  This work focuses on the derivation and the analysis of a novel,
strongly-coupled partitioned method for fluid-structure interaction problems.
The flow is assumed to be viscous and incompressible, and the structure is
modeled using linear elastodynamics equations. We assume that the structure is
thick, i.e., modeled using the same number of spatial dimensions as fluid. Our
newly developed numerical method is based on generalized Robin boundary
conditions, as well as on the refactorization of the Cauchy's one-legged
`theta-like' method, written as a sequence of Backward Euler-Forward Euler
steps used to discretize the problem in time. This family of methods,
parametrized by theta, is B-stable for any theta in [0.5,1] and second-order
accurate for theta=0.5+O(tau), where tau is the time step. In the proposed
algorithm, the fluid and structure subproblems, discretized using the Backward
Euler scheme, are first solved iteratively until convergence. Then, the
variables are linearly extrapolated, equivalent to solving Forward Euler
problems. We prove that the iterative procedure is convergent, and that the
proposed method is stable provided theta in [0.5,1]. Numerical examples, based
on the finite element discretization in space, explore convergence rates using
different values of parameters in the problem, and compare our method to other
strongly-coupled partitioned schemes from the literature. We also compare our
method to both a monolithic and a non-iterative partitioned solver on a
benchmark problem with parameters within the physiological range of blood flow,
obtaining an excellent agreement with the monolithic scheme.
