NODE POSITIONING ALGORITHM
which were developed using the PDE Modeler application within the program MATLAB. The CVBEM models correctly identified the LUST in the three problems that were examined, but the FEM models did not correctly identify the LUSTs. Part of the error of the FEM models came from the post-processing step of computing the gradient of the modeling outcome in order to obtain flowlines from the computed potential values. However, this step was not necessary in the CVBEM modeling as a consequence of the Cauchy-Riemann equations. The addi- tional accuracy provided by CVBEM models for these problems can be of immense importance as the ability or inability to track groundwater contamination can trigger environmental, health, and legal repercussions.
Acknowledgements
The authors are grateful to Hromadka & Associates, a consulting firm, for supporting this research.
References
[1] Hromadka II, T. & Guymon, G., Application of a Boundary Integral Equation to Prediction of Freezing Fronts in Soil, Cold Regions Science and Technology, 6, pp. 115–121, 1982.
[2] Hromadka II, T.V. & Guymon, G.L., A Complex Variable Boundary Element Method: Development, International Journal for Numerical Methods Engineering, 20, pp. 25–37, 1984.
[3] Wilkins, B.D., Greenberg, J., Redmond, B., Baily, A., Flowerday, N., Kratch, A., Hromadka II, T.V., Boucher, R., McInvale, H.D. & Horton, S., An Unsteady Two- Dimensional Complex Variable Boundary Element Method, SCIRP Applied Mathematics, 8(6), pp. 878–891, 2017.
[4] Wilkins, B.D., Hromadka II, T.V. & Boucher, R., A Conceptual Numerical Model of the Wave Equation Using the Complex Variable Boundary Element Method, Applied Mathematics, 8(5), p. 724, 2017.
[5] Hromadka II, T.V., A Multi-Dimensional Complex Variable Boundary Element Method, volume 40 of Topics in Engineering, WIT Press, Southampton and Boston, 2002.
[6] Hromadka II, T. & Whitley, R., Approximating three- dimensional steady-state potential flow problems using two- dimensional complex polynomials, Engineering Analysis with Boundary Elements, 29, pp. 190 – 194, 2005.
[7] Hromadka II, T. & Zillmer, D., Boundary element model- ing with variable nodal and collocation point locations, Advances in Engineering Software, 2011.
[8] Demoes, N.J., Bann, G.T., Wilkins, B.D., Grubaugh, K.E. & Hromadka II, T.V., Optimization Algorithm for Locating Computational Nodal Points in the Method of Fundamental Solutions to Improve Computational Accuracy in Geosciences Modeling, The Professional Geologist, 2019.
[9] Wilkins, B.D., Hromadka II, T. & McInvale, J., Comparison of Two Algorithms for Locating Computational Nodes in the Complex Variable Boundary Element Method (CVBEM), International Journal of Computational Methods and Experimental Measurements, 8(4), pp. 289-315, 2020.
[10] Brebbia, C.A., The Boundary Element Method for Engineers, Wiley, 1978.
[11] Brebbia, C. & Wrobel, L., Boundary element method for fluid flow, Advances in Water Resources, 2, pp. 83–89, 1979.
www.aipg.org EARLY PERMIAN!
INTRODUCING 300 MA
[12] Young, D., Chen, K., Chen, J. & Kao, J., A Modified Method of Fundamental Solutions with Source on the Boundary for Solving Laplace Equations with Circular and Arbitrary Domains, Computer Modeling in Engineering and Sciences, 19(3), pp. 197–221, 2007.
[13] Fornberg, B. & Flyer, N., Fast generation of 2-D node distributions for mesh-free PDE discretizations, Computers and Mathematics with Applications, 69, pp. 531–544, 2015.
[14] Hromadka II, T.V., Complex boundary elements for contaminant transport, Environmental Software, 6(2), pp. 81–86, 1991.
[15] Rasmussen, T.C. & Yu, G.Q., Complex Variable Boundary Integral Modeling of Groundwater Flow and Transport, in K.J. Hatcher, ed., Proceedings of the 1997 Georgia Water Resources Conference, The University of Georgia, 1997.
[16] Rasmussen, T.C. & Yu, G.Q., A complex variable boundary-element strategy for determining groundwater flow nets and travel times, Advances in Water Resources, 26, pp. 395–406, 2003.
[17] Brown, J.W. & Churchill, R.V., Complex Variables and Applications, McGraw-Hill, 8 edition, 2009.
[18] Kirchhoff, R.H., Potential Flows Computer Graphic Solutions, CRC Press, 1985.
[19] Hromadka II, T.V. & Yen, C.C., A model of groundwater contaminant transport using the CVBEM, Computational Mechanics, 1(2), pp. 105–113, 1986.
[20] Johnson, A.N. & Hromadka II, T.V., Modeling mixed boundary conditions in a Hilbert space with the complex variable boundary element method (CVBEM), MethodsX, 2, pp. 292–305, 2015.
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