A study of some multigrid ideas
This paper studies some questions related to the multigrid approach to the solution of elliptic partial differential equations. In order to standardize and simplify matters, a model problem \(-(pu')'+bu'+qu=0\), \(u(0)=u(1)=0\) is considered throughout. In terms of this two-point boundary value problem, estimates are made of the quality of the method for various choices that are available. In particular, if m Jacobi iterations with damping parameter a are used in the ''smoothing'' steps of the method, then a rate of convergence can be analysed for this choice. In the two-grid case this rate can be found exactly and in the general multigrid case, an upper bound can be found. The theoretical conclusions are complemented by numerical investigations for a number of special choices within the model problem.
scientific article; zbMATH DE number 3984488
scientific article