120831475
MULTIGRID METHODS FOR VARIATIONAL PROBLEMS: FURTHER RESULTS*
In an earlier paper [SIAM J. Numer. Anal., 19 (1982), pp. 924–929], we developed a convergence theory for a class of multigrid methods applied to positive definite self-adjoint differential boundary value problems, where the multigrid process used W-cycling and Richardson’s iteration. In the present paper, we extend this theory to include V-cycling and more general relaxation schemes such as Jacobi and (arbitrarily ordered) Gauss-Seidel.
120854547
Multigrid Methods for Variational Problems: General Theory for the V-Cycle
In two earlier papers [SIAM J. Numer. Anal., 19 (1982), pp. 924–929; 21 (1984), pp. 255–262], we developed an algebraic convergence theory for a class of multigrid methods applied to positive definite self-adjoint linear operator equations. The purpose of the present paper is to extend these results by eliminating an earlier approximation order restriction, developing additional rate estimates and allowing for very general relaxation schemes, including those that are nonstationary and nonsymmetric. These results apply to most well-known iterative methods and preconditioners.
116945349
A revised mesh refinement strategy for newton’s method applied to nonlinear two-point boundary value problems
The objective of this paper is the development of a mesh refinement technique for applying Newton’s method to the solution of nonlinear two-point boundary value problems. The process represents a significant improvement on an earlier approach both in its general applicability and in its numerical performance. This is demonstrated by several reported numerical examples.