Some numerical simulations of multi-scale physical phenomena consume a
significant amount of computational resources, since their domains are discretized on
high resolution meshes. An enormous wastage of these resources occurs in
refinement of sections of the domain where computation of the solution does not
require high resolutions. This problem is effectively addressed by adaptive mesh
refinement (AMR), a technique of local refinement of a mesh only in sections where
needed, thus allowing concentration of effort where it is required. Sections of the
domain needing high resolution are generally determined by means of a criterion
which may vary depending on the nature of the problem. Fairly straightforward
criteria could include comparing the solution to a threshold or the gradient of a
solution, that is, its local rate of change to a threshold. While the former criterion is
not particularly rigorous and hardly ever represents a physical phenomenon of
interest, it is simple to implement. However, the gradient criterion is not as simple to implement as a direct comparison of values, but it is still quick and a good indicator
of the effectiveness of the AMR technique.
The objective of this thesis is to arrive at an adaptive mesh refinement algorithm for
a finite difference scheme using a quadtree decomposition approach. In the AMR
algorithm developed, a mesh of increasingly fine resolution permits high resolution
computation in sub-domains of interest and low resolution in others. In this thesis
work, the gradient of the solution has been considered as the criterion determining
the regions of the domain needing refinement. Initial tests using the AMR algorithm
demonstrate that the paradigm adopted has considerable promise for a variety of
research problems. The tests performed thus far depict that the quantity of
computational resources consumed is significantly less while maintaining the quality
of the solution. Analysis included comparison of results obtained with analytical
solutions for four test problems, as well as a thorough study of a contemporary
problem in solid mechanics.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-1144 |
| Date | 15 May 2009 |
| Creators | Auviur Srinivasa, Nandagopalan |
| Contributors | Srinivasa, Arun R. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | electronic, application/pdf, born digital |
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