The full approximation storage multigrid scheme: A 1D finite element example

01/14/2021

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by   Ed Bueler, et al.

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This note describes the full approximation storage (FAS) multigrid scheme for an easy one-dimensional nonlinear boundary value problem. The problem is discretized by a simple finite element (FE) scheme. We apply both FAS V-cycles and F-cycles, with a nonlinear Gauss-Seidel smoother, to solve the resulting finite-dimensional problem. The mathematics of the FAS restriction and prolongation operators, in the FE case, are explained. A self-contained Python program implements the scheme, and its optimal performance is demonstrated.