MULTIGRID METHODS FOR THE SOLUTION OF POISSON EQUATION IN A THICK SPHERICAL-SHELL

Two multigrid methods designed for the solution of a finite-element discretization of Poisson's equation in spherical geometry are presented and compared. One of these, based upon an approximate local least-squares inverse (LS1), has been previously reported by J. R. Baumgardner and P. O. Frederickson [SIAM J. Numer. Anal., 22 (1985), pp. 1107-1115]; the other, developed by the authors, employs a "mass lumped" line Jacobi smoothing procedure that is entirely new. The new method is shown to be both more economical and considerably more robust than that based upon the LS1 smoothing iteration.