SOSORT consensus paper: school screening for scoliosis. Where are we today?

This report is the SOSORT Consensus Paper on School Screening for Scoliosis discussed at the 4th International Conference on Conservative Management of Spinal Deformities, presented by SOSORT, on May 2007. The objectives were numerous, 1) the inclusion of the existing information on the issue, 2) the analysis and discussion of the responses by the meeting attendees to the twenty six questions of the questionnaire, 3) the impact of screening on frequency of surgical treatment and of its discontinuation, 4) the reasons why these programs must be continued, 5) the evolving aim of School Screening for Scoliosis and 6) recommendations for improvement of the procedure

Boundary layer preconditioners for finite-element discretizations of singularly perturbed reaction-diffusion problems

We consider the iterative solution of linear systems of equations arising from the discretization of singularly perturbed reaction-diffusion differential equations by finite-element methods on boundary-fitted meshes. The equations feature a perturbation parameter, which may be arbitrarily small, and correspondingly, their solutions feature layers: regions where the solution changes rapidly. Therefore, numerical solutions are computed on specially designed, highly anisotropic layer-adapted meshes. Usually, the resulting linear systems are ill-conditioned, and so, careful design of suitable preconditioners is necessary in order to solve them in a way that is robust, with respect to the perturbation parameter, and efficient. We propose a boundary layer preconditioner, in the style of that introduced by MacLachlan and Madden for a finite-difference method (MacLachlan and Madden, SIAM J. Sci. Comput. 35(5), A2225–A2254 2013). We prove the optimality of this preconditioner and establish a suitable stopping criterion for one-dimensional problems. Numerical results are presented which demonstrate that the ideas extend to problems in two dimensions