  Typical pipelines for model geometry generation in computational biomedicine
stem from images, which are usually considered to be at rest, despite the
object being in mechanical equilibrium under several forces. We refer to the
stress-free geometry computation as the reference configuration problem, and in
this work we extend such a formulation to the theory of fully nonlinear
poroelastic media. The main steps are (i) writing the equations in terms of the
reference porosity and (ii) defining a time dependent problem whose steady
state solution is the reference porosity. This problem can be computationally
challenging as it can require several hundreds of iterations to converge, so we
propose the use of Anderson acceleration to speed up this procedure. Our
evidence shows that this strategy can reduce the number of iterations up to
80\%. In addition, we note that a primal formulation of the nonlinear mass
conservation equations is not consistent due to the presence of second order
derivatives of the displacement, which we alleviate through adequate mixed
formulations. All claims are validated through numerical simulations in both
idealized and realistic scenarios.
