Multigrid treatment of “Thin” domains

Abstract

Several attempts have been made to apply multigrid methods efficiently to problems on “thin”domains. In [J. Ruge and A. Brandt, “A multigrid approach for elasticity problems on 'thin' domains,” in Multigrid Methods: Theory, Applications and Supercomputing, S. F. McCormick, ed., Marcel Dekker, New York, 1988, pp. 541–555] a multigrid method is described that permits overcoming difficulties in the case of elasticity equations on a “thin” domain bounded by straight lines. Here a method is presented that can be used for a wide class of differential problems on “thin” domains with straight or curved boundaries. For this method applied to the equations of elasticity on a domain bounded by straight lines, the computer time and storage are lower, and the programming and extension to three-dimensional cases are easier, than for the method described by Ruge and Brandt.