A boundary element method for a second order elliptic partial differential equation with variable coefficients

Ang, W.T.; Kusuma, Jeffry; Clements, D. L.

doi:10.1016/s0955-7997(97)83178-5

Cited by 47 publications

(27 citation statements)

References 5 publications

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“…In applying this technique there are a number of possibilities in the choice of g(x) and λ (1) ij (x) in order to provide the coefficients (22) from the form given in equation (2). Two possible forms for g(x) and λ (1) ij (x) are considered here.…”

Section: Problemmentioning

confidence: 99%

“…For this problem an approximate solution is sought in the form (16) with one iteration; that isT =T (0) + T (1) , wherē T (0) andT (1) satisfy (10) and (17) for r = 0, 1 respectively. Table 1 compares the analytic and boundary element method (bem) results for a number of points in the domain Ω and for the cases when the boundary ∂Ω is divided into 8, 32 and 64 segments.…”

Section: C89mentioning

confidence: 99%

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A boundary element method for the numerical solution of a class of elliptic boundary value problems for anisotropic inhomogeneous media

Azis

Clements

Budhi

2003

ANZIAMJ

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Section: Problemmentioning

confidence: 99%

Section: C89mentioning

confidence: 99%

A boundary element method for the numerical solution of a class of elliptic boundary value problems for anisotropic inhomogeneous media

Azis

Clements

Budhi

2003

ANZIAMJ

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“…However, solving the problems of the nonlinear, non-homogeneous and variable coefficients by BEM is difficult, since the fundamental solutions of these problems can hardly obtain, except for some very special cases [6,7]. It was a good way that the fundamental solution of the linear problems to solve the problems of the nonlinear, nonhomogeneous, whereas domain integrals was involved in the resulting integral equations.…”

Section: Introductionmentioning

confidence: 99%

A time-domain precise BEM for solving transient heat conduction problems with variable heat conductivities

Yao

Gao

2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

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In this paper, the Green's function for the Laplace equation is adopted to derive the boundary integral equation for solving transient heat conduction problems with variable heat conductivities and heat sources. As a result, domain integrals are involved in the derived integral equations. Firstly, the radial integration method is used to convert the domain integrals into equivalent boundary integrals. Then, by expanding variables at a discrete time interval, the recursive formulation of the governing equation is derived. Finally, the recursive equation is solved by the radial integration boundary element method. A self-adaptive check technique is carried out to estimate how many expansion terms are needed in a time step size. Numerical results show satisfactory performance.

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“…One possible technique is to find a fundamental solution for the non-linear, non-homogeneous problem or problem with variable coefficients which can provide a pure boundary integral equation. Unfortunately, these fundamental solutions are only available for some very special cases [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods

AL-Jawary¹,

Wrobel²

2012

International Journal of Computer Mathematics

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Abstract. This paper presents new formulations of the boundary-domain integral equation (BDIE) and the boundary-domain integro-differential equation (BDIDE) methods for the numerical solution of the two-dimensional Helmholtz equation with variable coefficients. When the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or BDIDE. However, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. The radial integration method is then employed to convert the domain integrals arising in both BDIE and BDIDE methods into equivalent boundary integrals. The resulting formulations lead to pure boundary integral and integrodifferential equations with no domain integrals. Numerical examples are presented for several simple problems, for which exact solutions are available, to demonstrate the efficiency of the proposed methods.

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A boundary element method for a second order elliptic partial differential equation with variable coefficients

Abstract: A boundary element method is derived for solving a class of boundary value problems governed by an elliptic second order linear partial differential equation with variable coefficients. Numerical results are given for a specific test problem.

Cited by 47 publications

References 5 publications

A boundary element method for the numerical solution of a class of elliptic boundary value problems for anisotropic inhomogeneous media

A boundary element method for the numerical solution of a class of elliptic boundary value problems for anisotropic inhomogeneous media

A time-domain precise BEM for solving transient heat conduction problems with variable heat conductivities

Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods

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