W.T. Ang

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

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.

A boundary element model of the human eye undergoing laser thermokeratoplasty

In the present paper, a three-dimensional radially symmetric boundary element model of the human eye is proposed for simulating changes in corneal temperature during treatment of laser thermokeratoplasty. Energy absorption inside the cornea is modeled using the Beer-Lambert law. Heat transfer inside the eye is assumed to be governed by the classical heat diffusion equation. The resulting initial-boundary value problem is solved numerically using a time-stepping boundary element method. The temperature field is calculated for heating by both the pulsed laser and the continuous wave laser. The results obtained are compared with those from other models found in the literature.

A dual-reciprocity boundary element method for a class of elliptic boundary value problems for non-homogeneous anisotropic media

A dual-reciprocity boundary element method is proposed for the numerical solution of a two-dimensional boundary value problem (BVP) governed by an elliptic partial differential equation with variable coefficients. The BVP under consideration has applications in a wide range of engineering problems of practical interest, such as in the calculation of antiplane stresses or temperature in non-homogeneous anisotropic media. The proposed numerical method is applied to solve specific test problems.

On some crack problems for inhomogeneous elastic materials

Abstract The problem of a plane crack in an inhomogeneous material with certain elastic coefficients which exhibit slight variations along the direction perpendicular to the crack is examined in this paper. A series form solution to the problem is proposed and analytical expressions for the first two terms of the series are obtained using a Fourier transform technique. Approximate expressions for the relevant stress intensity factors are also derived.

A boundary element model for investigating the effects of eye tumor on the temperature distribution inside the human eye

A three-dimensional boundary element model of the human eye is developed to investigate the thermal effects of eye tumor on the ocular temperature distribution. The human eye is modeled as comprising several regions which have different thermal properties. The tumor is one of these regions. The thermal effects of the tumor are simulated by taking it to have a very high metabolic heat generation and blood perfusion rate. Inside the tumor, the steady state temperature is governed by the Pennes bioheat equation. Elsewhere, in normal tissues of the eye, the temperature satisfies the Laplaces equation. To compute the temperature on the corneal surface, the surface boundary of each region is divided into triangular elements.

The two-dimensional reaction-diffusion Brusselator system: a dual-reciprocity boundary element solution

Abstract The dual-reciprocity boundary element method is applied for the numerical solution of a class of two-dimensional initial-boundary value problems governed by a non-linear system of partial differential equations. The system, known as the reaction–diffusion Brusselator, arises in the modeling of certain chemical reaction–diffusion processes. Numerical results are presented for some specific problems.

A note on antiplane deformations of inhomogeneous elastic materials

This paper formally obtains the solution of the equations of antiplane inhomogeneous elasticity in terms of an arbitrary analytic function for the case when the shear modulus varies continuously with two Cartesian coordinates. The solution is used to solve a particular boundary value problem involving a crack in an inhomogeneous material.

Efficient parallel algorithm for the two-dimensional diffusion equation subject to specification of mass

An efficient L 0-stable parallel algorithm is developed for the two-dimensional diffusion equation with non-local time-dependent boundary conditions. The algorithm is based on subdiagonal Pade approximation to the matrix exponentials arising from the use of the method of lines and may be implemented on a parallel architecture using two processors running concurrently with each processor employing the use of tridiagonal solvers at every time-step. The algorithm is tested on two model problems from the literature for which discontinuities between initial and boundary conditions exist. The CPU times together with the associated error estimates are compared.

A complex variable boundary element method for elliptic partial differential equations in a multiple-connected region

A simple boundary element method based on the Cauchy integral formulae is proposed for the numerical solution of a class of boundary value problems involving a system of elliptic partial differential equations in a multiple-connected region of infinite extent. It can be easily and efficiently implemented on the computer.

A complex variable boundary element method for an elliptic partial differential equation with variable coefficients

A boundary element method based on the Cauchy integral formulae is proposed for the numerical solutionof a boundary value problem governed by a second-order elliptic partial differential equation with variablecoefficients. The boundary value problem has applications in engineering problems involving non-homogeneous media. The method reduces the boundary value problem to the task of solving a system of linear algebraic equations. It can be easily implemented on the computer. Copyright