الفهرس 
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Abstract
This Thesis presents a new fast multi-pole boundary element formulation for the
solution of Reissner’s plate bending problems. The solution of Reissner’s plate
bending problems using the conventional direct boundary element method leads to a
non-symmetric fully populated system of matrices. The complexity of the solution
then becomes of the order O(N3) mathematical operations, where N is the total number
of problem unknowns. Hence, the use of fast multi-pole technique becomes practically
essential in case of solving large-scale problems by the direct boundary element
method.
The suggested formulation is based on representing the fundamental solutions as
function of potentials. These potentials and their relevant fundamental solutions are
expanded by means of Taylor series expansions. In the present formulation, equivalent
collocations are based on the first shift expansion of kernels. This is achieved by
representation of far field integrations by series expansions and carrying out
summations of far clusters, whereas the near field integrations are kept to be computed
directly.
In the presented implementation, the fast multi-pole boundary element method is
coupled with the iterative solver: Generalized Minimal Residual System (GMRES).
The computational complexity is rapidly reduced to be O(N log N). Numerical
examples are presented to demonstrate the efficiency, time saving, and accuracy of the
formulation against the conventional direct BEM. The accuracy of the results is traced
by cutting Taylor series to few terms. It was proven via numerical examples that three
terms are enough to produce sufficient accuracy with substantial reduction of solution.