This is an introduction to multigrid methods for elliptic PDEs, possibly also with extensions to initial-boundary value problems in parabolic and hyperbolic equations. It includes a basic overview of elementary iterative methods for large, sparse, linear systems of equations. Upon the completion of this course, the student will have a basic understanding of how to construct, analyze, apply and implement a basic multigrid scheme using V-cycle iterations. The major mathematical ideas behind the numerical methods for solving differential equations and will have acquired a range of skills in the subject, both for analyzing methods and for applying them. A major computer project carried out in Matlab or Python is directed towards solving a large-scale applied problem, on the order of one hundred million unknowns.Instruction in the computer lab vill assist the student in developing his/her solver. Evaluation One computer project, evaluated on a pass/fail basis.
Multigrid methods are state-of-the-art methods for solving large-scale linear systems of equations, typically arising in partial differential equations or, e.g., image processing. They are used for systems consisting of many millions of equations, sometimes billions. We will focus on equation systems arising in elliptic PDEs (boundary value problems) such as the Laplace, Poisson and Helmholtz equations.
William L. Briggs, Van Emden Henson, Steve F McCormick A Multigrid Tutorial 2nd edition, SIAM: Society for Industrial and Applied Mathematics (2000).
The best option is to order the book on the web.