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

Autor:	Bueler, Ed
Rok vydání:	2021
Předmět:	Mathematics - Numerical Analysis 65M55 34B15
Druh dokumentu:	Working Paper
Popis:	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. Optimal performance, i.e. work proportional to the number of unknowns, is demonstrated for both kinds of cycles, including convergence nearly to discretization error in a single F-cycle. Comment: 19 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2101.05408 Zobrazit plný text záznamu View this record from Arxiv