In this folder you will find examples of how to use BLUEST with PDE models built using legacy FEniCS. We recommend that first-time BLUEST users start from the tutorial folder instead.
The extension of these examples to FEniCSx models is likely straightforward. Note that these examples require further dependencies, listed below.
Example 1 [.py]
Here we solve a simple diffusion equation with random coefficients and boundary conditions, and with a single quantity of interest. The script includes various estimator tests. For more info, see blue_models.py.
Example 2 [.py]
This is the same setup as for Example 1, but with multiple quantities of interest. The script includes various estimator tests. For more info, see blue_models.py.
In the paper_examples folder you will find the scripts used to generate the results of the paper
M. Croci, K. E. Willcox, S. J. Wright, Multi-output multilevel best linear unbiased estimators via semidefinite programming. Preprint (2023). URL https://export.arxiv.org/abs/2301.07831
On top of the standard BLUEST dependencies, these examples require legacy FEniCS (>=2018.1.0), Gmsh, pygmsh, matplotlib, meshio.
Ipopt and cyipopt are also needed for some tests, but are otherwise optional.
We remind that a docker file with all pre-installed dependencies is available, see main README.