology): “The FEniCS project is based on the DOLFIN problem-solving environment and connects a number of useful components for the automatic discretization and solution of finite-element problems.”
An overview of the modelling of fracture by gradient damage models (2016, positive): “Open-source finite element implementations based on the FEniCS library [29] are available at [32] and [18].”
Modular and flexible spectral-element waveform modelling in two and three dimensions (2018, methodology): “The results are inspired by popular finite-element packages such as FENICS (Logg et al. 2012), DEAL.”
Evaporating pure, binary and ternary droplets: thermal effects and axial symmetry breaking (2017, methodology): “For the implementation of the finite element method, the governing equations are converted to corresponding weak forms (Diddens 2017) and solved with the help of the finite element package FENICS (Logg 2012).”
Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms (2017, methodology): “Let us also mention that the normalization of both models is chosen so that, when considering the localized damage solution for a 1D bar in traction, the surface fracture energy corresponds exactly to Gc. 2.3 Numerical aspects The numerical code used in this work is inspired from the open-source imp”
Physics-informed deep learning for incompressible laminar flows (2020, methodology): “To examine the accuracy of the present results, we also compute the reference solutions by the open-source FEniCS solver (finite element-based) [15] and the ANSYS Fluent 18.”