Multilevel block factorizations in generalized hierarchical bases

This paper studies the use of a generalized hierarchical basis transformation at each level of a multilevel block factorization. The factorization may be used as a preconditioner to the conjugate gradient method, or the structure it sets up may be used to define a multigrid method. The basis transformation is performed with an averaged piecewise constant interpolant and is applicable to unstructured elliptic problems. The results show greatly improved convergence rate when the transformation is applied for solving sample diffusion and elasticity problems. The cost of the method, however, grows and can get very high with the number of of nonzeros per row. Copyright c © 2002 John Wiley & Sons, Ltd.