A parallel algorithm for solving linear parabolic equations

This repository supplements arXiv:2009.08875.

We implemented our algorithm in Python3 using the open source finite element library NGSolve for meshing and descretization of the bilinear forms in space and time, MPI through mpi4py for distributed computations, and SciPy for the sparse matrix-vector computations.

Requirements

• NGsolve (tested with v6.2.2): see install instructions.
• Python pacakges (requirements.txt): mpi4py, numpy, pets4py, psutil, scipy.

Run instructions

A normal, single-threaded, implementation is given in heateq.py.

python3 heateq.py --J_time=3 --J_space=6 --problem=square

The parallel MPI implementation, used for the numerical results in the paper, is given in heateq_mpi.py.

mpirun -np 2 python3 heateq_mpi.py --J_time=3 --J_space=6 --problem=square

The tests can be run using pytest.

pytest
mpirun -np 2 pytest

License

This project is licensed under the terms of the MIT license.