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Novel Numerical
Techniques for problems in Engineering Science Francesco Fedele 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.
If you have any comments about
my thesis drop me a line at ffedele3@gtsav.gatech.edu
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