The aggregated unfitted finite element method on parallel tree-based adaptive meshes

Abstract

In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting scheme on locally-adapted Cartesian forest-of-trees meshes. We propose a two-step algorithm to construct the finite element space at hand by means of a discrete extension operator that carefully mixes aggregation constraints of problematic degrees of freedom, which get rid of the small cut cell problem, and standard hanging degree of freedom constraints, which ensure trace continuity on non-conforming meshes. Following this approach, we derive a finite element space that can be expressed as the original one plus well-defined linear constraints. Moreover, it requires minimum parallelization effort, using standard functionality available in existing large-scale finite element codes. Numerical experiments demonstrate its optimal mesh adaptation capability, robustness to cut location and parallel efficiency, on classical Poisson $hp$-adaptivity benchmarks. Our work opens the path to functional and geometrical error-driven dynamic mesh adaptation with the aggregated finite element method in large-scale realistic scenarios. Likewise, it can offer guidance for bridging other scalable unfitted methods and parallel adaptive mesh refinement.

arXiv comment25 pages, 14 figures

References in corpus (12)

• Condition number analysis and preconditioning of the finite cell method
• The aggregated unfitted finite element method for elliptic problems
• Shape Optimization Using the Cut Finite Element Method
• A Nitsche-based cut finite element method for a fluid--structure interaction problem
• Recursive Algorithms for Distributed Forests of Octrees
• A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing
• Robust and parallel scalable iterative solutions for large-scale finite cell analyses
• Mixed aggregated finite element methods for the unfitted discretization of the Stokes problem
• Robust and scalable domain decomposition solvers for unfitted finite element methods
• Distributed-memory parallelization of the aggregated unfitted finite element method
• On a general implementation of $h$- and $p$-adaptive curl-conforming finite elements
• A tetrahedral space-filling curve for non-conforming adaptive meshes

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• High order unfitted finite element discretizations for explicit boundary representations
• A three-grid high-order immersed finite element method for the analysis of CAD models
• Space-time unfitted finite elements on moving explicit geometry representations