A Conjugate Gradient Finite Element Model of Flow for Large Multiaquifer Systems

Abstract

A quasi three‐dimensional finite element model based on the conjugate gradient technique is developed and applied to the analysis of subsurface flow occurring in complex heterogeneous multiaquifer systems. Transient leakage across the aquitards is fully taken into consideration using the convolution approach originally derived by Herrera (1970). The convolution integrals enhance the favorable features of the modified conjugate gradients (MCG), which prove to be a very efficient tool for the solution of the integrodifferential model. The high performance of MCG results from two combined factors: (1) the diagonal dominance of the assembled finite element matrix, which is emphasized by the integral contributions; (2) the essential reducibility of the matrix for a wide range of time step values, which is due to the virtual decoupling of the aquifer equations. The preconditioning of the conjugate gradient scheme is therefore improved, and a good convergence occurs after a number of iterations smaller than (N/n)½, N and n being the overall number of nodes and aquifers, respectively. The computational cost of the model is generally low, and its relative efficiency tends to increase for small to moderate time steps and for complex multiaquifer systems where several interconnected aquifers are simulated.