Application of Trefftz method for temperature rise analysis on human skin exposed to radiation

• Autorzy: Kita E. , Hirayama Y.
• Języki publikacji: EN

Abstrakty

EN

This paper describes the application of the Trefftz method to the temperature rise in human skin exposed to radiation from a cellular phone. A governing equation is given as the Poisson equation. An inhomogeneous term of the equation is approximated with a polynomial function in Cartesian coordinates. The use of the approximated term transforms the original boundary-value problem to that governed with a homogeneous differential equation. The transformed problem can be solved by the traditional Trefftz formulation. Firstly, the present method is applied to a simple numerical example in order to confirm the formulation. The temperature rise in a skin exposed to radiation is considered as a second example.

Słowa kluczowe

EN

Trefftz method; Poisson equation; polynomial function

PL

funkcja wielomianowa; metoda Trefftza; równanie Poissona

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2008
• Tom: Vol. 15, No. 1
• Strony: 45--52
• Opis fizyczny: Bibliogr. 23 poz., rys., tab., wykr.

Twórcy

autor

Kita E.

autor

Hirayama Y.

• Nagoya University, Graduate School of Information Science, Nagoya 464-8601, Japan

Bibliografia

• [1] C.J.S. Alves, C.S. Chen. Approximating functions and solutions of non homogeneous partial differential equations using the method of fundamental solutions. Advances in Computational Mathematics, Vol. 23, pp. 125-142, 2005.
• [2] E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen. LAPACK User's Manual. SIAM, 2nd edition, 1995.
• [3] W. Chen. Some recent advances on the RBF. In: C.A. Brcbbia, A. Tadcu, V. Popov, eds., Boundary Elements XXIV (Proc. 24th World Conf. on BEM, Sintra, Portugal, 2002), pp. 125-134. Comp. Mech. Pub., 2002.
• [4] Y.K. Cheung, W.G. Jin, O.C. Zienkiewicz. Direct solution procedure for solution of harmonic problems using complete, non-singular, Trefftz functions. Communications in Applied Numerical Methods, 5: 159-169, 1989.
• [5] M.A. Golberg, C.S. Chen, M. Ganesh. Particular solutions of 3D Helmholtz type equations using compactly supported radial basis functions. Engineering Analysis with Boundary Elements, 24: 539-547, 2000.
• [6] I. Herrera. Theory of connectivity: A systematic formulation of boundary element methods. In: C.A. Brebbia, ed., New Developments in Boundary Element Methods (Proc. 2nd Int. Seminar on Recent Advances in BEM, Southampton, England, 1980), pp. 45-58. Pentech Press, 1980.
• [7] A. Hirata, T. Shiozawa. Correlation of maximum temperature increase and peak SAR in the human head due to handset antennas. IEEE, Transactions on Microwave Theory and Techniques, 51(7): 1834-1841, 1999.
• [8] M.S. Ingber, C.S. Chen, J.A. Tanski. A mesh free approach using radial basis functions and parallel domain decomposition for solving three dimensional diffusion equations. International Journal for Numerical Methods in Engineering, 60: 2183-2201, 2004.
• [9] M. Karas, A.P. Zielinski. Application of Trefftz complete functional system to stress analysis in helical spring with an arbitrary wire cross-section. Strojnicky Casopis, 49: 426-437, 1998.
• [10] E. Kita, Y. Ikeda, N. Kamiya. Trefftz solution for boundary value problem of three-dimensional Poisson equation. Engineering Analysis with Boundary Elements, 29: 383-390, 2005.
• [11] V.M.A. Leitao, C.M. Tiago. The use of radial basis functions for one-dimensional structural analysis problems. In: C.A. Brebbia, A. Tadeu, V. Popov, eds., Boundary Elements XXIV (Proc. 24th World Conf. on BEM, Sintra, Portugal, 2002), pp. 165-179. Comp. Mech. Pub., 2002.
• [12] X. Li, C.S. Chen. A mesh free method using hyperinterpolation and fast Fourier transform for solving differential equations. Engineering Analysis with Boundary Elements, 28: 1253-1260, 2004. [13] G.R. Liu, Y.T. Gu. Boundary mesh-free methods based on the boundary point interpolation methods. In: C.A. Brebbia, A. Tadeu, V. Popov, eds., Boundary Elements XXIV (Proc. 24th World Conf. on BEM, Sintra,Portugal, 2002), pp. 57-66. Comp. Mech. Pub., 2002.
• [14] Z. Liu, J.G. Korvnik. Accurate solving the Poisson equation by combining multiscale radial basis functions and Gaussian quadrature. In: C.A. Brebbia, A. Tadeu, V. Popov, eds., Boundary Elements XXIV (Proc. 24th World Conf. on BEM, Sintra, Portugal, 2002), pp. 97-104. Comp. Mech. Pub., 2002
• [15] A.S. Mulshkov, M.A. Golberg, A.H.-D. Cheng, C.S. Chen. Polynomial particular solutions for Poisson equation. In: C.A. Brebbia, A. Tadeu, V. Popov, eds., Boundary Elements XXIV (Proc. 24th World Conf. on BEM, Sintra, Portugal, 2002), pp. 115-124. Comp. Mech. Pub., 2002.
• [16] A.J. Nowak. Application of the multiple reciprocity BEM to nonlinear potential problems. Engineering Analysis with Boundary Elements, 18: 323-332, 1995.
• [17] A.J. Nowak, A.C. Neves. The Multiple Reciprocity Boundary Element Method. Comp. Mech. Pub. / Springer Verlag, 1994.
• [18] T.W. Partridge. Towards criteria for selecting approximation functions in the dual reciprocity method. Engineering Analysis with Boundary Elements, 24(7): 519-529, 2000.
• [19] T.W. Partridge, C.A. Brebbia, L.C. Wrobel. The Dual Reciprocity Boundary Element Method. Comp. Mech. Pub. / Springer Verlag, 1992.
• [20] D. Poljak, N. Kovac, T. Samardzioska, A. Peratta, C.A. Brebbia. Temperature rise in the human body exposed to radiation from base station antennas. In: C.A. Brebbia, eel., Boundary Elements XXVI (Proc. 26th World Conf. on BEM, Bologna, Italy, 2004), pp. 381-390. WIT Press, 2004.
• [21] B. Sarler, J. Perko, C.S. Chen. Radial basis function collocation method solution of natural convection in porous media. International Journal of Numerical Methods for Heat and Fluid Flow, 14(2): 187-212, 2004.
• [22] E. Trefftz. Ein Gegenstück zum Ritzschen Verfahren. Proc. 2nd Int. Cong. Appl. Mech., Zurich, PP. 131-137, 1926.
• [23] S. Q. Xu, Kamiya N. A formulation for boundary element analysis of inhomogeneous-nonlinear problem; the case involving derivatives of unknown function. Engineering Analysis with Boundary Elements, 23 (5/6): 391, 1999.