Multigrid acceleration for domain decomposition mixed finite element simulation of groundwater flow

We present a multigrid acceleration for domain decomposition mixed finite element simulation of saturated groundwater flow. We employ the elements of Brezzi, Douglas and Marini [4], and the domain decomposition formulation of Glowinski and Wheeler [8]. The multigrid acceleration is distinguished by the use of a renormalized conductivity to define coarse grid operators and the transfer of the nonconforming interface solution between levels. We are most interested in large problems, and present simulation results with over two million degrees of freedom for heterogeneous conductivity fields with many length scales of variability and σ_{ln K} > 2.0. On a serial computer we compare the multigrid accelerated domain decomposition method with the closely related hybridization method solved using incomplete Cholesky preconditioning. For problems that fit in core, the hybrid formulation is more efficient. However, using the domain decomposition method we can solve much large problems than possible with the hybrid formulation.