Standard BEM Research Articles

Applying BEM to modelling of uptaking pollutants in clouds or fog drops

A one-dimensional coupled diffusion and chemical reaction steady-state problem in spherical geometry has been considered. This type of problem is often encountered in atmospheric chemistry when dealing with uptaking of gaseous pollutants in cloud or fog drops. A closed form fundamental solution of the governing equation has been obtained. Making use of this solution and following the standard BEM approach, the boundary value problem under consideration has been transformed into a nonlinear integral equation. The discretization of this equation resulted in a set of nonlinear algebraic equations solved by the Newton-Raphson solver. For specific, linear cases the results obtained have been compared with analytical solutions available in the literature. Good accuracy has been observed. Numerical examples dealing with two coupled nonlinear equations describing diffusion with chemical reaction of two species have been included.

Alternative formulation of boundary‐element method for two‐dimensional electromagnetic boundary‐value problems

AbstractAn alternative formulation of the Boundary Element Method for internal two‐dimensional electromagnetic boundary‐value problems related to Helmholtz equation is presented.The formulation does not require the computation of special functions and the speed of computation is considerably faster than in standard formulations of BEM. The method of moments is used to solve the integral equation of BEM and all the integrals are computed analytically.Several examples of application of the method to the study of planar structures are shown and a comparison with the results obtained with standard BEM analysis is presented.

A boundary integral method for internal piece-wise smooth crack problems

A new boundary integral method for plane elasticity problems with internal piece-wise smooth cracks is presented. The method can be applied to both infinite and finite geometries. A numerical technique which combines a collocation method for the cracks and the standard BEM technique for the outer boundary is used to solve the integral equations. Numerical examples are presented and compared either to existing solutions or to FEM calculations. All of the results provided by the present method are shown to be very accurate for both smooth and kinked cracks in both finite and infinite geometries.