helmholtz-x

helmholtz-x is a python library which solves a non-homogeneous Helmholtz equation using finite element method (FEM).

In helmholtz-x, the nonlinear eigenvalue problem is determined using PETSc, SLEPc and FEniCSx libraries.

We specifically address thermoacoustic Helmholtz equation within helmholtz-x. In its submodules, helmholtz-x exploits extensive parallelization with handled preallocations for the generation of nonlinear part of the thermoacoustic Helmlholtz equation. The thermoacoustic Helmholtz equation reads;

$$ \nabla\cdot\left( c^2 \nabla \hat{p}_1 \right) + \omega^2\hat{p}_1 = i\omega (\gamma-1)\hat{q}_1 $$

In matrix form;

$$ \textbf{A}\textbf{P} + \omega \textbf{B}\textbf{P} + \omega^2 \textbf{C} \textbf{P} = \textbf{D}(\omega)\textbf{P} $$

and we solve this matrix system with helmholtz-x.

Citation

We are currently writing a journal paper to describe internal mechanics of helmholtz-x, and the .bibtex will be available here after publication.

Installation

We advise to install those packages from source in Ubuntu/Linux OS, but there is a very simple option to run helmholtz-x: Docker.

Docker images

You can get packaged installation of dependencies such as PETSc, SLEPc and FEniCSx using Docker images. To install the docker into your system, you can find the instructions in this link.

The helmholtz-x runs with the v0.7.3 of DOLFINx. First, you need to clone the helmholtz-x repository by typing;

git clone https://github.com/ekremekc/helmholtz-x.git

in your Linux/Ubuntu terminal then cd into the helmholtz-x with

cd helmholtz-x

Now, you need to pull the docker container for DOLFINx. You can make a docker environment for helmholtz-x by typing;

sudo docker run -ti -e DISPLAY=$DISPLAY -v /tmp/.X11-unix:/tmp/.X11-unix -v $(pwd):/root/shared -w /root/shared --name=helmholtz-x dolfinx/dolfinx:v0.7.3

Pulling the image might take some time (5-10 min) depending on your system and internet connection. Then you will be in the new terminal within the docker container. At the present working directory (helmholtz-x), you should run;

pip3 install -e .

to install helmholtz-x within the docker container environment. Then, lastly you need to activate the complex number mode of DOLFINx, as the helmholtz-x utilizes complex builds of DOLFINx/PETSc/SLEPc. It can be activated running;

source /usr/local/bin/dolfinx-complex-mode

Now, you should be able to run the demos in the numerical_example directory.

When you exit the terminal by typing Ctrl+D, you can always log back into the docker container for helmholtz-x by typing;

sudo docker start -i helmholtz-x

then you are again in the helmholtz-x directory in the fresh terminal. It is important to note that, you always have to run

source /usr/local/bin/dolfinx-complex-mode

to activate the complex build of DOLFINx, upon your every new login to the docker container.

Conda

It is advised to use helmholtz-x using docker images. But, users may install the dependencies with the conda, which generally takes much longer time to install, compared to the installation of docker. Here is the livestock for PETSc/SLEPc/FEniCSx;

conda create -n helmholtzx-env
conda activate helmholtzx-env
conda install -c conda-forge python=3.10 mpich fenics-dolfinx hdf5=1.14.2 petsc=*=complex* slepc=*=complex*

Then helmholtz-x can be installed within this conda environment by typing.

pip3 install -e .

in the helmholtz-x directory.

How to use helmholtz-x?

You just need to navigate the example case you like in /numerical_examples folder and type

python3 -u file.py

in the terminal. Each example case includes runAll.sh, which includes the example commands for running files in serial as well as in parallel. It can be executed with;

source runAll.sh

to perform testing for serial and parallel runs and writes the log file in the /Results directory.

The flowchart and duties of the components within helmholtz-x are visualized below;