Mapping Educational Specialist knowHow (MESH): the building of a knowledge management system for research informed practice

In this invited article the authors present an evaluative report on the development of the MESHGuides project (http://www.meshguides.org/). MESHGuides’ objective is to provide education with an international knowledge management system. MESHGuides were conceived as research summaries for supporting teachers’ in developing evidence-based practice. Their aim is to enhance teachers’ capacity to engage actively with research in their own classrooms. The original thinking for MESH arose from the work of UK-based academics Professor Marilyn Leask and Dr Sarah Younie in response to a desire, which has recently gathered momentum in the UK, for the development of a more research-informed teaching profession and for the establishment of an on-line platform to support evidence-based practice (DfE, 2015; Leask and Younie 2001; OECD 2009). The focus of this article is on how the MESHGuides project was conceived and structured, the technical systems supporting it and the practical reality for academics and teachers of composing and using MESHGuides. The project and the guides are in the early stages of development, and discussion indicates future possibilities for more global engagement with this knowledge management system.

Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tesselations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.