Multigrid methods: development of fast solvers

摘要

Numerical and programming aspects are discussed of multigrid algorithms for the solution of discretized linear elliptic equations. The aim is to obtain software that is perceived and can be used just like any standard subroutine for solving systems of linear equations. The user has to specify only the matrix and the right-hand-side, and remains unaware of the underlying multigrid method. We find that a large class of equations can be solved efficiently in this way. The equation may be non-self-adjoint, and its coefficients are arbitrary. Special attention is given to the treatment of the convection-diffusion equation at high Péclet number. Details are given of an available portable FORTRAN code, which vectorizes satisfactorily on vector machines. CP time statistics are given for a CYBER-205.