Avalos-Patiño, J. E.; Neethling, S. J.; Piggott, M. D. A parameter-free LES model for anisotropic mesh adaptivity. (English) Zbl 07761331 Comput. Methods Appl. Mech. Eng. 416, Article ID 116365, 25 p. (2023). MSC: 76-XX 86-XX PDFBibTeX XMLCite \textit{J. E. Avalos-Patiño} et al., Comput. Methods Appl. Mech. Eng. 416, Article ID 116365, 25 p. (2023; Zbl 07761331) Full Text: DOI
Warder, Simon C.; Piggott, Matthew D. Optimal experiment design for a bottom friction parameter estimation problem. (English) Zbl 1487.86002 GEM. Int. J. Geomath. 13, Paper No. 7, 34 p. (2022). MSC: 86-08 86A32 PDFBibTeX XMLCite \textit{S. C. Warder} and \textit{M. D. Piggott}, GEM. Int. J. Geomath. 13, Paper No. 7, 34 p. (2022; Zbl 1487.86002) Full Text: DOI
Clare, Mariana C. A.; Wallwork, Joseph G.; Kramer, Stephan C.; Weller, Hilary; Cotter, Colin J.; Piggott, Matthew D. Multi-scale hydro-morphodynamic modelling using mesh movement methods. (English) Zbl 1478.86006 GEM. Int. J. Geomath. 13, Paper No. 2, 39 p. (2022). MSC: 86-10 65M60 65M50 35Q35 86A05 PDFBibTeX XMLCite \textit{M. C. A. Clare} et al., GEM. Int. J. Geomath. 13, Paper No. 2, 39 p. (2022; Zbl 1478.86006) Full Text: DOI
Wallwork, Joseph G.; Lu, Jingyi; Zhang, Mingrui; Piggott, Matthew D. E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation. arXiv:2207.11233 Preprint, arXiv:2207.11233 [cs.LG] (2022). MSC: 68T07 65N50 65N30 BibTeX Cite \textit{J. G. Wallwork} et al., ``E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation'', Preprint, arXiv:2207.11233 [cs.LG] (2022) Full Text: arXiv OA License
Zhang, Mingrui; Wang, Jianhong; Tlhomole, James; Piggott, Matthew D. Learning to Estimate and Refine Fluid Motion with Physical Dynamics. arXiv:2206.10480 Preprint, arXiv:2206.10480 [cs.LG] (2022). BibTeX Cite \textit{M. Zhang} et al., ``Learning to Estimate and Refine Fluid Motion with Physical Dynamics'', Preprint, arXiv:2206.10480 [cs.LG] (2022) Full Text: arXiv OA License
Song, Wenbin; Zhang, Mingrui; Wallwork, Joseph G.; Gao, Junpeng; Tian, Zheng; Sun, Fanglei; Piggott, Matthew D.; Chen, Junqing; Shi, Zuoqiang; Chen, Xiang; Wang, Jun M2N: Mesh Movement Networks for PDE Solvers. arXiv:2204.11188 Preprint, arXiv:2204.11188 [cs.LG] (2022). BibTeX Cite \textit{W. Song} et al., ``M2N: Mesh Movement Networks for PDE Solvers'', Preprint, arXiv:2204.11188 [cs.LG] (2022) Full Text: arXiv OA License
Nunez Rattia, J. M.; Percival, J. R.; Neethling, S. J.; Piggott, M. D. Modelling local scour near structures with combined mesh movement and mesh optimisation. (English) Zbl 1416.76123 J. Comput. Phys. 375, 1220-1237 (2018). MSC: 76M10 76T20 76D05 65M50 PDFBibTeX XMLCite \textit{J. M. Nunez Rattia} et al., J. Comput. Phys. 375, 1220--1237 (2018; Zbl 1416.76123) Full Text: DOI
Funke, S. W.; Farrell, P. E.; Piggott, M. D. Reconstructing wave profiles from inundation data. (English) Zbl 1439.76068 Comput. Methods Appl. Mech. Eng. 322, 167-186 (2017). MSC: 76M10 65M60 76B15 PDFBibTeX XMLCite \textit{S. W. Funke} et al., Comput. Methods Appl. Mech. Eng. 322, 167--186 (2017; Zbl 1439.76068) Full Text: DOI arXiv
