Dr Andrea Cangiani

Associate Professor Me

Department of Mathematics
University of Leicester
University Road - Leicester LE1 7RH
United Kingdom

Tel: +44 (0)116 252 3889

Email: Andrea.Cangiani@le.ac.uk

 


Personal details

  • 2004 D.Phil. in Numerical Analysis. University of Oxford, Computing Laboratory
  • 2000 M.Sc. in Mathematical Modelling and Scientific Computing (Distinction). University of Oxford, Mathematical Institute & Computing Laboratory
  • 1999 Laurea in Mathematics (BSc + MSc equivalent) University of Trento, Departments of Mathematics
  • View my full CV online

Websites

Google Scholar Profile

Teaching

Office hours: Monday 2.00-3.00pm

Advanced Readings in Mathematics

Finite Element Theory and Applications

Director of the MSc in Applied Computation and Numerical Modelling

Publications

Books

BuildingBridgesCover

Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Barrenechea, G.R., Brezzi, F., Cangiani, A., Georgoulis, E.H. (Eds.). Lecture Notes in Computational Science and Engineering, Springer, 2016.

ENUMATH Proc. cover

Numerical Mathematics and Advanced Applications 2011. Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011. A. Cangiani, R. L. Davidchack, E. Georgoulis, A. N. Gorban, J. Levesley, and M. V. Tretyakov editors, Springer, 2013.

 

Books chapters

  1. A. Cangiani, V. Gyrya, G. Manzini, and O. Sutton. Virtual element methods for elliptic problems on polygonal meshes. In: Kai Hormann and N. Sukumar, Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics. CRC Press, to appear.
  2. Paola F. Antonietti, A. Cangiani, J. Collis, Z. Dong, E. H. Georgoulis, S. Giani, and P. Houston. Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains. In: Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Barrenechea, G.R., Brezzi, F., Cangiani, A., Georgoulis, E.H. (Eds.). Lecture Notes in Computational Science and Engineering, Springer, 2016.

Peer reviewed articles

  1. A. Cangiani, E. H. Georgoulis, and Y. Sabawi. Adaptive discontinuous Galerkin methods for elliptic interface problems. Submitted for publication.
  2. A. Cangiani, Z. Dong, E. H. Georgoulis. hp-Version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes. SIAM J. Sci. Comput., accepted for publication, 2017.
  3. A. Cangiani, E. H. Georgoulis, T. Pryer, and O. Sutton. A Posteriori Error Estimates for the Virtual Element Method. Numerische Mathematik, 2017. doi:10.1007/s00211-017-0891-9
  4. A. Cangiani, V. Gyrya, and G. Manzini. The non-conforming Virtual Element Method for the Stokes equations. SIAM J. on Numer. Anal , 54(6), 3411–3435, 2016.
  5. A. Cangiani, E. H. Georgoulis, I. Kyza, and S. Metcalfe. Adaptivity and blow-up detection for nonlinear evolution problems. SIAM J. Sci. Comput., 38(6), 3833–3856, 2016.
  6. A. Cangiani, G. Manzini, and O. Sutton. Conforming and Nonconforming Virtual Element Methods for Elliptic Problems. IMA Journal of Numerical Analysis online, 2016.doi: https://doi.org/10.1093/imanum/drw036
  7. A. Cangiani, Z. Dong, E. H. Georgoulis and P. Houston. hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes. Mathematical Modelling and Numerical Analysis, Vol. 50(3), 699–725, 2016.
  8. A. Cangiani, E. H. Georgoulis and M. Jensen. Discontinuous Galerkin Methods for Fast Reactive Mass Transfer through Semi-Permeable Membranes. Applied Numerical Mathematics, Vol. 104, 3–14, 2016.
  9. A. Cangiani, G. Manzini, A. Russo, and N. Sukumar. Hourglass stabilization and the virtual element method. International Journal for Numerical Methods in Engineering, Vol. 102(3-4), 404–436April 2015.
  10. A. Cangiani, E. H. Georgoulis and P. Houston. hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Mathematical Models and Methods in Applied Sciences, Vol. 24, No. 10, 2009–2041, 2014.
  11. A. Cangiani, J. Chapman, E. H. Georgoulis and M. Jensen. On local super-penalization of interior penalty discontinuous Galerkin methods. International Journal of Numerical Analysis and Modeling, Vol. 11(3), 478–495, 2014.
  12. A. Cangiani, J. Chapman, E. H. Georgoulis and M. Jensen. On the Stability of Continuous-Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems. Journal of Scientific Computing, Vol. 57(2), 313–330, 2013.
  13. A. Cangiani, E. H. Georgoulis and M. Jensen. Discontinuous Galerkin methods for mass transfer through semi-permeable membranes . SIAM J. on Numer. Anal., Vol. 51(5), 2911–2934, 2013.
  14. A. Cangiani, E. H. Georgoulis and S. Metcalfe. An a posteriori error estimator for discontinuous Galerkin methods for non-stationary convection-diffusion problems. IMA Journal of Numerical Analysis, published online October, 2013.
  15. L. Beirao da Veiga, F. Brezzi, A. Cangiani, G. Manzini, D.L. Marini and A. Russo. Basic principles of Virtual Element Methods. Mathematical Models and Methods in Applied Sciences, Vol. 23(1), 199–214, 2013.
  16. A. Cangiani, F. Gardini and G. Manzini. Convergence of the Mimetic Finite Difference Method for eigenvalue problems in mixed form. Computer Methods in Applied Mechanics and Engineering, Vol. 200(9-12), 1150–1160, 2011.

