An Inverse Geometry Problem for the Localization of Skin Tumours by Thermal Analysis

In this paper, the Dual Reciprocity Method (DRM) is coupled to a Genetic Algorithm (GA) in an inverse procedure through which the size and location of a skin tumour may be obtained from temperature measurements at the skin surface. The GA is an evolutionary process which does not require the calculation of sensitivities, search directions or the definition of initial guesses. The DRM in this case requires no internal nodes. It is also shown that the DRM approximation function used is not an important factor for the problem considered here. Results are presented for tumours of different sizes and positions in relation to the skin surface

Dynamic analysis of shear deformable plates using the dual reciprocity method

The Dual Reciprocity Method is a popular mathematical technique to treat domain integrals in the boundary element method (BEM). This technique has been used to treat inertial integrals in the dynamic thin plate bending analysis using a direct formulation of the BEM based on the elastostatic fundamental solution of the problem. In this work, this approach was applied for the dynamic analysis of shear deformable plates based on the Reissner plate bending theory, considering the rotary inertia of the plate. Three kinds of problems: modal, harmonic and transient dynamic analysis, were analyzed. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed formulation. © 2011 Elsevier Ltd. All rights reserve

A NUMERICAL STUDY OF SUBSTANCE SPREAD IN THE POLL FROM TWO POINT SOURCES

Problems related to the purification of holding pool or reservoir become an interesting discussion in real events. In this paper, the author will modeling the distribution of the substance/purifier in a pool model with turbulent water flow using the diffusion-convection equation. The Dual Reciprocity Method is applied to the diffusion-convection equation whose derivation will be discussed in this paper. This method is chosen because the problem cannot be solved analytically, so it must be solved numerically. The Dual Reciprocity Method has good flexibility in problems of water infiltration, pollutant spread, and heat transfer. In this paper also discuss velocity profile of turbuelent flow from upcoming part of pool region. So before using DRM, will be used numerical solution of turbulent flow by k-epsilon turbulent model. In numerical calculations, two source points are selected whose positions are combined to see the most effective way to make the substance/purifier evenly distributed in the pool. &nbsp

Nonlinear Transient Field Problems with Phase Change using the Boundary Element Method

Peer reviewe

Symmetric boundary knot method

The boundary knot method (BKM) is a recent boundary-type radial basis function (RBF) collocation scheme for general PDEs. Like the method of fundamental solution (MFS), the RBF is employed to approximate the inhomogeneous terms via the dual reciprocity principle. Unlike the MFS, the method uses a nonsingular general solution instead of a singular fundamental solution to evaluate the homogeneous solution so as to circumvent the controversial artificial boundary outside the physical domain. The BKM is meshfree, superconvergent, integration free, very easy to learn and program. The original BKM, however, loses symmetricity in the presense of mixed boundary. In this study, by analogy with Hermite RBF interpolation, we developed a symmetric BKM scheme. The accuracy and efficiency of the symmetric BKM are also numerically validated in some 2D and 3D Helmholtz and diffusion reaction problems under complicated geometries

A coupled dual reciprocity BEM/Genetic algorithm for identification of blood perfusion parameters

The paper presents an inverse analysis procedure based on a coupled numerical formulation through which the coefficients describing non-linear thermal properties of blood perfusion may be identified. The numerical technique involves a combination of the Dual Reciprocity Boundary Element Method and a Genetic Algorithm for the solution of the Pennes bioheat equation. Both linear and quadratic temperature-dependent variations are considered for the blood perfusion

A meshless, integration-free, and boundary-only RBF technique

Based on the radial basis function (RBF), non-singular general solution and dual reciprocity method (DRM), this paper presents an inherently meshless, integration-free, boundary-only RBF collocation techniques for numerical solution of various partial differential equation systems. The basic ideas behind this methodology are very mathematically simple. In this study, the RBFs are employed to approximate the inhomogeneous terms via the DRM, while non-singular general solution leads to a boundary-only RBF formulation for homogenous solution. The present scheme is named as the boundary knot method (BKM) to differentiate it from the other numerical techniques. In particular, due to the use of nonsingular general solutions rather than singular fundamental solutions, the BKM is different from the method of fundamental solution in that the former does no require the artificial boundary and results in the symmetric system equations under certain conditions. The efficiency and utility of this new technique are validated through a number of typical numerical examples. Completeness concern of the BKM due to the only use of non-singular part of complete fundamental solution is also discussed

Boundary knot method: A meshless, exponential convergence, integration-free, and boundary-only RBF technique

Based on the radial basis function (RBF), non-singular general solution and dual reciprocity principle (DRM), this paper presents an inheretnly meshless, exponential convergence, integration-free, boundary-only collocation techniques for numerical solution of general partial differential equation systems. The basic ideas behind this methodology are very mathematically simple and generally effective. The RBFs are used in this study to approximate the inhomogeneous terms of system equations in terms of the DRM, while non-singular general solution leads to a boundary-only RBF formulation. The present method is named as the boundary knot method (BKM) to differentiate it from the other numerical techniques. In particular, due to the use of non-singular general solutions rather than singular fundamental solutions, the BKM is different from the method of fundamental solution in that the former does no need to introduce the artificial boundary and results in the symmetric system equations under certain conditions. It is also found that the BKM can solve nonlinear partial differential equations one-step without iteration if only boundary knots are used. The efficiency and utility of this new technique are validated through some typical numerical examples. Some promising developments of the BKM are also discussed.Comment: 36 pages, 2 figures, Welcome to contact me on this paper: Email: [email protected] or [email protected]