lusongno1 / ngsxfem

Add-On to NGSolve for unfitted finite element discretizations (XFEM, CutFEM, TraceFEM, etc...)

About ngsxfem

ngsxfem is an add-on library to the finite element package Netgen/NGSolve which enables the use of unfitted finite element technologies known as XFEM, CutFEM, TraceFEM, Finite Cell, ... . ngsxfem is an academic software. Its primary intention is to facilitate the development and validation of new numerical methods for partial differential equations.

The features of ngsxfem

The main features of ngsxfem are:

• Tools to work on an a subset of the triangulation, the "active mesh" only

• Numerical integration on geometries that are (implicitly) described through level set functions.

• Higher order representation of level set geometries

• Space-Time Finite Elements for the treatment of moving domain problems

• All these features combined with the usual flexibility and power of NGSolve.

ngsxfem has been used in a variety of applications. In doc/paper.md more details on the features and references to applications where ngsxfem is used are given.

Not all features of ngsxfem and NGSolve can directly be combined. Here is an overview of ngsxfem and NGSolve features and if they can directly be combined:

Features ⇲	CFE	XFE	DGF	Iso	MLS	STF	GhP	Hex	Tet	MPI
CFE: CutFEM form.	/	/	yes	yes	yes	no	yes	yes	yes	yes
XFE: XFEM formulation	/	/	yes	yes	no	no	yes	yes	yes	yes
DGF: Discont. Galerkin	yes	yes	/	yes	no	no	yes	no	yes	no
Iso: isoparametric map	yes	yes	yes	/	no	yes	yes	yes	yes	yes
MLS: multiple level set	yes	no	no	no	/	no	yes	no	yes	yes
STF: space-time FEM	yes	no	no	yes	no	/	yes	yes	yes	yes
GhP: Ghost penalty	yes	yes	yes	yes	yes	yes	/	yes	yes	no
Hex: quads / hexes	yes	yes	no	yes	no	yes	yes	/	/	yes
Tet: trigs./tets	yes	yes	yes	yes	yes	yes	yes	/	/	yes
MPI: MPI	yes	yes	no	yes	yes	yes	no	yes	yes	/

Some of the nos are work in progress (e.g. MLS&STF) and some have not been considered so far (e.g. DGF&STF). If you need a certain combination to work, please contact us and we will see what we can do.

Examples and Documentation

We provide two main sources with which to learn how to use ngsxfem:

• At https://github.com/ngsxfem/ngsxfem-jupyter you can find tutorial-style jupyter notebooks for ngsxfem. These explain the core functionalities and usage of the tools provided by ngsxfem. You can run those tutorials interactively (without the need of a local installation) through binder.
• in the demos-directory we provide several examples that demonstrate the usage of ngsxfem features. See demos/README.md for details.

Installation

We provide installation instructions for building/installing through pip and building/installing from sources in INSTALLATION.md. Further, a docker image is available which can be used to run ngsxfem through docker.

List of contributing authors (with major contributions)

• Christoph Lehrenfeld (main author)
• Fabian Heimann (cut integration, space-time)
• Thomas Ludescher (multigrid)
• Janosch Preuss (space-time)
• Henry von Wahl (multiple levelsets)

Community guidelines

If you observe any problems with the software / examples / documentation / installation or want to contribute, you can get in touch with us through either:

• the github issue tracker
• the NGSolve user forum.