Welcome to my academic web page. I am currently a Research Software Engineer at University College London. On this page, you will find a summary of my main research interests, followed by full lists of my (click to scroll):

You can also find a list of my papers on my Google Scholar and ORCID pages.

My research interested are mostly in the areas of numerical analysis and scientific computing, where I have been working finite element methods (FEM) and boundary element methods (BEM). My work has included both the theoretical analysis of these methods, and the implementation of these methods in open-source software projects.

During my postdoc in Cambridge, I began working on FEniCSx, the new version of the FEniCS finite element method library. FEniCS is a C++ finite element library with a Python user interface.

My contributions to FEniCSx include the implementation degree-of-freedom (DOF) transformations that ensure that the positions and orientations of DOFs of higher order spaces are consistent on edges and faces of elements. This removes the need to re-order the data in the mesh that the user inputs, and allows for a consistent implementation on triangular, tetrahedral, quadrilateral and hexahedral cells. Details of this can be found in Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes (2022).

I am one of the main contributors to Basix, the finite element tabulation library that forms part of FEniCSx. Basix's features are described in Basix: a runtime finite element basis evaluation library (2022)

During my PhD, I became heavily involved in developing Bempp, an open-source boundary element method library. My contributions to the software include work on FEM-BEM coupling, Maxwell's equations, dual function spaces, and the weak imposition of boundary conditions.

You can read more about Bempp in Bempp-cl: A fast Python based just-in-time compiling boundary element library (2021) and Designing a high-performance boundary element library with OpenCL and Numba (2021).

More recently, we have been working on a new version of Bempp (Bempp-rs), written in Rust.

In 2020, I started working on DefElement, an (online) encyclopedia of finite element definitions.

DefElement contains information about the definition of a large (and growing) range of discrete finite element spaces, with examples and references to papers where they were first defined. It is intended to be useful reference tool for anyone working with finite element methods.

The examples shown on DefElement are generated using my open-source symbolic finite element definition and tabulation library Symfem.

I am one of the organisers of the Scientific Computing in Rust annual virtual workshop, and one of the editors of the Scientific Computing in Rust monthly newsletter.

This workshop and newsletter are a way for people using Rust for scientific applications to share project with each other, and come together to plan future collaborations.