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

by   Eric Neiva, et al.

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.



There are no comments yet.


page 11

page 12

page 13

page 17

page 18

page 19

page 20


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

In this work, we present an adaptive unfitted finite element scheme that...

The aggregated unfitted finite element method for elliptic problems

Unfitted finite element techniques are valuable tools in different appli...

Robust high-order unfitted finite elements by interpolation-based discrete extension

In this work, we propose a novel formulation for the solution of partial...

Scalable solvers for complex electromagnetics problems

In this work, we present scalable balancing domain decomposition by cons...

A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems

We propose a domain decomposition method for the efficient simulation of...

Linking ghost penalty and aggregated unfitted methods

In this work, we analyse the links between ghost penalty stabilisation a...

Immersed Virtual Element Methods for Maxwell Interface Problems in Three Dimensions

Finite element methods for Maxwell's equations are highly sensitive to t...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.