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

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