Joe Wallwork

Numerical methods for solving PDEs, including:

• Anisotropic mesh adaptation
• Adjoint methods
• Goal-oriented error estimation
• Automatic differentiation

Applications in coastal ocean modelling, including:

• Tidal turbine modelling
• Tsunami propagation modelling
• Desalination outfall modelling

• J. G. Wallwork, A. Angeloudis, N. Barral, L. Mackie, S. C. Kramer, M. D. Piggott, Tidal turbine array modelling using goal-oriented mesh adaptation. In: Journal of Ocean Engineering and Marine Energy (2022), doi:10.1007/s40722-023-00307-9.
• T. Karna, J. G. Wallwork, and S. C. Kramer,  Adjoint-based optimization of a regional water elevation model. In: Journal of Advances in Modeling Earth Systems (2022), doi:10.1029/2022MS003169.
• W. Song, M. Zhang, J. G Wallwork, J. Gao, Z.Tian, F.Sun, M. Piggott, J. Chen, Z. Shi, X. Chen, and J. Wang. M2N: Mesh movement networks for PDE solvers. In: Advances in Neural Information Processing Systems, 35:7199–7210, 2022. URL https://proceedings.neurips.cc/paperfiles/paper/
  2022/file/2f88d8061f12abae9d14d376fd69c933-Paper-Conference.pdf.
• J. G. Wallwork, M.G. Knepley, N. Barral, M. D. Piggott, Parallel Metric-Based Mesh Adaptation in PETSc using ParMmg. Research note, 30th International Meshing Roundtable (2022), arXiv:2201.02806.
• J. G. Wallwork, L. Mackie, S. C. Kramer, N. Barral, A. Angeloudis, M.D. Piggott, Goal-Oriented Metric-Based Mesh Adaptive Tidal Farm Modelling. In: IX International Conference on Computational Methods in Marine Engineering (2022). doi:10.2218/marine2021.6795.
• J. G. Wallwork, N. Barral, D. A. Ham, M. D. Piggott, Goal-Oriented Error Estimation and Mesh Adaptation for Tracer Transport Modelling. Computer-Aided Design, 145:103187 (2022), doi:10.1016/j.cad.2021.103187.
• M. C. A. Clare, J. G. Wallwork, S. C. Kramer, H. Weller, C. J. Cotter, M. D. Piggott, Multi-scale hydro-morphodynamic modelling using mesh movement methods. GEM - International Journal on Geomathematics, 13:1 (2022), doi:10.1007/s13137-021-00191-1.
• J. G. Wallwork, Mesh Adaptation and Adjoint Methods for Finite Element Coastal Ocean Modelling. PhD thesis, Imperial College London, doi:10.25560/92820 (2021), URL: https://spiral.imperial.ac.uk/handle/10044/1/92820.
• J. G. Wallwork, N. Barral, S. C. Kramer, D. A. Ham, M. D. Piggott, Goal-Oriented Error Estimation and Mesh Adaptation for Shallow Water Modelling, Springer Nature Applied Sciences, volume 2, pp.1053--1063 (2020). doi:10.1007/s42452-020-2745-9, URL: https://rdcu.be/b35wZ.
• J. G. Wallwork, N. Barral, D. A. Ham, M. D. Piggott, Anisotropic Goal-Oriented Mesh Adaptation in Firedrake. In: 28th International Meshing Roundtable, pp.83-100, (2020). doi:10.5281/zenodo.3653101. URL: https://doi.org/10.5281/zenodo.3653101.

• S.Li, E. Johnson, J. G. Wallwork, S. C. Kramer, and M. D. Piggott. Machine learning assisted mesh adaptation for geophysical fluid dynamics. In 11th International Conference on Adaptive Modeling and Simulation, (2023). doi:10.23967/admos.2023.051.
• J. G. Wallwork, J. Lu, M. Zhang, and M. D. Piggott. E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation. arXiv preprint, (2022). arXiv:2207.11233.
• J. G. Wallwork, H. Zhang, P. D. Hovland, O. Marin, Computing Derivatives for PETSc Adjoint Solvers using Algorithmic Differentation, arXiv preprint (2019) arXiv:1909.02836.