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OPTIMIZATION ALGORITHM


location point locations. If the ordered pairs listed in Table 1 were the only pos- sible combinations that could be used for the approximation, then the algorithm would choose ordered pair 3 because it has the least error.


Utilizing a test pool of 1000 nodes and 729 collocation points, the best node to collocation point pair to approximate this pressure source is node (.01,.01,.01) and collocation point (3.18,5,1.36). The RMS error associated with this pair is .000164 and the max error was 0.00116. This result is expected because the approxi- mation function picks the node that is closest to where the actual source func- tion is located. Essentially, when using a one node model to model a single source the approximation function will simply attempt to ”copy” the source.


Following the algorithm, the one node 


Table 1 - Record of Computational Error for the Single Node Models


selected in the next two node model and also is removed from the candidate ordered pairs for future selections. The algorithm now tests for the best two node solution keeping the optimum node and collocation pair from the one node model as one of the two nodes. This process is then repeated for each additional node until there are n basis functions in the approximation function.


Figures 4 - 9 are visualizations of the Approximate Solution using the Complex Variable Boundary Element Method optimization algorithm developed in this paper (left hand graphs), the analytical solution (center graphs) and the differ- ence between them (right hand graphs) for representative orthogonal planar sections through the problem domain shown in Fig.1., using 10 nodes. The contours are unitless and display the


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Welcome, Figure 4: Computational results on the x-z plane where y=5.


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Figure 5: Computational results on the x-z plane where y=1.


Figure 6: Computational results on the x-y plane where z=3. www.aipg.org


University of Alabama Student Chapter Group Photo: Marcella McIntyre- Redden, Geological Survey of Alabama and Alabama Geological Society; Richard Katz, Retired Mining Engineer/ Geologist (Speakers on Left); Dr. Andrus University of Alabama Dept Chair, Geological Sciences; Student Officers, Caryl Orr AIPG Member Sponsor


Jan.Feb.Mar 2019 • TPG 9


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