Partitioned heat conduction with overlapping Schwarz-type domain decomposition

We solve a simple heat equation. The domain is partitioned and the coupling is established in an overlapping-Schwarz-type domain decomposition.

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Updated 19 Nov 24

Note: Get the case files of this tutorial. Read how in the tutorials introduction.

Setup

We solve a partitioned heat equation, but apply an overlapping Schwarz-type domain decomposition method in this tutorial.

Case setup of partitioned-heat-conduction case with overlapping Schwarz-type domain decomposition

Note that this case applies an overlapping Schwarz-type coupling method and not (like most other tutorials in this repository) a Dirichlet-Neumann coupling. This results in a symmetric setup of the solvers.

Configuration

preCICE configuration (image generated using the precice-config-visualizer):

preCICE configuration visualization

Running the simulation

This tutorial is for FEniCS.

For choosing whether you want to run the left or right participant, please provide the following commandline input:

python3 heat.py left flag will run the left participant.
python3 heat.py right flag will run the right participant.

Like for the case partitioned-heat-conduction (using Dirichlet-Neumann coupling), we can also expect for the overlapping domain decomposition applied here to recover the analytical solution. errorcomputation.py checks this explicitly, by comparing the numerical to the analytical solution and raising an error, if the approximation error is not within a given tolerance.