The Boundary Element Dual Reciprocity Method - Multidomain Approach for Solving 3D Potential Problems
Bruno Natalini, who holds a degree in Mechanical Engineering and a Master in Applied Mechanics from the Universidad Nacional del Nordeste, Argentina, has recently completed his PhD degree at Wessex Institute of Technology entitled ‘The Boundary Element Dual Reciprocity Method – Multidomain Approach for Solving 3D Potential Problems’. The external examiner was Prof Maria da Cunha from the Universidade de Coimbra, Portugal and the internal examiner was Dr Robert Adey the Head of Industrial Research Division at WIT.
The research was focused in the extension of the Boundary Element Dual Reciprocity Method - Multidomain Approach (DRM-MD) to problems defined in three-dimensional domains.
The DRM-MD is a technique to approach domain dominant problems that combines the DRM and domain subdivision in the limiting case when the mesh looks like a Finite Element mesh. It has the advantage on the single domain formulation that the resulting system of equations is sparse and well conditioned and that iterative solvers can be used, which makes the method suitable to model large problems.
The DRM-MD had been applied only in a relatively small number of 2D linear and non linear problems, mainly related to fluid dynamics, showing good performance regarding both accuracy and versatility. The extension of the procedure to 3D cases, and especially to large 3D problems, is not straightforward since factors such as continuity of the elements, DRM approximation function, scaling, number of internal DRM nodes, etc., which largely affect the performance of the code, need to be selected.
3D DRM-MD codes were built to solve the Poisson equation, flow in both saturated and unsaturated porous media, both steady-state and transient transport in porous media under a variety of schemes. The results give a comprehensive insight on 3D implementation of DRM-MD for an even wider range of problems with emphasise on those details that optimize the approach of large problems.
The BEM solution for flow in unsaturated media has been reported previously in the literature, but for 1D and 2D problems only. This was the first time that flow in unsaturated porous media had been modelled using a 3D BEM code. In addition, Compactly Supported Radial Basis Functions were used for the first time in DRM-MD codes. The DRM-MD showed to be as versatile and efficient when applied to problems defined in 3D domains as it is when solving 2D problems.
Bruno gave a good presentation of his work and after questions from both examiners was recommended for the award of Doctor of Philosophy.