Schwedes, Tobias; Ham, David A.; Funke, Simon W.; Piggott, Matthew D. Mesh dependence in PDE-constrained optimisation. An application in tidal turbine array layouts. (English) Zbl 1384.65039 SpringerBriefs in Mathematics of Planet Earth. Cham: Springer (ISBN 978-3-319-59482-8/pbk; 978-3-319-59483-5/ebook). viii, 110 p. (2017). Reviewer: Armin Hoffmann (Ilmenau) MSC: 65K10 65-02 49J20 86A05 86-08 35Q53 PDFBibTeX XMLCite \textit{T. Schwedes} et al., Mesh dependence in PDE-constrained optimisation. An application in tidal turbine array layouts. Cham: Springer (2017; Zbl 1384.65039) Full Text: DOI
Viré, A.; Spinneken, J.; Piggott, M. D.; Pain, C. C.; Kramer, S. C. Application of the immersed-body method to simulate wave-structure interactions. (English) Zbl 1408.76166 Eur. J. Mech., B, Fluids 55, Part 2, 330-339 (2016). MSC: 76D05 74F10 76M10 PDFBibTeX XMLCite \textit{A. Viré} et al., Eur. J. Mech., B, Fluids 55, Part 2, 330--339 (2016; Zbl 1408.76166) Full Text: DOI
Adam, Alexandros; Buchan, Andrew G.; Piggott, Matthew D.; Pain, Christopher C.; Hill, Jon; Goffin, Mark A. Adaptive Haar wavelets for the angular discretisation of spectral wave models. (English) Zbl 1349.65502 J. Comput. Phys. 305, 521-538 (2016). MSC: 65M70 PDFBibTeX XMLCite \textit{A. Adam} et al., J. Comput. Phys. 305, 521--538 (2016; Zbl 1349.65502) Full Text: DOI
Barral, Nicolas; Knepley, Matthew G.; Lange, Michael; Piggott, Matthew D.; Gorman, Gerard J. Anisotropic mesh adaptation in Firedrake with PETSc DMPlex. arXiv:1610.09874 Preprint, arXiv:1610.09874 [math.NA] (2016). BibTeX Cite \textit{N. Barral} et al., ``Anisotropic mesh adaptation in Firedrake with PETSc DMPlex'', Preprint, arXiv:1610.09874 [math.NA] (2016) Full Text: arXiv OA License
Jacobs, Christian T.; Piggott, Matthew D.; Kramer, Stephan C.; Funke, Simon W. On the validity of tidal turbine array configurations obtained from steady-state adjoint optimisation. arXiv:1601.08091 Preprint, arXiv:1601.08091 [physics.flu-dyn] (2016). BibTeX Cite \textit{C. T. Jacobs} et al., ``On the validity of tidal turbine array configurations obtained from steady-state adjoint optimisation'', Preprint, arXiv:1601.08091 [physics.flu-dyn] (2016) Full Text: arXiv OA License
Funke, Simon W.; Kramer, Stephan C.; Piggott, Matthew D. Design optimisation and resource assessment for tidal-stream renewable energy farms using a new continuous turbine approach. arXiv:1507.05795 Preprint, arXiv:1507.05795 [cs.CE] (2015). BibTeX Cite \textit{S. W. Funke} et al., ``Design optimisation and resource assessment for tidal-stream renewable energy farms using a new continuous turbine approach'', Preprint, arXiv:1507.05795 [cs.CE] (2015) Full Text: arXiv OA License
Barnett, George L.; Funke, Simon W.; Piggott, Matthew D. Hybrid global-local optimisation algorithms for the layout design of tidal turbine arrays. arXiv:1410.2476 Preprint, arXiv:1410.2476 [math.OC] (2014). BibTeX Cite \textit{G. L. Barnett} et al., ``Hybrid global-local optimisation algorithms for the layout design of tidal turbine arrays'', Preprint, arXiv:1410.2476 [math.OC] (2014) Full Text: arXiv OA License
Funke, S. W.; Farrell, P. E.; Piggott, M. D. Tidal turbine array optimisation using the adjoint approach. arXiv:1304.1768 Preprint, arXiv:1304.1768 [math.OC] (2013). BibTeX Cite \textit{S. W. Funke} et al., ``Tidal turbine array optimisation using the adjoint approach'', Preprint, arXiv:1304.1768 [math.OC] (2013) Full Text: arXiv OA License
