Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems

Abstract

This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the aggregated finite element method atop a highly-scalable Cartesian forest-of-trees mesh engine. It follows the classical approach of weakly coupling nonmatching discretisations at the interface to model internal discontinuities at the interface. We propose a natural extension of a single-domain parallel cell aggregation scheme to problems with a finite number of interfaces; it straightforwardly leads to aggregated finite element spaces that have the structure of a Cartesian product. We demonstrate, through standard numerical analysis and exhaustive numerical experimentation on several complex Poisson and linear elasticity benchmarks, that the new technique enjoys the following properties: well-posedness, robustness with respect to cut location and material contrast, optimal ($h$-adaptive) approximation properties, high scalability and easy implementation in large-scale finite element codes. As a result, the method offers great potential as a useful finite element solver for large-scale interface problems modelled by partial differential equations.

arXiv comment24 pages, 13 figures

References in corpus (12)

• Condition number analysis and preconditioning of the finite cell method
• High order unfitted finite element methods on level set domains using isoparametric mappings
• 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
• A stabilized cut discontinuous Galerkin framework: I. Elliptic boundary value and interface problems
• CutIGA with Basis Function Removal
• Mixed aggregated finite element methods for the unfitted discretization of the Stokes problem
• Distributed-memory parallelization of the aggregated unfitted finite element method
• Numerical modelling of heat transfer and experimental validation in Powder-Bed Fusion with the Virtual Domain Approximation
• On a general implementation of $h$- and $p$-adaptive curl-conforming finite elements
• The aggregated unfitted finite element method on parallel tree-based adaptive meshes

Cited by in corpus (6)

• Linking ghost penalty and aggregated unfitted methods
• Geometrical discretisations for unfitted finite elements on explicit boundary representations
• A robust and scalable unfitted adaptive finite element framework for nonlinear solid mechanics
• High order unfitted finite element discretizations for explicit boundary representations
• Space-time unfitted finite elements on moving explicit geometry representations
• Unfitted finite element interpolated neural networks