  We propose a computational framework for vascular fluid-structure interaction
(FSI), focusing on biomechanical modeling, geometric modeling, and solver
technology. The biomechanical model is constructed based on the unified
continuum formulation. We highlight that the chosen time integration scheme
differs from existing implicit FSI integration methods in that it is indeed
second-order accurate, does not suffer from the overshoot phenomenon, and
optimally dissipates high-frequency modes in both subproblems. We propose a
pipeline for generating subject-specific meshes for FSI analysis for
anatomically realistic geometric modeling. Unlike most existing methodologies
that operate directly on the wall surface mesh, our pipeline starts from the
image segmentation stage. With high-quality surface meshes obtained, the
volumetric meshes are then generated, guaranteeing a boundary-layered mesh in
the fluid subdomain and a matching mesh across the fluid-solid interface. In
the last, we propose a combined suite of nonlinear and linear solver
technologies. Invoking a segregated algorithm within the Newton-Raphson
iteration, the problem reduces to solving two linear systems in the
multi-corrector stage. The first linear system can be addressed by the
algebraic multigrid (AMG) method. The matrix related to the balance equations
presents a two-by-two block structure in both subproblems. Using the Schur
complement reduction (SCR) technique reduces the problem to solving matrices of
smaller sizes of the elliptic type, and the AMG method again becomes a natural
candidate. The benefit of the unified formulation is demonstrated in
parallelizing the solution algorithms as the number of unknowns matches in both
subdomains. We use the Greenshields-Weller benchmark as well as a
patient-specific vascular model to demonstrate the robustness, efficiency, and
scalability of the overall FSI solver technology.
