Abstract
To investigate applicability of the eXtended Element-Free Galerkin method (X-EFG) to realistic problems, the X-EFG has been applied to an electrostatic problem in a dielectric composite material. Numerical experiments show that the electrostatic potential obtained by the X-EFG is naturally distributed in the dielectric composite material, and the accuracy of the numerical solution obtained by the X-EFG is almost the same as that of the Standard EFG (S-EFG). In addition, the condition numbers of the coefficient matrices of the linear systems generated by the X-EFG are considerably less than those of the S-EFG.
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References
Atluri, S.N., Zhu, T.: A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech. 22, 117–127 (1998)
Belytschko, T., Lu, Y.Y., Gu, L.: Element-free Galerkin methods. Int. J. Numer. Methods Eng. 37, 229–256 (1994)
Coppoli, E.H.R., Mesquita, R.C., Silva, R.S.: Induction machines modeling with meshless methods. IEEE Trans. on Magnetics 48(2), 847–850 (2012)
Davis, T.A., Gilbert, J.R., Larimore, S., Ng, E.: A column approximate minimum degree ordering algorithm. ACM Trans. Mathematical Software 30, 353–376 (2004)
Demmel, J.W., Eisenstat, S.C., Gilbert, J.R., Li, X.S., Liu, J.W.H.: A supernodal approach to sparse partial pivoting. SIAM J. Matrix Analysis and Applications 20, 720–755 (1999)
Ikuno, S., Hanawa, T., Takayama, T., Kamitani, A.: Evaluation of parallelized meshless approach: Application to shielding current analysis in HTS. IEEE Trans. on Magn. 44, 1230–1233 (2008)
Ikuno, S., Takayama, T., Kamitani, A.: Weight function control of moving least-squares interpolants: Application to axisymmetric shielding current analysis in hts. IEEE Trans. on Magn. 46(8), 3097–3100 (2010)
Kamitani, A., Takayama, T., Itoh, T., Nakamura, H.: Extension of meshless Galerkin/Petrov-Galerkin approach without using Lagrange multipliers. Plasma and Fusion Research 6(2401074) (2011)
Liu, G.R.: Meshfree Methods: Moving beyond the Finite Element Method, 2nd edn. CRC Press LLC, Boca Raton (2009)
Manzin, A., Ansalone, D.P., Bottauscio, O.: Numerical modeling of biomolecular electrostatic properties by the element-free Galerkin method. IEEE Trans. on Magn. 47(5), 1382–1385 (2011)
Nakata, S., Takeda, Y., Fujita, N., Ikuno, S.: Parallel algorithm for meshfree radial point interpolation method on graphics hardware. IEEE Trans. on Magn. 47(5), 1206–1209 (2011)
Ni, G., Ho, S.L., Yang, S., Ni, P.: Meshless local Petrov-Galerkin method and its application to electromagnetic field computations. International Journal of Applied Electromagnetics and Mechanics 19, 111–117 (2004)
Wang, J.G., Liu, G.R.: A point interpolation meshless method based on radial basis functions. Int. J. Numer. Meth. Engng. 54(11), 1623–1648 (2002)
Xianyi, Z., Qian, W., Chothia, Z.: Openblas homepage, http://xianyi.github.com/OpenBLAS/
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Itoh, T., Saitoh, A., Ikuno, S., Kamitani, A. (2013). Electrostatic Simulation in Dielectric Composite Material by Extended Element-Free Galerkin Method. In: Tan, G., Yeo, G.K., Turner, S.J., Teo, Y.M. (eds) AsiaSim 2013. AsiaSim 2013. Communications in Computer and Information Science, vol 402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45037-2_59
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DOI: https://doi.org/10.1007/978-3-642-45037-2_59
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