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Dr Lawrence Mitchell

Assistant Professor

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Assistant Professor in the Department of Computer ScienceMCS 2024 


I am an Assistant Professor in the Department of Computer Science at Durham University. My research is in high performance computing and computational mathematics. Much of my recent focus has been in the development of compilers and software abstractions for the development of numerical models implemented using the finite element method. This research is concretely realised in the open source Firedrake project. I am particularly interested in preconditioning techniques for challenging problems in computational and atmospheric fluid dynamics.

Research interests

The focus of my work is how to address the increasingly sophisticated needs of computational science practitioners by changing the way we think about numerical models. I develop computational mathematical abstractions that enable the automation of efficient implementations of complex, multiscale, numerical methods on modern supercomputers.

Compilers for numerical software

In the Firedrake project, I work on capturing the mathematical abstractions in numerical models, blending symbolic reasoning and numerical computation. This enables an approach to numerical software development that leverages symbolic information to synthesise high performance, parallel implementations of mathematical algorithms. This is possible through careful design of software abstractions, and development of domain-specific optimising compilers.

Fast solvers for geophysical flows

A large part of sophisticated numerical model development is in the design of robust linear and nonlinear solvers for the equations of interest. I have a particular interest in fast solvers for structure-preserving discretisations in atmospheric fluid dynamics. With Eike Müller, I developed a mesh-, and parameter- independent multigrid scheme for the mixed finite element discretisation proposed for the UK "GungHo" Dynamical Core project. We are presently working on multilevel schemes for the hybridised formulation of these equations, which should permit faster solvers. This latter work is in close collaboration with Colin Cotter, and Thomas Gibson.

Block preconditioners: software and numerics

For many challenging problems, the best performing preconditioning schemes exploit block factorisations and the development of PDE-specific approximations to the block inverses. With Rob Kirby, I developed a mechanism in Firedrake for simple user-defined preconditioners, significantly reducing the development effort necessary to employ optimal solvers in numerical models.

For block saddle-point systems, I am interested in augmented Lagrangian approaches, and am working on parameter robust methods for the Navier-Stokes equations with Patrick Farrell and Florian Wechsung, magnetohydrodynamics with Patrick Farrell and Fabian Laakmann, and hybrised mixed methods in thin domains with Colin Cotter. We are also looking at the same approach for fully-implicit timestepping schemes with large timesteps.

Research groups

  • Innovative Computing


Authored book

  • Gibson, Thomas H., McRae, Andrew T. T., Cotter, Colin J., Mitchell, Lawrence & Ham, David A. (2019). Compatible finite element methods for geophysical flows: automation and implementation using Firedrake. Springer International Publishing.

Chapter in book

  • Markall, Graham R., Rathgeber, Florian, Mitchell, Lawrence, Loriant, Nicolas, Bertolli, Carlo, Ham, David A. & Kelly, Paul H. J. (2013). Performance-Portable Finite Element Assembly Using PyOP2 and FEniCS. In Supercomputing: 28th International Supercomputing Conference, ISC 2013, Leipzig, Germany, June 16-20, 2013. Proceedings. Kunkel, Julian Martin, Ludwig, Thomas & Meuer, Hans Werner Berlin, Heidelberg: Springer. 7905: 279-289.

Conference Paper

  • Rathgeber, Florian, Markall, Graham R., Mitchell, Lawrence, Loriant, Nicolas, Ham, David A., Bertolli, Carlo & Kelly, Paul H.J. (2012), PyOP2: A High-Level Framework for Performance-Portable Simulations on Unstructured Meshes, 2012 SC Companion: High Performance Computing, Networking Storage and Analysis. IEEE, 1116.
  • Mitchell, Lawrence, Sloan, Terence M., Mewissen, Muriel, Ghazal, Peter, Forster, Thorsten, Piotrowski, Michal & Trew, Arthur S. (2011), A parallel random forest classifier for R, 2nd international workshop on Emerging computational methods for the life sciences - ECMLS '11. San Jose, California, USA, Association for Computing Machinery, New York, NY, USA, 1.
  • Piotrowski, Michal, Forster, Thorsten, Dobrezelecki, Bartosz, Sloan, Terence M., Mitchell, Lawrence, Ghazal, Peter, Mewsissen, Muriel, Petrou, Savvas, Trew, Arthur & Hill, Jon (2011), Optimisation and parallelisation of the partitioning around medoids function in R, 2011 International Conference on High Performance Computing & Simulation. 707.

Journal Article

Working Paper

  • Laakmann, Fabian, Farrell, Patrick E. & Mitchell, Lawrence (2021). An augmented Lagrangian preconditioner for the magnetohydrodynamics equations at High Reynolds and coupling numbers.
  • Farrell, Patrick E., Mitchell, Lawrence, Scott, L. Ridgway & Wechsung, Florian (2021). Robust multigrid methods for nearly incompressible elasticity using macro elements. IMA Journal of Numerical Analysis

Supervision students