What is multigrid?

Multigrid is a numerical solver method for partial differential equations that solves the problem by coarsening the grid (making the grid spacing larger) and solving the problem on the coarser grid. Once the solution is obtained on the coarse grid, it is interpolated back to the finer grid. This process is repeated, with the grid being coarsened again and again until the solution on the finest grid is obtained.

The multigrid method is particularly effective for problems with smooth solutions (i.e., solutions that vary slowly over space), and is often used for problems in fluid dynamics, electromagnetics, and engineering, among other fields. It is known for its high efficiency and scalability, and can solve large-scale problems that would be prohibitively expensive to solve with traditional solvers.

There are several different types of multigrid methods, including geometric multigrid, algebraic multigrid, and non-linear multigrid. Each method has its own strengths and weaknesses, and the choice of method depends on the specific problem being solved.

Multigrid is also often used in combination with other numerical solver methods, such as finite element or finite difference methods, to further improve their efficiency and accuracy.