Multigrid

Part of speech: noun

Definitions

1. A method that utilizes several grid levels to enhance the solution process for differential equations while improving computational speed and accuracy
2. A numerical technique incorporating multiple grids that improves the efficiency of solving equations by accelerating convergence across different scales
3. A computational strategy that employs various grid resolutions to effectively solve numerical problems and optimize the performance of algorithms in simulations

Etymology: "Multigrid" is a plain compound: "multi-" (from Latin "multus", meaning "many") joined to "grid". The grid in question is the mesh of points or cells that numerical simulations lay over a physical space, such as the air around an aircraft wing or the fluid in a pipe, so that equations can be solved at each node. The method's central idea is to solve a problem on several grids of different coarseness at once. Coarse grids capture the broad, slowly varying parts of the solution cheaply, while fine grids handle small-scale detail. Passing corrections back and forth between these resolutions lets the calculation converge far faster than working on a single fine grid alone. The word therefore names both the technique and the family of grid hierarchies it uses.