Basix: a runtime finite element basis evaluation
library

Scroggs, Matthew W.; Baratta, Igor A.; Richardson, Chris N.; Wells, Garth N.

doi:10.21105/joss.03982

Cited by 66 publications

(33 citation statements)

References 23 publications

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“…In this section, we use several two-dimensional numerical examples to apply the methodology described in section 3. All experiments have been implemented using the open-source computing platform FEniCSx [36,2]. A docker image to reproduce the numerical results is available at https://doi.org/10.5281/zenodo.7442458.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation

Burman¹,

Garg²,

Preuß³

2023

Preprint

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In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier-Stokes equation. We derive quantitative local error estimates for the velocity, which account for noise level and polynomial degree, using the stability of the continuous problem in the form of a conditional stability estimate. Numerical examples illustrate the performances of the method with respect to the polynomial order and perturbations in the data. We observe that the higher order polynomials may be efficient for ill-posed problems, but are also more sensitive for problems with poor stability due to the ill-conditioning of the system.

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Section: Numerical Simulationsmentioning

confidence: 99%

Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation

Burman¹,

Garg²,

Preuß³

2023

Preprint

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“…The chosen orientation of the reference element, and the numbering of each entity, is arbitrary. In all examples presented, we follow the ordering convention used by Basix [30]: for simplices, this follows the UFC ordering convention that orders sub-entities by the numbers of the vertices that are non-incident to the sub-entity [4]. For other cells, the subentities are ordered using the numbers of the vertices that are incident to the sub-entity.…”

Section: Permuting and Transforming Cell Basis Functionsmentioning

confidence: 99%

Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes

Scroggs

Dokken

Richardson

et al. 2022

ACM Trans. Math. Softw.

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We develop a method for generating degree-of-freedom maps for arbitrary order Ciarlet-type finite element spaces for any cell shape. The approach is based on the composition of permutations and transformations by cell sub-entity. Current approaches to generating degree-of-freedom maps for arbitrary order problems typically rely on a consistent orientation of cell entities that permits the definition of a common local coordinate system on shared edges and faces. However, while orientation of a mesh is straightforward for simplex cells and is a local operation, it is not a strictly local operation for quadrilateral cells and in the case of hexahedral cells not all meshes are orientable. The permutation and transformation approach is developed for a range of element types, including arbitrary degree Lagrange, serendipity, and divergence- and curl-conforming elements, and for a range of cell shapes. The approach is local and can be applied to cells of any shape, including general polytopes and meshes with mixed cell types. A number of examples are presented and the developed approach has been implemented in open-source libraries.

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“…The additional measurements allowed for the construction of a high fidelity map of the electric field within the chamber. FENiCSx was used to solve the Laplace equation for the potential with specified boundary conditions and take the gradient [14,15,16]. The boundary conditions, in this case, included the upper and lower anodes, field shapers, and measured potential on the polyethylene panels.…”

Section: 'Fine' Polyethylene Measurementsmentioning

confidence: 99%

Characterization of XIA UltraLo-1800 Response to Measuring Charged Samples

Joshua¹,

Calkins²,

Andrew³

2022

Preprint

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Commercial alpha counters are used in science and industry applications to screen materials for surface radon progeny contamination. In this paper, we characterize an XIA UltraLo-1800, an ionization drift alpha counter, and study the response to embedded charge in polyethylene sample measurements. We show that modeling such effects is possible in a Geant4-based simulation framework and attempt to derive corrections. This paper also demonstrates the effectiveness of an anti-static fan to eliminate the charge on the same and recover a 97.73% alpha detection efficiency.

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Basix: a runtime finite element basis evaluation library

Cited by 66 publications

References 23 publications

Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation

Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation

Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes

Characterization of XIA UltraLo-1800 Response to Measuring Charged Samples

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