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Numerical calculations of the potential on the rectangular and ellpitic domains with various aspect ratios

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Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the current study, the Laplace equation is solved for rectangular and elliptical computational domains by using the boundary element method (BEM). For this accomplishment, 120 different aspect ratios in a rectangular and elliptical computational domains are designed. The Dirichlet and Neumann boundary conditions are used respectively for a rectangular and elliptical domains. Also, the Gaussian quadrature integral method is applied to solve the influence coefficient matrix in BEM. To assess a different aspect ratio on the potential solution, two different measurement positions are intended. According to our finding, with an increase of the aspect ratio, the potential value is increased for both rectangular and elliptical domains. However, a potential increment with aspect ratio enhancement is more visible in the elliptical domain.
Rocznik
Strony
73--83
Opis fizyczny
Bibliogr. 35 poz., rys.
Twórcy
autor
  • Department of Maritime Engineering, Amirkabir University of Technology Tehran, Iran
autor
  • Department of Maritime Engineering, Amirkabir University of Technology Tehran, Iran
autor
  • Department of Maritime Engineering, Amirkabir University of Technology Tehran, Iran
Bibliografia
  • [1] Blazek J., Computational fluid dynamics: principles and applications, Butterworth-Heinemann, 2015.
  • [2] Wang H., Yao Zh., Application of a new fast multipole BEM for simulation of 2D elastic solid with large number of inclusions, Acta Mechanica Sinica 2004, 6, 613-622.
  • [3] Li G., Xing-Yuan M., Yuan-Tai H., Wang J., Analysis of smart beams with piezoelectric elements using impedance matrix and inverse Laplace transform, Smart Materials and Structures 2013, 22, 11, 115001.
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  • [5] Smith G.D., Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford University Press, 1985.
  • [6] Chen J.T., Lin S.R., Chen K.H., Degenerate scale problem when solving Laplace's equation by BEM and its treatment, International Journal for Numerical Methods in Engineering 2005, 62, 233-261.
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  • [8] Gerdes K., Demkowicz L., Solution of 3D-Laplace and Helmholtz equations in exterior domains using hp-infinite elements, Computer Methods in Applied Mechanics and Engineering 1996, 137, 3-4, November.
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  • [10] Mukherjee Y.X., Subrata M., The boundary node method for potential problems, International Journal for Numerical Methods in Engineering 1997, 40, March, 797-815.
  • [11] Zhi Qian, Chu-Li Fu, Zhen-Ping Li, Two regularization methods for a Cauchy problem for the Laplace equation, Journal of Mathematical Analysis and Applications 2008, 338, 479-489.
  • [12] Lesnic D., Elliott L., Ingham D.B, An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation, Engineering Analysis with Boundary Elements 1997, 20, 2, September.
  • [13] Jeng-Tzong Chen, Wen-Cheng Shen, Null-field approach for Laplace problems with circular boundaries using degenerate kernels, Numerical Methods for Partial Differential Equations 2009, 25, 63-85.
  • [14] Jeng-Tzong Chen, Ming-Hong Tsai, Chein-Shan Liu, Conformal mapping and bipolar coordinate for eccentric Laplace problems, Computer Applications in Engineering Education 2009, 18, September.
  • [15] Chen J.T., Shieh H.C., Lee Y.T., Lee J.W., Bipolar coordinates image method and the method of fundamental solutions for Green’s functions of Laplace problems containing circular boundaries. 2011, Vol. 35, 236-243.
  • [16] Chen J.T., Shieh H.C., Lee Y.T., Lee J.W., Image solutions for boundary value problems without sources, Applied Mathematics and Computation 2010, 216, May.
  • [17] Morales M., Rodolfo Diaz R.A., Herrera W.J., Solutions of Laplace’s equation with simple boundary conditions, and their applications for capacitors with multiple symmetries, Journal of Electrostatics 2015, 78, 31-45.
  • [18] Qinlong Ren, Cho Lik Chan, Analytical evaluation of the BEM singular integrals for 3D Laplace and Stokes flow equations using coordinate transformation, Engineering Analysis with Boundary Elements 2015, 53, 1-8.
  • [19] Jones W.P., Moore J.A., Simplified aerodynamic theory of oscillating thin surfaces in subsonic flow, American Institute of Aeronautics and Astronautics 1973, 11, 1305-1307.
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  • [22] Graeme Fairweather, Frank J Rizzo, David J Shippy, Yensen S Wu, On the numerical solution of two-dimensional potential problems by an improved boundary integral equation method, Journal of Computational Physics 1979, 31, 1, April.
  • [23] Li Z.C., Zhang L.P., Wei Y., Lee M.G., Chiang J.Y., Boundary methods for Dirichlet problems of Laplace’s equation in elliptic domains with elliptic holes, Engineering Analysis with Boundary Elements 2015, 61, December.
  • [24] Lee M.G., Li Z.C., Huang H.T., Chiang J.Y., Neumann problems of Laplace’s equation in circular domains with circular holes by methods of field equations, Engineering Analysis with Boundary Elements 2015, 51, February.
  • [25] Sibei Yang, The Neumann problem of Laplace’s equation in semionvex domains, Nonlinear Analysis: Theory, Methods & Applications 2016, 133, March.
  • [26] Caratelli D., Ricci P.E., Gielis J., The Robin problem for the Laplace equation in a three dimensional star like domain, Applied Mathematics and Computations 2011, 218, 3, October.
  • [27] Kamel Al-Khaled, Numerical solutions of the Laplace’s equation, Applied Mathematics and Computations 2005, 170, 2, November.
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  • [29] Keysuke Hayashi, Kazuei Onishi, Yoko Ohura, Direct numerical identification of boundary values in the Laplace equation, Journal of Computational and Applied Mathematics 2003, 152, March.
  • [30] Jorge A.B., Riberio G.O., Cruse T.A., Fisher T.S., Self-regular boundary integral equation formulations for Laplace’s equation in 2-D, International Journal for Numerical Methods in Engineering, 2001, March.
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  • [32] Bamdadinejad M., Ghassemi H., Ketabdari M.J., Calculation of quantity rate on the rectangular domain by boundary element method, Applied Mathematics and Physics 2017, 5, 40-46.
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  • [34] Ghassemi H., Panahi S., Kohnsal A.R., Solving the Laplace’s equation by FDM and BEM using mixed boundary conditions, American Journal of Applied Mathematics and Statistics 2016, 4, 37-42.
  • [35] Katsikadelis J.T., Boundary Element, Theory and Application, Elsevier Publication, 2002.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-dec731c3-b4f9-4ea6-a2a6-48f08e736838
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