Geometrical discretisations for unfitted finite elements on explicit boundary representations
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Publication:6379316
DOI10.1016/J.JCP.2022.111162arXiv2110.01378WikidataQ114163337 ScholiaQ114163337MaRDI QIDQ6379316
Santiago Badia, Francesc Verdugo, Pere A. Martorell
Publication date: 9 September 2021
Abstract: Unfitted (also known as embedded or immersed) finite element approximations of partial differential equations are very attractive because they have much lower geometrical requirements than standard body-fitted formulations. These schemes do not require body-fitted unstructured mesh generation. In turn, the numerical integration becomes more involved, because one has to compute integrals on portions of cells (only the interior part). In practice, these methods are restricted to level-set (implicit) geometrical representations, which drastically limit their application. Complex geometries in industrial and scientific problems are usually determined by (explicit) boundary representations. In this work, we propose an automatic computational framework for the discretisation of partial differential equations on domains defined by oriented boundary meshes. The geometrical kernel that connects functional and geometry representations generates a two-level integration mesh and a refinement of the boundary mesh that enables the straightforward numerical integration of all the terms in unfitted finite elements. The proposed framework has been applied with success on all analysis-suitable oriented boundary meshes (almost 5,000) in the Thingi10K database and combined with an unfitted finite element formulation to discretise partial differential equations on the corresponding domains.
Numerical and other methods in solid mechanics (74Sxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Computer aspects of numerical algorithms (65Yxx)
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