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

TL;DR

This paper presents a new robust, scalable, and adaptive unfitted finite element method for large-scale interface elliptic problems, demonstrating high accuracy, robustness, and efficiency in complex simulations.

Contribution

It introduces a novel $h$-adaptive aggregated unfitted finite element method with a scalable Cartesian mesh engine for interface problems, extending existing approaches to complex multi-interface scenarios.

Findings

Method is well-posed and robust against cut location and material contrast.

Achieves optimal $h$-adaptive approximation properties.

Demonstrates high scalability and ease of implementation in large-scale codes.

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.