  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 equations, employing the equivalent pore pressure. In
practice a monolithic solver is not always available, defining the requirement
for a linearization scheme to allow the use of separate simulators, which is
not met by the classical Newton method. We propose three different
linearization schemes incorporating the fixed-stress splitting scheme, coupled
with an L-scheme, Modified Picard and Newton linearization of the flow. All
schemes allow the efficient and robust decoupling of mechanics and flow
equations. In particular, the simplest scheme, the Fixed-Stress-L-scheme,
employs solely constant diagonal stabilization, has low cost per iteration, and
is very robust. Under mild, physical assumptions, it is theoretically shown to
be a contraction. Due to possible break-down or slow convergence of all
considered splitting schemes, Anderson acceleration is applied as
post-processing. Based on a special case, we justify theoretically the general
ability of the Anderson acceleration to effectively accelerate convergence and
stabilize the underlying scheme, allowing even non-contractive fixed-point
iterations to converge. To our knowledge, this is the first theoretical
indication of this kind. Theoretical findings are confirmed by numerical
results. In particular, Anderson acceleration has been demonstrated to be very
effective for the considered Picard-type methods. Finally, the
Fixed-Stress-Newton scheme combined with Anderson acceleration provides a
robust linearization scheme, meeting the above criteria.
