Study of Some Multi-Grid Ideas

摘要

In an effort to understand certain ideas and concepts associated with multi-grid iterations the authors give an in-depth study of a particular simple problem. They consider a standard finite-difference system associated with a two-point boundary value problem. -(pu' + bu' + qu = O, u(O) =u(1) =O. The operators Ih2h, Ih2h are 'operator' based interpolation and projection operators while the smoothers are the dampled Jacobi iterations with parameter a > O. This document determines the exact rates of convergence for the two-grid scheme and upper bounds for the multi-grid schemes. Experimental results are discussed. (Author)