Source Code for Multiscale modeling of linear elastic heterogeneous structures via localized model order reduction

This repository contains the source code for the article Multiscale modeling of linear elastic heterogeneous structures via localized model order reduction. In this paper a multiscale approach to modeling linear elastic heterogeneous structures is presented. Key points are: * additive split into coarse and fine scale solution, * physically informed boundary conditions in the oversampling problem used to construct local reduced spaces, * continuos coupling of fine-scale edge modes, * proof of concept for the proposed methodology using specific examples.

Publication in IJNME (Wiley)

The manuscript is published in the International Journal for Numerical Methods in Engineering (Wiley) under a CC-BY license and open access.

Make this paper

Welcome! Besides all the code for the paper, the python package multicode and suitable software environments are necessary to reproduce this paper.

The source code for the paper can be obtained via git clone git@github.com:pdiercks/nme-7326.git The source code for the multi package (multicode) can be obtained via git clone git@github.com:pdiercks/multicode.git Note that a specific version of the multicode package (tag nme-7326) is required. If you downloaded an archive from arXiv, then the folder multicode should already exist besides the source code for the paper.

The workflow is divided into several workflow implementations, which require different compute environments. * wf_preprocessing.py mesh generation for all examples (docker image pdiercks/multix:latest), * wf_block.py tasks for the block example (docker image pdiercks/multix:latest), * wf_beam.py tasks for the beam example (docker image pdiercks/multix:latest), * wf_lpanel.py tasks for the lpanel example (docker image pdiercks/multix:latest), * wf_postproc.py containing tasks for postprocessing (docker image pdiercks/multix:latest), * wf_pv.py postprocessing tasks using paraview (conda env, see envs/paraview_v5.11.0.yaml), * wf_tex.py tex related tasks to finally compile the PDF (conda env, see envs/tex.yaml).

To build the paper run something like the following. Using udocker first create the container. udocker create --name=<container-name> <repo/image:tag> Then run the container (make sure to bind the source code for the paper and for the multicode package). Assuming in the current working directory you have the code for the paper under $PWD/paper and the code for the multicode package under $PWD/multicode udocker run -v $PWD/paper:/mnt/paper -v $PWD/multicode:/mnt/multicode <container-name> In the container we then install multicode first $PYTHON -m pip install /mnt/multicode/multi Each part of the workflow can be run either in DEBUG or in PAPER mode for a fixed number of realizations. In the DEBUG mode the same examples are run, but with a small number of coarse grid elements (subdomains). First, build all grids with (assuming the root of the paper as cwd, that is /mnt/paper in the container) doit -f wf_preprocessing.py mode=PAPER nreal=10 run The examples are run accordingly. doit -f wf_block.py mode=PAPER nreal=10 run doit -f wf_beam.py mode=PAPER nreal=10 run doit -f wf_lpanel.py mode=PAPER nreal=10 run This will take a while. The post-processing can be done with doit -f wf_postproc.py mode=PAPER nreal=10 run Now, we only need to make some plots using the paraview conda environment mentioned above doit -f wf_pv.py run and compile the final tex document. doit -f wf_tex.py run