Fang, F.; Pain, C. C.; Navon, I. M.; Gorman, G. J.; Piggott, M. D.; Allison, P. A. The independent set perturbation adjoint method: a new method of differentiating mesh-based fluids models. (English) Zbl 1285.76015 Int. J. Numer. Methods Fluids 66, No. 8, 976-999 (2011). MSC: 76M10 65M99 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 66, No. 8, 976--999 (2011; Zbl 1285.76015) Full Text: DOI
García, Xavier; Pavlidis, Dimitrios; Gorman, Gerard J.; Gomes, Jefferson L. M. A.; Piggott, Matthew D.; Aristodemou, Elsa; Mindel, Julian; Latham, John-Paul; Pain, Christopher C.; ApSimon, Helen A two-phase adaptive finite element method for solid – fluid coupling in complex geometries. (English) Zbl 1429.76101 Int. J. Numer. Methods Fluids 66, No. 1, 82-96 (2011). MSC: 76S05 76M10 65M50 74F10 PDFBibTeX XMLCite \textit{X. García} et al., Int. J. Numer. Methods Fluids 66, No. 1, 82--96 (2011; Zbl 1429.76101) Full Text: DOI
Fang, F.; Pain, C. C.; Navon, I. M.; Gorman, G. J.; Piggott, M. D.; Allison, P. A.; Goddard, A. J. H. A POD goal-oriented error measure for mesh optimization. (English) Zbl 1425.65096 Int. J. Numer. Methods Fluids 63, No. 2, 185-206 (2010). MSC: 65M15 65M50 86A05 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 63, No. 2, 185--206 (2010; Zbl 1425.65096) Full Text: DOI
Farrell, P. E.; Piggott, M. D.; Pain, C. C.; Gorman, G. J.; Wilson, C. R. Conservative interpolation between unstructured meshes via supermesh construction. (English) Zbl 1228.76105 Comput. Methods Appl. Mech. Eng. 198, No. 33-36, 2632-2642 (2009). MSC: 76M25 PDFBibTeX XMLCite \textit{P. E. Farrell} et al., Comput. Methods Appl. Mech. Eng. 198, No. 33--36, 2632--2642 (2009; Zbl 1228.76105) Full Text: DOI
Piggott, M. D.; Farrell, P. E.; Wilson, C. R.; Gorman, G. J.; Pain, C. C. Anisotropic mesh adaptivity for multi-scale ocean modelling. (English) Zbl 1192.86009 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 367, No. 1907, 4591-4611 (2009). MSC: 86A05 65N50 76M25 PDFBibTeX XMLCite \textit{M. D. Piggott} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 367, No. 1907, 4591--4611 (2009; Zbl 1192.86009) Full Text: DOI
Slingo, Julia; Bates, Kevin; Nikiforakis, Nikos; Piggott, Matthew; Roberts, Malcolm; Shaffrey, Len; Stevens, Ian; Vidale, Pier Luigi; Weller, Hilary Developing the next-generation climate system models: challenges and achievements. (English) Zbl 1185.86020 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 367, No. 1890, 815-831 (2009). MSC: 86A10 65Y99 PDFBibTeX XMLCite \textit{J. Slingo} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 367, No. 1890, 815--831 (2009; Zbl 1185.86020) Full Text: DOI
Fang, F.; Pain, C. C.; Navon, I. M.; Piggott, M. D.; Gorman, G. J.; Farrell, P. E.; Allison, P. A.; Goddard, A. J. H. A POD reduced-order 4D-Var adaptive mesh ocean modelling approach. (English) Zbl 1163.86002 Int. J. Numer. Methods Fluids 60, No. 7, 709-732 (2009). MSC: 86A05 76M10 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 60, No. 7, 709--732 (2009; Zbl 1163.86002) Full Text: DOI
Fang, F.; Pain, C. C.; Navon, I. M.; Piggott, M. D.; Gorman, G. J.; Allison, P. A.; Goddard, A. J. H. Reduced-order modelling of an adaptive mesh ocean model. (English) Zbl 1155.86004 Int. J. Numer. Methods Fluids 59, No. 8, 827-851 (2009). MSC: 86A05 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 59, No. 8, 827--851 (2009; Zbl 1155.86004) Full Text: DOI
