The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform

A.j. Davies - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear Transient Field Problems with Phase Change using the Boundary Element Method
    Engineering Analysis with Boundary Elements, 2004
    Co-Authors: M. E. Honnor, A.j. Davies
    Abstract:

    Abstract This paper presents the Generalized Newmark Dual Reciprocity Boundary Element Method and the Single Step Dual Reciprocity Boundary Element Method for solving nonlinear transient field problems with phase change. Both are a combination of a general family of single step time marching schemes and the Dual Reciprocity Boundary Element Method. Iterations are performed at each time step using the Newton–Raphson Method with line searches. Latent heat effects due to phase change are incorporated using a fixed-grid apparent heat capacity Method.

  • Parallel implementations of the Boundary Element Method
    Computers & Mathematics with Applications, 1996
    Co-Authors: A.j. Davies
    Abstract:

    Abstract The Boundary Element Method has its origins in the Boundary integral equation Method [1] and has, in the past two decades, become a well-established technique for the solution of problems in engineering and applied science. A significant amount of work has been focused on the development of computer programs, the vast majority of which have been written to run on sequential computers. However, the Boundary Element Method exhibits inherent parallelisms which may be mapped onto a variety of parallel architectures. Over the past few years, Boundary Element researchers have started to realize the possibilities that parallel computing environments offer. Applications from elasticity, electromagnetics, fluid dynamics, etc., have had implementations on both fine-grained and coarse-grained architectures.

M. E. Honnor - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear Transient Field Problems with Phase Change using the Boundary Element Method
    Engineering Analysis with Boundary Elements, 2004
    Co-Authors: M. E. Honnor, A.j. Davies
    Abstract:

    Abstract This paper presents the Generalized Newmark Dual Reciprocity Boundary Element Method and the Single Step Dual Reciprocity Boundary Element Method for solving nonlinear transient field problems with phase change. Both are a combination of a general family of single step time marching schemes and the Dual Reciprocity Boundary Element Method. Iterations are performed at each time step using the Newton–Raphson Method with line searches. Latent heat effects due to phase change are incorporated using a fixed-grid apparent heat capacity Method.

Xinyu Yang - One of the best experts on this subject based on the ideXlab platform.

Shijun Liao - One of the best experts on this subject based on the ideXlab platform.

  • On parallel computing for the general Boundary Element Method
    WIT Transactions on Information and Communication Technologies, 2002
    Co-Authors: X. Y. Zhao, Shijun Liao
    Abstract:

    Liao [2-5] proposed a so-called general Boundary Element Method, which is valid for nearly all nonlinear differential equations, especially those with strong nonlinearity. However, it is well known that, domain integral appears when the BEM is employed to solve a nonlinear problem, which considerably increases the CPU time, In this paper, we propose a parallel general Boundary Element Method. To show its validity, our approach is applied to the viscous flow in a driven square cavity, and we obtain the convergent numerical results even at quite high Reynolds number Re = 7500.

  • On the general Boundary Element Method
    Engineering Analysis with Boundary Elements, 1998
    Co-Authors: Shijun Liao
    Abstract:

    Abstract The basic ideas of the general Boundary Element Method (BEM) proposed by Liao (The quite general BEM for strongly nonlinear problems, in: C. A. Brebbia, S. Kim, T. A. Osswald, H. Power (Eds.), Boundary Elements XVII , Computational Mechanics Publications, Southampton, 1995, pp. 67–74. International Journal of Numerical Methods for Fluids , 1996, 23 , 739–751. International Journal of Numerical Methods in Fluids , 1997, 24 , 863–873) and Liao and Chwang ( International Journal of Numerical Methods for Fluids , 1996, 23 , 467–483) are further greatly generalized by introducing two nonzero parameters to construct homotopies. This general BEM is valid for strongly nonlinear problems, including even those whose governing equations and Boundary conditions do not contain any linear terms. Therefore, it can greatly enlarge the application areas of the Boundary Element Method as a numerical Methodology. A two-dimensional nonlinear differential equation is used to verify the validity of the further generalized Boundary Element Method. Moreover, this example illustrates that, by means of the proposed general Boundary Element Method, iteration is not absolutely necessary for nonlinear problems. This shakes the absolutely governing place of iterative Methodology of the Boundary Element Method for nonlinear problems, and might be beneficial for us to understand the essence of solving nonlinear problems.

  • Boundary Element Method for general nonlinear differential operators
    Engineering Analysis With Boundary Elements, 1997
    Co-Authors: Shijun Liao
    Abstract:

    In this paper, the basic ideas of homotopy in topology is applied to give a kind of high-order Boundary Element Method (BEM) formulations for strongly nonlinear problems governed by quite general nonlinear differential operators which may NOT contain any linear operators at all. As a result, the traditional BEM which treats the nonlinear parts as the inhomogeneities is only a special case of the proposed formulations. Two simple examples are used to illustrate its effectiveness.

Whye-teong Ang - One of the best experts on this subject based on the ideXlab platform.

  • Modeling of PCF with multiple reciprocity Boundary Element Method.
    Optics express, 2004
    Co-Authors: Xiaoyan Wang, Junjun Lou, Chun Liu Zhao, Whye-teong Ang
    Abstract:

    The multiple reciprocity Boundary Element Method (MRBEM) is applied to the modeling of Photonic Crystal Fiber (PCF). With the MRBEM, the Helmholtz equation is converted into an integral equation using a series of higher order fundamental solutions of the Laplace equation. It is a much more efficient Method to analyze the dispersion, birefringence and nonlinearity properties of PCFs compared with the conventional direct Boundary Element Method (BEM).