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Diagnostic tool and online resource providing mathematics support for non-specialists (2019)
Conference Proceeding
Henderson, K., Gwynllyw, R., Walsh, E., Haslam, O., O'Flynn, P., Elvidge, D., & Golden, K. (2019). Diagnostic tool and online resource providing mathematics support for non-specialists. In ICERI2019 Proceedings, (7756-7764). https://doi.org/10.21125/iceri.2019

We report on the development of a diagnostic tool to provide support for non-mathematics students. This tool has been designed to aid the transition onto university courses where mathematics is required during the course, but is not a pre-requisite.... Read More about Diagnostic tool and online resource providing mathematics support for non-specialists.

Stochastic domain decomposition for time dependent adaptive mesh generation (2015)
Journal Article
Bihlo, A., Haynes, R. D., & Walsh, E. (2015). Stochastic domain decomposition for time dependent adaptive mesh generation. https://doi.org/10.4208/jms.v48n2.15.02

The efficient generation of meshes is an important component in the numerical solution of problems in physics and engineering. Of interest are situations where global mesh quality and a tight coupling to the solution of the physical partial different... Read More about Stochastic domain decomposition for time dependent adaptive mesh generation.

The geometry of r-adaptive meshes generated using optimal transport methods (2014)
Journal Article
Walsh, E., Budd, C. J., Russell, R. D., & Walsh, E. (2015). The geometry of r-adaptive meshes generated using optimal transport methods. Journal of Computational Physics, 282, 113-137. https://doi.org/10.1016/j.jcp.2014.11.007

© 2014 Elsevier Inc. The principles of mesh equidistribution and alignment play a fundamental role in the design of adaptive methods, and a metric tensor and mesh metric are useful theoretical tools for understanding a method's level of mesh alignmen... Read More about The geometry of r-adaptive meshes generated using optimal transport methods.

The geometry of r-adaptive meshes generated using optimal transport methods (2014)
Journal Article
Budd, C. J., Russell, R. D., & Walsh, E. (2014). The geometry of r-adaptive meshes generated using optimal transport methods

The principles of mesh equidistribution and alignment play a fundamental role in the design of adaptive methods, and a metric tensor M and mesh metric are useful theoretical tools for understanding a methods level of mesh alignment, or anisotropy. We... Read More about The geometry of r-adaptive meshes generated using optimal transport methods.

Monge-Ampére based moving mesh methods for numerical weather prediction, with applications to the Eady problem (2013)
Journal Article
Budd, C. J., Cullen, M. J., & Walsh, E. J. (2013). Monge-Ampére based moving mesh methods for numerical weather prediction, with applications to the Eady problem. Journal of Computational Physics, 236(1), 247-270. https://doi.org/10.1016/j.jcp.2012.11.014

We derive a moving mesh method based upon ideas from optimal transport theory which is suited to solving PDE problems in meteorology. In particular we show how the Parabolic Monge-Ampére method for constructing a moving mesh in two-dimensions can be... Read More about Monge-Ampére based moving mesh methods for numerical weather prediction, with applications to the Eady problem.


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