Numerical Solution of the Poisson Equation Using Finite Difference Matrix Operators

The Poisson equation frequently emerges in many fields of science and engineering. As exact solutions are rarely possible, numerical approaches great interest. Despite this, a succinct discussion systematic approach to constructing flexible general solver can be difficult find. In this introductory paper, comprehensive is presented on how build finite difference matrix that solve the for arbitrary geometry boundary conditions. conditions implemented way enables easy modification different problems. An image-based geometry-definition also discussed. Python code recipe made publicly available. Numerical examples show set up