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BEM/MRM 31 Post Conference Report

31st International Conference on Boundary Elements and Other Mesh Reduction Methods

2 - 4 September 2009
New Forest, UK



The 31st International Conference on Boundary Element Methods and other Mesh Reduction Methods (BEM/MRM) took place recently at the Wessex Institute of Technology Campus in the New Forest UK.

Professor Carlos Brebbia, Director of WIT, opened the Conference by referring to the continuous success and vitality of the Boundary Elements Research which continues to surprise not only all newcomers to the technique but even researchers like himself who have been deeply committed to its development since its very beginning.

The term Boundary Elements was coined in 1977 together with the methodology presented in a paper that Carlos wrote with Jose Dominguez and which was published in the International Journal of Applied Mathematical Modelling. The paper was the culmination of an effort to link the then recent developments in finite elements with the boundary integral theory. This work set up the basis for the boundary element method as we know it, even providing the notation now widespread in the literature. It also consolidated a series of ideas related to mixed type variational statements which were essential to pave the way for applications of boundary integral equations beyond the limitations of linearity.

Boundary integral techniques were able to expand their range of applications through their interpretation in terms of BEM. This was the result of cross fertilisation between the Russian school, the mixed principles developed at MIT and the computational advances of the UK Group.

The simplicity and elegance of BEM led to a wider awareness of the potentialities of the method and the realisation that integral equations were also open to experimentation and approximations.

This was conducive to a new type of development, typical of which was the Dual Reciprocity Method, a totally different conceptual approach. DRM not only applied the novel idea of using localised particular solutions but also allowed for them to be approximated. The fortunate discovery that they worked well with radial basis functions was also of great importance for the development of a whole new generation of meshless methods.

In parallel to the DRM developments, work was proceeding in other ways to transfer internal effects to the boundary using exact solutions, ie the Green’s functions themselves. The generalisation of that concept led to the development of the Multiple Reciprocity Method. The beauty of this method is that it led not just to meshless domains but that also bypassed the need to have any internal nodes as in the case of DRM. The limitation of requiring analytical expression for the internal terms led however to lack of sustained interest in the MRM, which was seen as less versatile than DRM.

Many other approaches have been put forward following those basic ideas as evidenced by the numerous papers on meshless methods which continue to be published in the Journal of Engineering Analysis with Boundary Elements.


The next stage, Carlos said, will be for one or more of the meshless methods to achieve maturity and become a practical tool, in much the same way as classical BEM. The papers published in this Conferences dealing with mesh reduction methods demonstrate their continuous evolution and the possibility of having reliable and robust meshless techniques in engineering practice in the future.

It is always a source of personal pleasure for Carlos to see the way in which the original BEM ideas continue to develop in the hands of new researchers as well as our senior colleagues.

The quality and originality of the papers presented at this Conference is a demonstration of the continuous evolution of BEM research.

Carlos also referred to the work carried out at WIT and in particular the new developments in modelling methods using Mesh Reduction Methods. This work is carried out in the different research divisions of WIT, ie Environmental Fluid Mechanics under Professor Viktor Popov; Damage Mechanics headed by Professor Alex Galybin; Information and Communications Engineering under Dr Andres Peratta; and the Industrial Research Unit headed by Dr Robert Adey.

The most important of WIT's activities, Carlos continued, is the one carried out by the Conference Division which organises a series of meetings and courses held all over the world. These activities involve the transfer of knowledge between academia, research organisations and industry. The transfer of knowledge is also the objective of WIT Press, the academic publisher of the Institute, which has recently launched a series of new journals, all of them dealing with interdisciplinary work.

Carlos ended his welcoming address by inviting the participants to visit the main building on Campus where the research activities are carried out.

Finally, Carlos announced the early departure of our friend and colleague Professor Steve Gipson, who contributed so much to the development of BEM and participated in many of these conferences. Steve was born in Jackson, Mississippi in 1952 and lived in Stillwater, Oklahoma, where he was Professor of Structural Engineering and Mechanics at Oklahoma State University. He was educated at Louisiana State University where he received a BS in Physics, a Master and a PhD in Engineering Sciences.

He organised the XIII Boundary Element Methods Conference in Tulsa, Oklahoma, in 1991, wrote a very successful book on the mathematical basis of BEM and served for a long time as a Member of the Editorial Board of the International Journal of Engineering Analysis with Boundary Elements. He passed away at the beginning of 2009 and will be sorely missed by the BEM community, among whom he was very much liked for his friendliness and generous behaviour, as well as for the excellence of his scientific research.

