Computational methods in biomechanics and physics

This dissertation considers the numerical solution of linear and non-linear wave propagation problems and numerical modeling of blood flow in compliant vessels.; We consider the solution of the linear wave equation with discontinuous coefficients by a domain decomposition method. A time explicit finite difference scheme combined with a piecewise linear finite element method in space is used on semimatching grids. We apply a boundary supported Lagrange multiplier technique on the interface between the subdomains.; We examine the numerical solution of the wave scattering problem via a fictitious domain method. We use a mixed variational formulation to construct a discrete problem, which is explicit in time along with a boundary supported Lagrange multipliers to enforce the boundary condition on the interface.; The next problem deals with the solution of a vector-valued constrained nonlinear wave equation. We use a methodology based on the penalty treatment of the constraint. The numerical scheme combines the use of a continuous piecewise linear finite element approximation along with an implicit in time discretization. The stability and uniqueness results are provided for the forementioned problems.; The goal of the next problem is to develop an efficient methodology for the numerical simulation of blood flow in bifurcated human arteries. The model is derived using an asymptotic reduction of the Navier-Stokes equations to model the blood, with Navier equation for the wall. We use Riemann invariants analysis in order to describe the continuity of pressure and momentum at the bifurcation point. We calculate shear stress rates for several different prostheses data and obtain results that indicate high shear stress rates in graft limbs where thrombosis is typically observed. Based on our findings, we suggest the optimal design of endovascular prostheses for endoluminal treatment of an aortic abdominal aneurysm.