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Master of Science
Date of Defense
To avoid the meshing problems with traditional engineering analysis methods many
meshfree methods have been developed, and one of the most powerful methods proposed
is meshfree method with distance fields. This research work aims at reducing
the computational cost of meshfree method with distance fields. The main idea of the
proposed approach is to apply a solution structure operator only to those basis functions
whose supports are in the vicinity of the boundary and leave other basis functions
unaffected. Unfortunately, straightforward implementation of this approach leads to
elevated errors in partial derivatives of the solution. To overcome this drawback I propose
to modify distance fields in such a way that they behave as a Euclidean distance
in the region near the boundary and have smooth transition to a constant value within
some distance away from the boundary. The uniqueness of the proposed method over
other approaches is its adaptability to all kinds of boundary conditions. This narrow
band technique improves the computational cost of meshfree method with distance
fields with reasonable impact on accuracy. Another technique proposed in this work
is to glue the global solution structures of meshfree method with distance fields with
radial basis functions (RBF) and collocation technique. RBF with collocation method
itself is proved to give good accurate results with less computational cost . So using RBF-collocation technique with meshfree method with distance fields demands
for more accuracy even with less computational cost.
Later, these techniques are applied to solve heat transfer problems and the results are
compared with global solution techniques to show that the proposed methods are close
to global approach and computationally very effective.
Posireddy, Sudhir Reddy, "Optimization of Meshfree Method with Distance Fields using Localized Solution Structure and Radial Basis Function Collocation Method" (2009). FIU Electronic Theses and Dissertations. Paper 279.