Finite elements software and applications
AhmedAhmed S.E.
2020
The contents of this thesis are a detailed study of the software
for the finite element method. In the text, the finite element method
is introduced from both the engineering and mathematical points of view.
The computer implementation of the method is explained with samples of
mainframe, mini- and micro-computer implementations. A solution is
presented for the problem of limited stack size for both mini- and
micro-computers which possess stack architecture.
Several finite element programs are presented. Special purpose
programs to solve problems in structural analysis and groundwater flow
are discussed. However, an efficient easy-to-use finite element program
for general two-dimensional problems is presented. Several problems in
groundwater flow are considered that include steady, unsteady flows in
different types of aquifers. Different cases of sinks and sources in
the flow domain are also considered. The performance of finite element
methods is studied for the chosen problems by comparing the numerical
solutions of test problems with analytical solutions (if they exist) or
with solutions obtained by other numerical methods. The polynomial
refinement of the finite elements is studied for the presented problems
in order to offer some evidence as to which finite element simulation
is best to use under a variety of circumstances.