On some variational acceleration techniques and related methods for local refinement

摘要

This paper shows that the well-known variational acceleration method described by Wachspress (E. Wachspress, Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics, Prentice-Hall, Englewood Cliffs, NJ, 1966) and later generalized to multilevels (known as the additive correction multigrid method (B. R Hutchinson and G. D. Raithby, Numer. Heat Transf., 9, 511-537 (1986)) is similar to the FAC method of McCormick and Thomas (S. F McCormick and J. W. Thomas, Math. Comput., 46, 439-456 (1986)) and related multilevel methods. The performance of the method is demonstrated for some simple model problems using local refinement and suggestions for improving the performance of the method are given.