Piggott, M. D.; Gorman, G. J.; Pain, C. C.; Allison, P. A.; Candy, A. S.; Martin, B. T.; Wells, M. R. A new computational framework for multi-scale ocean modelling based on adapting unstructured meshes. (English) Zbl 1220.76045 Int. J. Numer. Methods Fluids 56, No. 8, 1003-1015 (2008). MSC: 76M10 76U05 86A05 65Y05 PDFBibTeX XMLCite \textit{M. D. Piggott} et al., Int. J. Numer. Methods Fluids 56, No. 8, 1003--1015 (2008; Zbl 1220.76045) Full Text: DOI
Pain, C. C.; Eaton, M. D.; Smedley-Stevenson, R. P.; Goddard, A. J. H.; Piggott, M. D.; De Oliveira, C. R. E. Streamline upwind Petrov-Galerkin methods for the steady-state Boltzmann transport equation. (English) Zbl 1175.76094 Comput. Methods Appl. Mech. Eng. 195, No. 33-36, 4448-4472 (2006). MSC: 76M10 76P05 PDFBibTeX XMLCite \textit{C. C. Pain} et al., Comput. Methods Appl. Mech. Eng. 195, No. 33--36, 4448--4472 (2006; Zbl 1175.76094) Full Text: DOI
Pain, C. C.; Eaton, M. D.; Smedley-Stevenson, R. P.; Goddard, A. J. H.; Piggott, M. D.; De Oliveira, C. R. E. Space-time streamline upwind Petrov-Galerkin methods for the Boltzmann transport equation. (English) Zbl 1175.76093 Comput. Methods Appl. Mech. Eng. 195, No. 33-36, 4334-4357 (2006). MSC: 76M10 76P05 PDFBibTeX XMLCite \textit{C. C. Pain} et al., Comput. Methods Appl. Mech. Eng. 195, No. 33--36, 4334--4357 (2006; Zbl 1175.76093) Full Text: DOI
Power, P. W.; Pain, C. C.; Piggott, M. D.; Fang, F.; Gorman, G. J.; Umpleby, A. P.; Goddard, A. J. H.; Navon, I. M. Adjoint a posteriori error measures for anisotropic mesh optimisation. (English) Zbl 1206.65250 Comput. Math. Appl. 52, No. 8-9, 1213-1242 (2006). MSC: 65N50 65N15 PDFBibTeX XMLCite \textit{P. W. Power} et al., Comput. Math. Appl. 52, No. 8--9, 1213--1242 (2006; Zbl 1206.65250) Full Text: DOI
Fang, F.; Pain, C. C.; Piggott, M. D.; Gorman, G. J.; Goddard, A. J. H. An adaptive mesh adjoint data assimilation method applied to free surface flows. (English) Zbl 1134.86004 Int. J. Numer. Methods Fluids 47, No. 8-9, 995-1001 (2005). MSC: 86-08 86A05 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 47, No. 8--9, 995--1001 (2005; Zbl 1134.86004) Full Text: DOI
Budd, C. J.; Piggott, M. D. Geometric integration and its applications. (English) Zbl 1062.65134 Cucker, F. (ed.), Handbook of numerical analysis. Vol. XI. Special volume: Foundations of computational mathematics. Amsterdam: North-Holland (ISBN 0-444-51247-0/hbk). Handb. Numer. Anal. 11, 35-139 (2003). Reviewer: Ivan Secrieru (Chişinău) MSC: 65P10 34A26 65L06 65L12 65M06 37M15 65M12 35Q55 35K55 34A34 PDFBibTeX XMLCite \textit{C. J. Budd} and \textit{M. D. Piggott}, Handb. Numer. Anal. 11, 35--139 (2003; Zbl 1062.65134)
Budd, C. J.; Leimkuhler, B.; Piggott, M. D. Scaling invariance and adaptivity. (English) Zbl 0998.65070 Appl. Numer. Math. 39, No. 3-4, 261-288 (2001). Reviewer: A.Dishliev (Sofia) MSC: 65L05 65L50 34A34 65P10 37M10 PDFBibTeX XMLCite \textit{C. J. Budd} et al., Appl. Numer. Math. 39, No. 3--4, 261--288 (2001; Zbl 0998.65070) Full Text: DOI
Budd, C. J.; Piggott, M. D. The geometric integration of scale-invariant ordinary and partial differential equations. (English) Zbl 0974.65095 J. Comput. Appl. Math. 128, No. 1-2, 399-422 (2001). Reviewer: Plamen Yordanov Yalamov (Russe) MSC: 65M70 65M50 35Q55 76S05 PDFBibTeX XMLCite \textit{C. J. Budd} and \textit{M. D. Piggott}, J. Comput. Appl. Math. 128, No. 1--2, 399--422 (2001; Zbl 0974.65095) Full Text: DOI