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【期刊论文】Numerical evaluation of two-dimensional singular boundary integrals—Theory and Fortran code
高效伟, Xiao-Wei Gao
X. -W. Gao. Journal of Computational and Applied Mathematics 188 (2006) 44-64,-0001,():
-1年11月30日
In this paper, an approach is presented for the numerical evaluation of weakly, strongly, hyper- and super-singular boundary integrals which exist in the Cauchy principal value sense in two-dimensional problems. In this approach, the singularities involved in integration kernels are analytically removed by expressing the nonsingular parts of the integration kernels as polynomials of the distance r. A self-contained Fortran code is listed and described for implementation of the proposed approach. The attached code is also able to evaluate general regular integrals using Gaussian quadrature, which enables the code to evaluate any two-dimensional boundary integral. Some examples are provided to verify the correctness of the presented formulations and the included code.
Boundary integral, Singular integrals, Boundary element, Gaussian quadrature, Fortran subroutine
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高效伟, Xiao-Wei Gao
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids (in press),-0001,():
-1年11月30日
In this paper, explicit boundary-domain integral equations for evaluating velocity gradients are derived from the basic velocity integral equations. A free term is produced in the new strongly singular integral equation, which is not included in recent formulations using the complex variable differentiation method (CVDM) to compute velocity gradients (Int. J. Numer Meth. Fluids 2004; 45:463-484; Int. J. Numer Meth. Fluids 2005; 47:19-43). The strongly singular domain integrals involved in the new integral equations are accurately evaluated using the radial integration method (RIM). Considerable computational time for evaluating integrals of velocity gradients can be saved by using present formulation than using CVDM. The formulation derived in this paper together with those presented in reference (Int. J. Numer. Meth. Fluids 2004; 45:463-484) for 2D and in (Int. J. Numer Meth. Fluids 2005; 47:19-43) for 3D problems constitutes a complete boundary-domain integral equation system for solving full Navier-Stokes equations using primitive variables. Three numerical examples for steady incompressible viscous flow are given to validate the derived formulations. Copyright 2007 John Wiley & Sons, Ltd.
viscous flow, Navier-Stokes equations, boundary element method (, BEM), , complex variable differentiation method (, CVDM), , fundamental solution
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高效伟, Xiao-Wei Gao
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2006; 66: 1411-1431,-0001,():
-1年11月30日
In this paper, a new and simple boundary-domain integral equation is presented for heat conduction problems with heat generation and non-homogeneous thermal conductivity. Since a normalized temperature is introduced to formulate the integral equation, temperature gradients are not involved in the domain integrals. The Green’s function for the Laplace equation is used and, therefore, the derived integral equation has a unified form for different heat generations and thermal conductivities. The arising domain integrals are converted into equivalent boundary integrals using the radial integration method (RIM) by expressing the normalized temperature using a series of basis functions and polynomials in global co-ordinates. Numerical examples are given to demonstrate the robustness of the presented method.
boundary element method, meshless method, heat conduction, heat generation rate, non-homogeneous media
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高效伟, Xiao-Wei Gao
X. -W. Gao. Journal of Computational and Applied Mathematics 175 (2005) 265-290,-0001,():
-1年11月30日
In this paper, a set of boundary integrals are derived based on a radial integration technique to accurately evaluate two dimensional (2D) and three dimensional (3D), regular and singular domain integrals. A self-contained Fortran code is listed and described for numerical implementation of these boundary integrals. The main feature of the theory is that only the boundary of the integration domain needs to be discretized into elements. This feature can not only save considerable efforts in discretizing the integration domain into internal cells (as in the conventional method), but also make computational results for singular domain integrals more accurate since the integrals have been regularized. Some examples are provided to verify the correctness of the presented formulations and the included code.
Domain integral, Boundary integral, Radial integration, Singular integrals, Fortran subroutine
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【期刊论文】ADAPTIVE INTEGRATION IN ELASTO-PLASTIC BOUNDARY ELEMENT ANALYSIS
高效伟, Xiao-Wei Gao, Trevor G. Davies
Journal of the Chinese Institute of Engineers, Vol. 23, No. 3, pp. 349-356 (2000),-0001,():
-1年11月30日
addaptive integration, elasto-plasticity, method boundary element
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