|
[1] Barone MR, Caulk DA. Optimal arrangement of holes in a two-dimensional heat conductor by a special boundary integral method. Int J Num Meth Engng 1982; 18: 675-685. [2] Cheng HW, Greengard L. On the numerical evaluation of electrostatic field in dense random dispersions of cylinders. J Comput Phys 1997; 136: 629-639. [3] Caulk DA. Analysis of elastic torsion in a bar with circular holes by a special boundary integral method. J Appl Mech Trans ASME 1983; 50: 101-108. [4] Chen JT, Hong H-K, Chyuan SW. Boundary element analysis and design in seepage problems using dual integral formulations. Finite Elem Anal Des 1994; 17(1): 1-20. [5] Hutchinson JR. An alternative BEM formulation applied to membrane vibrations. In: Brebbia CA, Maier G, editors. Boundary Elements VII, Berlin: Springer-Verlag; 1985. [6] Chen KH, Chen JT, Chou CR, Yueh CY, Dual boundary element analysis of oblique incident wave passing a thin submerged breakwater. Eng Anal Bound Elem 2002; 26: 917-928. [7] Chen JT, Chen KH. Dual integral formulation for determining the acoustic modes of a two-dimensional cavity with a degenerate boundary. Eng Anal Bound Elem 1998; 21(2): 105-116. [8] García-Castillo LE, Gómez-Revuelto I, Sáez de Adana F, Salazar-Palma M. A finite element method for the analysis of radiation and scattering of electromagnetic waves on complex environments. Comput Meth Appl Mech Eng 2005; 194: 637-655. [9] Chen JT, Chen PY, Chen CT. Surface motion of multiple alluvial valleys for incident plane SH-waves by using a semi-analytical approach. Soil Dyn Earthq Eng 2008; 28: 58-72. [10] Mills RD. Computing internal viscous flow problems for the circle by integral methods. J Fluid Mech 1977; 73: 609-624. [11] Hutchinson JR. Vibration of plates. In: Brebbia CA, editors. Boundary Elements X, Berlin: Springer-Verlag; 1988. [12] Brebbia CA. Boundary Element Methods. Berlin: Springer-Verlag; 1981. [13] Chen JT, Hong H-K. Boundary Element Method. Taipei: New World Press; 1992. [in Chinese]. [14] Muskhelishvil NI. Some basic problems of the mathematical theory of elasticity. New York: Springer; 1953. [15] Muskhelishvil NI. Singular Integral Equations. (Translated by Radok JRM) New York: Dover; 1992. [16] Hromadka II TV. Linking the complex variable boundary element method to the analytic function method. Numer Heat Transf 1984; 7: 235-240. [17] Whitley RJ, Hromadka II TV. Complex logarithms, Cauchy principal values, and the complex variable boundary element method. Appl Math Modell 1994; 18: 423-428. [18] Whitley RJ, Hromadaka II TV. Theoretical developments in the complex variable boundary element method. Eng Anal Bound Elem 2006; 30: 1020-1024. [19] Chou SI, Shamas-Ahmadi M. Complex variable boundary element method for torsion of hollow shafts. Nucl Eng Des 1992; 136: 255-263. [20] Linkov AM. Boundary Integral Equations in Elasticity Theory. Dordrecht: Springer; 2002. [21] Gu L, Huang MK. A complex variable boundary element method for solving plane and plate problems of elasticity. Eng Anal Bound Elem 1991; 8(6): 266-272. [22] Kolhe R, Ye W, Hui CY, Mukherjee S. Complex variable functions for usual and hypersingular integral equations for potential problems with applications to corners and cracks. Comput Mech 1996; 17: 279-286. [23] Chen JT, Chen YW. Dual boundary element analysis using complex variables for potential problems with or without a degenerate boundary, Eng Anal Bound Elem 2000; 24(1): 671-684. [24] Di Paola M, Pirrotta A, Santoro R. Line element-less method (LEM) for beam torsion solution (truly no-mesh method). Acta Mech 2008; 195: 349-363. [25] Barone G, Pirrotta A. CVBEM application to a novel potential function providing stress field and twist rotation at once. J. Eng. Mech.-ASCE 2013; 139: 1290-1293. [26] Hromadka II TV, Guymon LG. Complex polynomial approximation of the Laplace equation. J Hydraul Eng 1984; 110: 329-339. [27] Pirrotta A. Complex potential function in elasticity theory: shear and torsion solution through line integrals. Acta Mech 2012; 223(6): 1251-1259. [28] Barone G, Pirrotta A. CVBEM for solving De Saint-Venant solid under shear forces. Eng Anal Bound Elem 2013; 37: 197-204. [29] Pompeiu D. Sur une classe de fonctions d’une variable complexe et sur certaines équations intégrales. Rendiconti del Circolo Matematico di Palermo 1913; 35: 277-281. [30] Begehr H. Boundary value problems in complex analysis I. Boletín de la Asociación Mathemática Venezolana 2005; 12: 65-85. [31] Hamilton WR. On quaternions; or on a new system of imaginaries in algebra. Philos Mag 1844; 25: 10-13. [32] Fueter R. Die Funktionentheorie der Differentialgleichungen ∆u = 0 und ∆∆u = 0 mit vier reellen Variablen. Comment Math Helv 1935; 7: 307-330. [33] Fueter R. Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen. Comment Math Helv 1935; 8: 371-378. [34] Haefeli H. Hyperkomplexe Differentiale. Comment Math Helv 1947; 20: 382-420. [35] Deavours CA. The quaternion calculus. Amer Math Monthly 1973; 80: 995-1008. [36] Clifford WK, Applications of Grassmann's extensive algebra. Amer J Math 1978; 1: 350-358. [37] Hestenes D. Oersted medal lecture 2002: reforming the mathematical language of physics. Am J Phys 2003; 71,(2): 104-121. [38] Macdonald A. Linear and Geometric Algebra. CreateSpace Independent Publishing Platform; 2011. [39] Hestenes D, Sobczyk G. Clifford Algebra to Geometric Calculus. Holland: Reidel Dordrecht; 1987. [40] Ablamowicz R, Sobczyk G. Lectures on Clifford (Geometric) Algebras and Applications. New York: Springer Science+Business Media; 2004. [41] Chappell JM, Drake SP, Seidel CL, Gunn LJ, Iqbal A, Allison A, Abbott D. Geometric algebra for electrical and electronic engineers. Proc IEEE 2014; 102(9): 1340-1363. [42] Sudbery A. Quaternionic analysis. Math Proc Camb Philos Soc 1979; 85: 199-225. [43] Gürlebeck K, Sprössig W. Quaternionic Analysis and Elliptic Boundary Value Problems. Basel: Birkh¨auser Verlag AG; 1990. [44] Gürlebeck K, Sprössig W. Quaternionic and Clifford Calculus for Physicists and Engineers, New York: John Wiley; 1997. [45] Gilbert J, Murray MAM. Clifford Algebras and Dirac Operators in Harmonic Analysis. Cambridge Univ Press; 1991. [46] Ryan J. Basic Clifford analysis. Cubo Mathématiques Educacional 2000; 2: 226-256. [47] Lounesto P. Clifford Algebras and Spinors. Cambridge, England: Cambridge University Press; 2001. [48] Delanghe R. Clifford Analysis: History and Perspective. Comput Methods Funct Theory 2001; 1: 107-153. [49] Liu LW, Hong H-K. A Clifford algebra formulation of Navier-Cauchy equation. Procedia Eng 2014; 79: 184-188. [50] Liu LW, Hong H-K. A new method for three-dimensional problems of anisotropic elasticity. The 39th National Conference on Theoretical and Applied Mechanics, Taipei, Taiwan, November 20-21, 2015. [51] Lin KF. Boundary integral equation in Clifford analysis, Department of Civil Engineering, National Taiwan University, Taipei, Taiwan, 2008. [52] Hong H-K, Liu LW. Complex boundary integral equations extended to three-dimensional problems using Clifford analyses. The 4th Asia-Pacific International Conference on Computational Methods in Engineering, Kyoto, Japan, 2012. [53] Hong H-K, Liu LW. Clifford valued boundary integral equations. The 2nd TWSIAM Annual Meeting, National Dong Hwa University, Hualien, Taiwan, 2014. [54] Liu LW, Hong H-K. Applications of quaternion-valued boundary element method in the magnetostatic problems. The 38th National Conference on Theoretical and Applied Mechanics, Keelung, Taiwan, ROC, November 21-22, 2014 [55] Liu LW, Hong H-K. Solving three-dimensional elasticity by Clifford valued boundary integral equations. Engineering Mechanics Institute International Conference, Hong-Kong, 7-9 January 2015. [56] Gerus OF, Shapiro M. On a Cauchy-type integral related to the Helmholtz operator in the plane. Bol. Soc. Mat. Mexicana 2004; 10(1): 63-82. [57] Vu Thi Ngoc Ha, Begehr H. Integral representations in quaternionic analysis related to the helmholtz operator. Complex Var 2003; 48(12): 1005-1021. [58] Chantaveerod A, Seagar AD, Angkaew T. Calculation of electromagnetic field with integral equation based on Clifford algebra. PIERS Proceedings, August 27-30, Prague, Czech Republic, 2007; 62-71. [59] Chantaveerod A, Angkaew T. Numerical computation of electromagnetic far-field from near-field using integral equation based on Clifford algebra. Proceedings of Asia-Pacific Microwave Conference 2007. [60] Chantaveerod A, Seagar AD. Iterative solutions for electromagnetic fields at perfectly feflective and transmissive interfaces using Clifford algebra and the multidimensional Cauchy integral. IEEE Trans. Antennas Propag 2009; 57(11): 3489-3499. [61] Chen JT, Lee YT. Torsional rigidity of a circular bar with multiple circular inclusions using the null-field integral approach. Comput Mech 2009; 44: 221-232. [62] Tang RJ. Torsion theory of the crack cylinder. Shanghai: Shanghai Jiao Tong University Publisher; 1996. [in Chinese] [63] Chen JT, Shen WC, Chen PY. Analysis of circular torsion bar with circular holes using null-field approach. CMES-Comp Model Eng Sci 2006; 12(2): 109-119. [64] Timoshenko S, Goodier JN. Theory of Elasticity (Third Edition). New York: McGraw Hill; 1970. [65] Aleynikov SM, Stromov AV. Comparison of complex methods for numerical solutions of boundary problems of the Laplace equation. Eng Anal Bound Elem 2004; 28: 615-622. [66] Reismann H, Pawlik PS. Elasticity Theory and Applications. New York: Wiley; 1980. [67] Balanis CA. Antenna Theory Analysis and Design. New York: Wiley; 1997. [68] Chen G, Zhou J. Boundary Element Methods. New York: Academic Press; 1992. [69] Kisu, H. and Kawahara, T. Boundary element analysis system based on a formulation with relative quantity. Boundary Elements X (Eds. Brebbia, C.A.) 1988; Springer-Verlag: 111-121. [70] Weeks JR. The Shape Of Space: How To Visualize Surfaces and Three-dimensional Manifolds. New York: Marcel Dekker; 1985. [71] Chen JT, Kuo SR, Chen WC, Liu LW. On the free terms of the dual BEM for the two and three-dimensional Laplace problems. J Mar Sci Technol-Taiwan 2000; 8: 8-15.
|