In this paper, we will discuss the cascadic multigrid preconditioned conjugate gradient method for the linear finite element approximation of the second order elliptic boundary value problem -[nabla]*(w[nabla]u) = f, in [OMEGA] u = [g.
of Macau) stick to the practical as they introduce students to iterative methods for solving Toeplitz systems based on the preconditioned conjugate gradient method.
n] related to a continuous generating function f(x) there exist various preconditioning techniques that ensure fast convergence of the preconditioned conjugate gradient (pcg) method; see [2, 7] and the references therein.
We consider a class of such methods, where the multigrid only appears as a black-box tool for constructing the preconditioner of the stiffness matrix, and the base iterative algorithm is one of well-known off-the-shelf preconditioned gradient methods such as the locally optimal block preconditioned conjugate gradient method.