An introduction into multigrid method fundamentals

Numerical methods are a eld of mathematics concerned with the creation of mathematical tools to solve applied problems. In this paper, we concentrate on multigrid methods, an approach that can be used for solving systems of lin- ear equations that arise from discretizing ordinary di erential equations, among many other things. Multigrid methods are an advanced topic not usually taught to undergraduates. Furthermore, self-learning is made challenging as most exist- ing literature is written in a style typical to mathematics, which can be di cult to decipher for the inexperienced. However, the core concepts behind multigrid can be easily understood. In this paper, I provide introductions to these cen- tral ideas (iterative methods and the smoothing property, coarse grids, residual correction, transfer operators, and recursion), with the intention of bridging the knowledge gap that exists before more popular multigrid literature can be approached.