A multigrid method combines relaxation of high-frequency fine-grid errors with coarse-grid correction of smooth errors. Residual restriction, an approximate coarse error solve, error prolongation and post-smoothing form a two-grid cycle; recursive coarse solves give multilevel cycles.
For residual , restrict to a coarse grid, solve approximately, and update by . This corrects error that is smooth on the fine grid but representable on the coarse grid.
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The multigrid method is a computational technique used to solve a wide range of problems, particularly those involving partial differential equations (PDEs). It is designed to accelerate the convergence of iterative methods for solving such equations, especially when the problem is large and complex. ### Key Concepts: 1. **Multi-Level Approach**: The multigrid method works on multiple levels of discretization, typically on a hierarchy of grids with different resolutions.