Process-based hydrological models have a long history dating back to the 1960s. Criticized
by some as over-parameterized, overly complex, and difficult to use, a more nuanced view is …

Core Ideas The numerical solution of Richards' equation remains challenging. Space/time
discretization affects both computational effort and accuracy. Adaption of space and time …

This work concerns linearization methods for efficiently solving the Richards equation, a
degenerate elliptic-parabolic equation which models flow in saturated/unsaturated porous …

This paper concerns an acceleration method for fixed-point iterations that originated in work
of DG Anderson [J. Assoc. Comput. Mach., 12 (1965), pp. 547–560], which we accordingly …

Integrated, process‐based numerical models in hydrology are rapidly evolving, spurred by
novel theories in mathematical physics, advances in computational methods, insights from …

This paper provides theoretical justification that Anderson acceleration (AA) improves the
convergence rate of contractive fixed-point iterations in the vicinity of a fixed-point. AA has …

Most efficient linear solvers use composable algorithmic components, with the most common
model being the combination of a Krylov accelerator and one or more preconditioners. A …

A one-step analysis of Anderson acceleration with general algorithmic depths is presented.
The resulting residual bounds within both contractive and noncontractive settings reveal the …

In this paper, we study the robust linearization of nonlinear poromechanics of unsaturated
materials. The model of interest couples the Richards equation with linear elasticity …

Abstract The Hermitian and skew-Hermitian splitting iteration method (HSS) is commonly an
effective linear iterative method for solving sparse non-Hermite positive definite equations …