The use of and interest in Boundary Integral Methods and their variants have been growing at an ever-increasing rate over the last three decades.
The 8th UK Conference on Boundary Integral Methods was held at the University of Leeds, UK, during 4–5 July 2011. The main aim of the conference (which traditionally maintained a low conference registration fee of £60 only) was for all the researchers in the UK (both senior academics and research staff), and elsewhere, who are working on Boundary Integral Methods (including meshless approximation methods) to meet in an informal way to present their current research work.
As one outcome of the conference, eight selected papers were approved for publication in a Special Issue on ‘Boundary Integral Methods’ of the International Journal of Computer Mathematics (IJCM). These papers represent a good balance between some of the fundamental concepts of boundary element methods (BEMs) and some interesting numerical variants and applications. All the accepted papers are of high standard and continue to bring to the attention of the boundary element community new ideas in the field of boundary integral methods (BIMs).
The papers were internationally refereed, each of them being evaluated by two independent reviewers. Therefore, I must acknowledge those colleagues whose anonymous work is greatly appreciated. I also thank the authors who have worked hard to prepare the full versions of their papers. Finally, I am greatly indebted to Professor Choi-Hong Lai, Editor-in-Chief of IJCM, who kindly approved the publication of the Special Issue and who was also very supportive along the entire review process.
Below, I briefly describe how each paper included in the Special Issue advances the work in the field of Boundary Integral Methods.
A classical BIM for the numerical reconstruction of harmonic functions in three-dimensional multilayer domains containing a bounded cavity is described by Chapko et al. Citation2.
It is well known that the classical BEM based on the explicit availability of a fundamental solutions restricts the application of the method to mainly linear partial differential equations with constant coefficients. If the coefficients are not constant, then one can develop a similar BIM, but based on the parametrix instead of the fundamental solution. These new advances are described in the works by AL-Jawary and Wrobel Citation1, and Mikhailov and Mohamed Citation8.
Applications of the BEM to fluid flow and elasto-plastic problems are described by Khatir and Lucey Citation7, and Elleithy Citation4, respectively.
Finally, inverse problems are addressed using the BEM and a meshless variant of it given by the method of fundamental solutions in the papers by Hào et al. Citation5, Johansson et al. Citation6, and Dawson et al. Citation3.
We hope that the readers will find the material useful and interesting from both the academic and practical points of view.
References
- Chapko , R. , Johansson , B. T. and Protsyuk , O. 2012 . A direct boundary integral equation method for the numerical construction of harmonic functions in three-dimensional layered domains containing a cavity . Int. J Comput. Math. , 89 : 1448 – 1462 .
- AL-Jawary , M. A. and Wrobel , L. C. 2012 . Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods . Int. J Comput. Math. , 89 : 1463 – 1487 .
- Mikhailov , S. E. and Mohamed , N. A. 2012 . Numerical solution and spectrum of boundary-domain integral equation for the Neumann BVP with a variable coefficient . Int. J Comput. Math. , 89 : 1488 – 1503 .
- Khatir , Z. and Lucey , A. D. 2012 . A combined boundary integral and vortex method for the numerical study of three-dimensional fluid flow systems . Int. J Comput. Math. , 89 : 1504 – 1524 .
- Elleithy , W. 2012 . Multi-region adaptive finite element-boundary element method for elasto-plastic analysis . Int. J Comput. Math. , 89 : 1525 – 1539 .
- Hào , D. N. , Thanh , P. X. , Lesnic , D. and Johansson , B. T. 2012 . A boundary element method for a multi-dimensional inverse heat conduction problem . Int. J Comput. Math. , 89 : 1540 – 1554 .
- Johansson , B. T. , Lesnic , D. and Reeve , T. 2012 . A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems . Int. J Comput. Math. , 89 : 1555 – 1568 .
- Dawson , M. , Borman , D. , Hammond , R. B. , Lesnic , D. and Rhodes , D. 2012 . Detection of a two-dimensional moving cavity . Int. J Comput. Math. , 89 : 1569 – 1582 .