How to generate four-node quadrilateral mesh and element?

1

Question 1: Q4 mesh
Suppose we have two matrices A and B describing Node and Coordinate relationships, and Element and Node relationships, respectively:

A: (Node and Coordinate relationships)
Node1 x1 y1
Node2 x2 y2
Node3 x3 y3
…

B: (Element and Node relationships)
Element1 Node1 Node2 Node3 Node4
Element2 Node1 Node2 Node3 Node4
Element3 Node1 Node2 Node3 Node4
…

How could we transfer these two relationships of four-node quadrilateral mesh (not just square or rectangle mesh) into mesh entities such as the one obtained from RectangleMesh in FEniCS?

Question 2: Q4 element
Once we obtain a mesh entity containing the Q4 mesh, do we need to do some other modifications in the code?

2

For quadrilateral and hexahedral elements, it is recommended to use dolfin-x, as the support for these elements has been vastly improved. See for instance: dolfinx/test_higher_order_mesh.py at main · FEniCS/dolfinx · GitHub

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3

Hi Dokken, thanks for your reply very much, and I just have two follow-up questions:

(1) Does the dolfinx contain all the contents in dolfin? That is, can I use from dolfinx import * to replace from dolfin import *?

(2) I am a newcomer to docker and I have installed docker in the windows 10 system. I use docker command to download dolfinx (about 3.16 GB). But when I try to use from dolfinx import *, a warning appears that ‘no module named dolfinx’. What should I do then?
I am using VScode and Ubuntu 18.04LTS, and the classical dofinx runs very smoothly.

4

Dolfin-X is quite different from dolfin. They both use UFL, but the syntax has changed quite alot. See for instance: The FEniCSx tutorial — FEniCSx tutorial for an overview of the new syntax.

The docker image you should use is the dolfinx/dolfinx image on Dockerhub. You shoul be able to pull the image, create a container and run python3 -c "import dolfinx" without any error message.

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5

Hi Dokken, I try to pull the image by using Docker, but the warning still exists. Could you please tell me how to deal with it?

image
image802×481 33.1 KB

This is my image list:

image
image1270×394 25.6 KB

This is my container:

image
image769×162 8.15 KB

I think I can only run dolfinx in this way:
image
But it will change the file directory. Is there some elegant way to run it?

6

The dolfinx docker image is like any other docker image. You need to start a container using docker run to be able to access a terminal that has dolfinx installed. A docker container always have its own file system, and you can share a folder with the container by running the following:

docker run -ti -v $(pwd):/root/shared -w /root/shared --rm dolfinx/dolfinx
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7

Thank you, Dokken! You help me a lot. Now I can run my code with dolfinx.
But when I try to reproduce the result in this tutorial: Implementation — FEniCS-X tutorial (jorgensd.github.io), there is a warning: No module named ‘pyvista’. For other parts, they work well.

8

Pyvista has to be installed, as it is an optional dependency of dolfinx. You should run the following inside your container

apt-get -qq update && \
    apt-get -y install libgl1-mesa-dev \
    xvfb 
pip3 install pyvista matplotlib
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