Y. Ochiai

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 435-446, 2001, DOI:10.3970/cmes.2001.002.435

Abstract The boundary element method (BEM) is useful in solving the steady heat conduction problem of orthotropic bodies without heat generation. However, for cases with arbitrary heat generation, a number of internal cells are necessary. In this paper, it is shown that the problem of steady heat conduction in orthotropic bodies with heat generation can be solved without internal cells by the triple-reciprocity BEM. In this method, the distribution of heat generation is interpolated using integral equations. In order to solve the problem, the values of heat generation at internal points and on the boundary are used. Furthermore, a new interpolation… More >

M.A. Golberg¹, C.S. Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.1, pp. 87-96, 2001, DOI:10.3970/cmes.2001.002.087

Abstract The purpose of this paper is to develop a highly efficient mesh-free method for solving nonlinear diffusion-reaction equations in R^d, d=2, 3. Using various time difference schemes, a given time-dependent problem can be reduced to solving a series of inhomogeneous Helmholtz-type equations. The solution of these problems can then be further reduced to evaluating particular solutions and the solution of related homogeneous equations. Recently, radial basis functions have been successfully implemented to evaluate particular solutions for Possion-type equations. A more general approach has been developed in extending this capability to obtain particular solutions for Helmholtz-type equations by using polyharmonic spline… More >

M. Kögl, L. Gaul²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 27-44, 2000, DOI:10.3970/cmes.2000.001.479

Abstract A Boundary Element formulation is presented for the solution of three-dimensional problems of anisotropic elastodynamics. Due to the complexity of the dynamic fundamental solutions for anisotropic materials and the resulting high computational costs, the approach at hand uses the fundamental solution of the static operator. This leads to a domain integral in the representation formula which contains the inertia term. The domain integral can be transformed to the boundary using the Dual Reciprocity Method. This results in a system of ordinary differential equations in time with time-independent matrices. Several general questions concerning the anisotropic solutions, the use of DRM, and… More >

Chia-Cheng Tsai ¹

CMC-Computers, Materials & Continua, Vol.22, No.3, pp. 197-218, 2011, DOI:10.3970/cmc.2011.022.197

Abstract This paper describes the combination of the method of fundamental solutions (MFS) and the dual reciprocity method (DRM) as a meshless numerical method to solve problems of Kirchhoff plates under arbitrary loadings. In the solution procedure, a arbitrary distributed loading is first approximated by either the multiquadrics (MQ) or the augmented polyharmonic splines (APS), which are constructed by splines and monomials. The particular solutions of multiquadrics, splines and monomials are all derived analytically and explicitly. Then, the complementary solutions are solved formally by the MFS. Furthermore, the boundary conditions of lateral displacement, slope, normal moment, and effective shear force are… More >

Eduardo Divo¹, Alain J. Kassab²

CMC-Computers, Materials & Continua, Vol.2, No.4, pp. 277-288, 2005, DOI:10.3970/cmc.2005.002.277

Abstract A Dual Reciprocity Boundary Element Method is formulated to solve non-linear heat conduction problems. The approach is based on using the Kirchhoff transform along with lagging of the effective non-linear thermal diffusivity. A posteriori error estimate is used to provide effective estimates of the temporal and spatial error. A numerical example is used to demonstrate the approach. More >