Invited Presentations

The papers presented at the Meeting included a series of invited presentations as follows:

  • “Multipole expansion BEM for simultaneous Poisson’s equations” by T. Matsumoto, Nagoya University, Japan
  • “Equivalence between the Trefftz method and the method of fundamental solutions for Green’s function of concentric spheres using the addition theorem and image concept” by JT Chen, Taiwan Ocean University, Taiwan
  • “The radial basis integral equation method for convection-diffusion problems” by V Popov, Wessex Institute of Technology, UK
  • “Meshless implementations of local integral equations” by V Sladek, Slovak Academy of Sciences, Slovakia
  • “Local and virtual RBF meshless method for high-speed flows” by A Kassab, University of Central Florida, USA
  • “Boundary element modelling of non-linear buckling for symmetrically laminated plates” by S Syngellakis, University of Southampton, UK
  • “Effective properties of fibers with various ratios of phase stiffness” by P Prochazka, Czech Technical University, Prague
  • “On stress reconstruction in composite domains from discrete data on principal directions” by A Galybin, Wessex Institute of Technology, UK
  • “Cohesive crack propagation using a boundary element formulation with a tangent operator”, by ED Leonel, University of S. Paolo at S. Carlos, Brazil
  • “Velocity-based integral equation formulation in the time domain” by GD Manolis, University of Thessaloniki, Greece
  • “Trefftz collocation for frequency domain elastodynamic problems” by VMA Leitao, Instituto Superior Tecnico, Portugal
  • “Numerical Green’s function for a two-dimensional diffusion equation” by WJ Mansur, COPPE, Federal University of Rio, Brazil
  • “Coupling the BEM/TBEM and the MFS for the numerical simulation of acoustic wave propagation and transient conduction heat transfer” by A Tadeu, University of Coimbra, Portugal
  • “The shape factor in multiquadratic collocation for high accuracy computation”, by AH-D Cheng, University of Mississippi, USA
  • “Meshless, BE, FE and FD methods analysis of the flow and concentration in a water reservoir” by M Kanoh, Kyushu Sangyo University, Japan
  • “Natural convection around a 3D hotstrip simulated by BEM” by J Ravnik, University of Maribor, Slovenia
  • “Motion of nanoscale contaminant particle in air bearings under electrostatic charges: a case study” by BW Yeigh, SUNY Institute of Technology, USA
  • “Boundary element modelling of horizontal grounding electrodes using the set of generalized telegrapher’s equations” by D Poljak, University of Split, Croatia

Conference Topics


The conference papers were grouped under the following topics:

  • Advanced formulations
  • Advanced meshless and mesh reduction methods
  • Computational methods
  • Advanced structural applications
  • Damage mechanics and fracture
  • Dynamics and vibrations
  • Fluid flow
  • Electrical engineering and electromagnetic

Social Activities

The participants had ample opportunities for socialising and getting to know each other better. The lunch break during the first day of the conference took place during a visit to Lymington, a scenic coastal town, full of interesting sights, museums and shops. Lymington is famous for its sailing heritage which is reflected now in its many sailing clubs. During the middle ages Lymington had a thriving ship-building business. The port was very busy and although the majority of the work was legal, the town became infamous for smuggling. Many of the numerous local inns were used as hideouts for illegal activities. The industry thrived, with the most popular contraband being brandy and silks.

EABE Meeting


The Meeting of the Editorial Board of the International Journal of Engineering Analysis with Boundary Elements and other Mesh Reduction Methods took place after dinner during the first evening of the Conference. Elsevier’s Publisher responsible for the Journal reported to the Members on the advances made by the Journal during the last year. This included the growth in the number of papers received, a larger number of papers published and a substantial increase in the size of the 2009 Volume. The success of the publication reflects the increasing research work carried out by the international scientific community and the decision taken five or so years ago to attract papers on all types of mesh reduction techniques which was a direct consequence of the evaluation of research in boundary problems.

An important special issue was put together by Professor Andreas Karageorghis on Fundamental Solutions in honour of the late Professor Michael Golberg who served for many years on the Board of the Journal. The issue on Fundamental Solutions will be a most appropriate memorial to Mike’s work.

Hog Roast and Conference Dinner


Participants were invited to a lunch time Hog Roast on the second day of the meeting around the pool are which them another chance to socialise. The weather, atrocious until then, was bright and sunny for the event which was characterised by a friendly atmosphere. They also had occasion to see some of the more recent developments at Ashurst Lodge, including the newly built BBQ house!

The Conference dinner took place in a local restaurant, renowned for its excellent cuisine and a unique wine cellar. The event provided another opportunity for interaction among the delegates in a friendly environment.

The Conference, which was very successful, will be reconvened from 7 to 9 September 2010 also at Ashurst Lodge.

Publication of Papers


The proceedings of Boundary Elements and Other Mesh Reduction Methods XXXI, 432pp (Print ISBN: 1-84564-197-9; On-line ISBN: 1-84564-374-4; Print ISSN: 1746-4064) are available from WIT Press priced at £164/US$295/€213. Orders can be placed by telephone: +44 (0) 238 029 3223, fax: +44 (0) 238 029 2853, e-mail: or via the WIT Press web site at

Papers from the conference will also be hosted online at the WIT eLibrary as volume 49 of WIT Transactions on Modelling and Simulation (On-line ISSN: 1743-1743-355X). For more details visit the WIT eLibrary at

For further information about other BEM publications or the International Journal of Engineering Analysis with Boundary Methods and other Mesh Reduction Methods, please contact Information about the BEM Community can be found at

Patagonia a forgotten land – from Magellan to Peron, by C.A. Brebbia, 384 pp (ISBN 978-1-84564-061-3) is available in hard back from WIT Press, priced at £33/US$59/€49.50. Orders can be placed as above.

The New Forest: A Personal View, by C.A. Brebbia, 128pp (ISBN 1-84564-145-0) is available in hard back from WIT Press, priced at £19.50/US$39/€26. Orders can be placed as above.


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