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Fedele, F. G.

Civil and Environmental Engineering

2005

PhD

In this thesis novel numerical techniques are proposed for application to different problems in engineering science. Three categories of numerical techniques are investigated: collocation methods, finite element methods (FEM) and boundary element methods (BEM). In the context of collocation methods a new numerical technique called LOCOM (LOcalized COllocation Method) has been proposed. This method is able to reduce the degrees of freedom of the classical Hermite collocation to one single degree for each collocation node, still maintaining higher order accuracy. This new methodology has been applied to an existing Hermite Collocation Fortran code that solves multiphase flow problems.
In the context of the Finite Element Method, a special form of the Petrov-Galerkin method has been formulated for the sub-grid stabilization of advection-diffusion partial differential equations on triangular meshes. This new method is able to damp out the spurious oscillations occurring near a sharp front when the standard finite element method is applied. An adjoint FEM has been developed in the context of fluorescence tomography and a Galerkin technique has been formulated to investigate the hydrodynamic stability of pulsatile Poiseuille flow in a pipe. Finally, a 3D boundary element method is presented for the numerical solution of general coupled elliptic differential equations. This methodology has application in some areas of optical tomography where small heterogeneities immersed in a homogenous domain need to be detected.