utkarsh530 / amf.jl Goto Github PK

Contains solvers for the second-order PDE: $$\frac{\mathrm{d} u}{\mathrm{d} t} = A u_{xx} + B u_{yy} + C u_{xy} + g(u).$$

The main focus is on incorporating Approximate Matrix Factorization (AMF) into the approaches. File descriptions:

src/finite_differences.jl: Implements a spatial discretization approach to the PDE, with an option to use AMF.

src/method_of_lines.jl: An alternative implementation to verify correctness. This file hasn't been maintained in a while and is not useed in the analysis.

scripts/minimal.jl: minimal example.

scripts/analysis_clean.jl: preliminary analysis of the methods.

Open Julia in this directory and run the following in Julia's package manager:

] activate scripts
] dev .
] instantiate

in Julia's REPL package manager, which activates the environment in the scripts directory, develops the src code in the AMF.jl module here, and then builds the environment. The scripts should now be runnable in this environment.