The Frequency Decomposition Multi-Grid Algorithm

Multi-grid methods are known as very fast solvers of a large class of discretised partial differential equations. However, the multi-grid method cannot be understood as a fixed algorithm. Usually, the components of the multi-grid iteration have to be adapted to the given problem and sometimes the problems are modified into those acceptable for multi-grid methods. In particular, the smoothing iteration is the most delicate part of the multi-grid process.