High order unfitted finite element methods on level set domains using isoparametric mappings

TL;DR

This paper presents a novel high order unfitted finite element method that uses isoparametric mappings to accurately integrate over implicitly defined curved surfaces and volumes, improving interface reconstruction quality.

Contribution

The paper introduces a new isoparametric unfitted finite element method combining parametric mesh mappings with high order accuracy for level set domain integration.

Findings

Enhanced interface reconstruction accuracy

High order convergence demonstrated in numerical examples

Improved integration over complex geometries

Abstract

We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is suitable for the case of piecewise planar interfaces is combined with a parametric mapping of the underlying mesh resulting in an isoparametric unfitted finite element method. The parametric mapping is constructed in a way such that the quality of the piecewise planar interface reconstruction is significantly improved allowing for high order accurate computations of (unfitted) domain and surface integrals. This approach is new. We present the method, discuss implementational aspects and present numerical examples which demonstrate the quality and potential of this method.