FFC: the FEniCS form compiler

Logg, Anders; Ølgaard, Kristian Breum; Rognes, Marie E.; Wells, Garth N.

doi:10.1007/978-3-642-23099-8_11

Cited by 79 publications

(71 citation statements)

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“…Then the code generation components of FEniCS (UFL+FFC+UFC [42]) generate code containing information about the cell integrals of the given forms and information about the elements such as the degrees of freedom maps. In particular, libCut-FEM uses an extension developed in earlier works of the components FFC [44,45] and UFC [46]. In these works, FFC and UFC were extended [33,47,48] to provide generated code for the cell integration over cut cell parts (see right box in Figure 14).…”

Section: Software For Cutfem-type Methodsmentioning

confidence: 99%

“…where denotes the popcorn surface described by the level-set function (45). Then, the cut finite element method for the Laplace-Beltrami problem is to seek U 2 W …”

Section: Laplace-beltrami Problem On a Surface Using A Bulk-meshmentioning

confidence: 99%

“…For the bulk mesh, the mesh size is approximately h 0:04. Figure 22 depicts the solution U on the popcorn surface (45). Figure 21 shows the UFL input file used in libCutFEM to specify the Laplace-Beltrami problem.…”

Section: Laplace-beltrami Problem On a Surface Using A Bulk-meshmentioning

confidence: 99%

See 2 more Smart Citations

CutFEM: Discretizing geometry and partial differential equations

Burman

Claus

Hansbo

et al. 2014

Numerical Meth Engineering

677

603

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Section: Software For Cutfem-type Methodsmentioning

confidence: 99%

“…where denotes the popcorn surface described by the level-set function (45). Then, the cut finite element method for the Laplace-Beltrami problem is to seek U 2 W …”

Section: Laplace-beltrami Problem On a Surface Using A Bulk-meshmentioning

confidence: 99%

See 1 more Smart Citation

CutFEM: Discretizing geometry and partial differential equations

Burman

Claus

Hansbo

et al. 2014

Numerical Meth Engineering

677

603

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show abstract

“…It includes several components such as DOLFIN (Logg and Wells, 2010;Logg et al, 2012c), FFC (Kirby and Logg, 2006;Logg et al, 2012b;Ølgaard and Wells, 2010) and FIAT (Kirby, 2004(Kirby, , 2012, which enable automatic solution of linear and non-linear problems once the variational forms of the PDEs are expressed in the Unified Form Language (UFL; Alnaes et al, 2014;Alnaes, 2012).…”

Section: Fenics Softwarementioning

confidence: 99%

Modelling debris transport within glaciers by advection in a full-Stokes ice flow model

Wirbel¹,

Jarosch²,

Nicholson³

2018

The Cryosphere

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Abstract. Glaciers with extensive surface debris cover respond differently to climate forcing than those without supraglacial debris. In order to include debris-covered glaciers in projections of glaciogenic runoff and sea level rise and to understand the paleoclimate proxy recorded by such glaciers, it is necessary to understand the manner and timescales over which a supraglacial debris cover develops. Because debris is delivered to the glacier by processes that are heterogeneous in space and time, and these debris inclusions are altered during englacial transport through the glacier system, correctly determining where, when and how much debris is delivered to the glacier surface requires knowledge of englacial transport pathways and deformation. To achieve this, we present a model of englacial debris transport in which we couple an advection scheme to a full-Stokes ice flow model. The model performs well in numerical benchmark tests, and we present both 2-D and 3-D glacier test cases that, for a set of prescribed debris inputs, reproduce the englacial features, deformation thereof and patterns of surface emergence predicted by theory and observations of structural glaciology. In a future step, coupling this model to (i) a debris-aware surface mass balance scheme and (ii) a supraglacial debris transport scheme will enable the co-evolution of debris cover and glacier geometry to be modelled.

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“…[1]. We discretize (32) by a finite-element scheme using FEniCS [15] and N equally distributed linear hat functions which leads to an SDC system with N degrees of freedom in the state and a single input. The output matrix C ∈ R 5,N is defined to observe the solution at the spatial locations z = 0, z = 0.5, z = 1, z = 1.5, and z = 2.…”

Section: Numerical Examplesmentioning

confidence: 99%

Exponential stability and stabilization of extended linearizations via continuous updates of Riccati‐based feedback

Benner

Heiland

2017

Intl J Robust & Nonlinear

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Many recent works on stabilization of nonlinear systems target the case of locally stabilizing an unstable steady state solutions against small perturbation. In this work we explicitly address the goal of driving a system into a nonattractive steady state starting from a well developed state for which the linearization based local approaches will not work. Considering extended linearizations or state-dependent coefficient representations of nonlinear systems, we develop sufficient conditions for stability of solution trajectories. We find that if the coefficient matrix is uniformly stable in a sufficiently large neighborhood of the current state, then the state will eventually decay. Based on these analytical results we propose an update scheme that is designed to maintain the stabilization property of Riccati based feedback constant during a certain period of the state evolution. We illustrate the general applicability of the resulting algorithm for setpoint stabilization of nonlinear autonomous systems and its numerical efficiency in two examples.

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FFC: the FEniCS form compiler

Cited by 79 publications

References 0 publications

CutFEM: Discretizing geometry and partial differential equations

CutFEM: Discretizing geometry and partial differential equations

Modelling debris transport within glaciers by advection in a full-Stokes ice flow model

Exponential stability and stabilization of extended linearizations via continuous updates of Riccati‐based feedback

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