Numerical integration of area and volume integrals (also known as cubature) is a fundamental, but often overlooked, component of many computational techniques in continuum mechanics. This is especially the case for the Finite Element Method (FEM), where simple cubature techniques have been successfully used for many decades.
This PhD project will focus on developing new cubature techniques (or “rules”) for use in computational mechanics applications, going beyond the standard rules based on outer products of Gaussian quadrature rules. These rules have the potential to allow more accurate integration, while potentially using fewer sampling points than current methods).
This is especially important in the case of computational multiscale methods, where the advantage of fewer sampling points is very important even if it involves a more expensive computation of the cubature rule itself. The possibility of developing more efficient embedded cubature rules will also be considered, with important applications to p-FEM methods involving high-polynomial-order interpolation.
The research in this project will be based on existing preliminary work and proof-of-concept tools using both computer algebra software for symbolic calculatations (Maple) and numerical computation software (Matlab). New results obtained within the project will be implemented and tested within commercial computational mechanics codes, such as the Abaqus FEM software.
Minimum entry qualification - an Honours degree at 2:1 or above (or International equivalent) in a relevant science or engineering discipline, possibly supported by an MSc Degree. Further information on English language requirements for EU/Overseas applicants.
Candidates must have a good background in computational mechanics, numerical analysis or scientific computating.
Applications are welcomed from self-funded students, or students who are applying for scholarships from the University of Edinburgh or elsewhere.