Interpolation-based immersed finite element and isogeometric analysis
arXiv:2209.06892 · doi:10.1016/j.cma.2023.115890
Abstract
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the domain geometry but is otherwise subject to minimal constraints on element quality or connectivity. This is a generalization of the concept of Lagrange extraction from the isogeometric analysis literature and also related to certain variants of the finite cell and material point methods. Crucially, the interpolation may be approximate without sacrificing high-order convergence rates, which distinguishes the present method from existing finite cell, CutFEM, and immersogeometric approaches. The interpolation paradigm also permits non-invasive reuse of existing finite element software for immersed analysis. We analyze the properties of the interpolation-based immersed paradigm for a model problem and implement it on top of the open-source FEniCS finite element software, to apply it to a variety of problems in fluid, solid, and structural mechanics where we demonstrate high-order accuracy and applicability to practical geometries like trimmed spline patches.
References in corpus (8)
- DOLFIN: Automated Finite Element Computing
- A compiler for variational forms
- Condition number analysis and preconditioning of the finite cell method
- Robust and parallel scalable iterative solutions for large-scale finite cell analyses
- Weak Boundary Condition Enforcement for Linear Kirchhoff-Love Shells: Formulation, Error Analysis, and Verification
- CutIGA with Basis Function Removal
- Coupling of non-conforming trimmed isogeometric Kirchhoff-Love shells via a projected super-penalty approach
- A projection-based numerical integration scheme for embedded interface: Application to fluid-structure interaction
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- Automated shape and thickness optimization for non-matching isogeometric shells using free-form deformation
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- Advances on the finite element discretization of fluid-structure interaction problems
- Robust Containment Queries over Collections of Trimmed NURBS Surfaces via Generalized Winding Numbers