In this repository, we provide a Python library with solvers for the Poisson equation on a square domain with Dirichlet conditions using Monte Carlo methods, including our own custom solver with significant optimizations.
To install the Python library, run the following command:
pip install git+https://github.com/johnny-godoy/poisson-fast-mc.git
After that, you can import solvers from the following files:
monte_carlo_solvers.pyUses the usual implementation, obtained from here. It also adds bayesian estimations for the probability of an endpoint being reached from a starting point.subwalk_monte_carlo_solvers.pyUses our own custom implementation which improves runtime by reusing every subwalk of the generated random walks.finite_difference_solver.pyThe usual finite difference solver.hybrid_solver.pyA hybrid solver that uses the subwalk solver to obtain a primer, and then uses conjugate gradient iterations starting from the primer to solve the finite difference system.
With the Python code:
from poisson_mc_comparison import {solver_filename}
The report directory contains a Jupyter Notebook, a poster and a slideshow,
and were designed to explain the algorithms and their performances. Note that these are in Spanish. You may also view the Jupyter Notebook report as HTML here.
The reports were done as a capstone project for the course MA5307: "Numerical Analysis in Partial Differential Equations, Theory and Practice", taught by Axel Osses at Universidad de Chile, Department of Mathematical Engineering.
The original subject of this project was to compare the performance of a simple MC solver with the finite difference solver, but we ended up also designing the subwalk solver to improve performance over the usual MC solver.