  17. A. Cangiani and R. Natalini. A spatial model of cellular molecular trafficking including active transport along microtubules. Journal of Theoretical Biology, Vol. 267, 614–625, 2010.
  18. A. Cangiani, G. Manzini and A. Russo. Convergence analysis of the Mimetic Finite Difference Method for elliptic problems. SIAM J. on Numer. Anal., Vol. 47(4), 2612–2637, 2009.
  19. A. Cangiani and G. Manzini. Flux reconstruction and solution post-processing in Mimetic Finite Difference Methods. CMAME, Vol. 197, 933–945, 2008.
  20. A. Cangiani and E. Suli. The Residual-free bubble finite element method on anisotropic partitions. SIAM J. on Numer. Anal., Vol. 45, 1654–1678, 2007.
  21. P. Bagnerini, A. Buffa and A. Cangiani. A fast algorithm for determining the propagation path of multiply diffracted rays. IEEE Transactions on Antennas and propagation, Vol. 55(5), 1416–1422, 2007.
  22. A. Cangiani and E. Suli. Enhanced RFB Method. Numerische Mathematik, Vol. 101(2), 275–308, 2005.
  23. A. Cangiani and E. Suli. Enhanced residual-free bubble method for convection-diffusion problems. International Journal for Numerical Methods in Fluid, Vol. 47(10-11), 1307–1313, 2005.

Conference proceedings

  1. A. Cangiani, J. Chapman, E. H. Georgoulis and M. Jensen.  Implementation of the Continuous-Discontinuous Galerkin Finite Element Method. In: Numerical Mathematics and Advanced Applications 2011. Proceedings of ENUMATH 2011 Conference, Springer, 2013.
  2. A. Cangiani, E. H. Georgoulis, and M. Jensen. Discontinuous Galerkin methods for convection-diffusion problems modelling mass transfer through semipermeable membranes. Proceedings of the Congress on Numerical Methods in Engineering, Coimbra, 2011.
  3. A. Cangiani, E. H. Georgoulis and M. Jensen. Continuous and discontinuous finite element methods for convection-diffusion problems: a comparison. In G. Lube and G. Rapin, editors, Proceedings of the International Conference on Boundary and Interior Layers (BAIL) - Computational and Asymptotic Methods, 2006.

Other publications

  1. F. Brezzi, A. Cangiani, G. Manzini and A. Russo. Mimetic Finite Differences and Virtual Element Methods for diffusion problems on polygonal meshes. Technical Report LA-UR-12-22743, Los Alamos National Laboratory, 2012.
  2. A. Cangiani. Modeling and simulation of Ran-mediated nuclear import. Universita' di Milano Bicocca, Department of Mathematics Research Report, 10, 2009.
  3. A. Cangiani. Biochemical pathways simulation. IAC-CNR Research Report, 2008.
  4. A. Cangiani and E. Suli. A-posteriori error estimators and RFB. Computing Laboratory Technical Report NA-04/22, 2004.
  5. A. Cangiani. The Residual-Free Bubble Method for Problems with Multiple Scales. Oxford University, DPhil Thesis, 2004.
  6. A. Cangiani. Implied Volatility Estimation using Adjoint Monte Carlo Methods. Oxford University MSc Thesis, 2000.

  7. A. Cangiani. Metodi di decomposizione del dominio per le equazioni di Maxwell. Universita di Trento, Tesi di Laurea, 1999.

Research

Funded projects: Virtual Element Method project (EPSRC)XX

Numerical analysis of partial differential equations: Generalised Finite elements, discontinuous Galerkin (dG), Mimetic Finite Difference (MFD) methods, Virtual Element Method (VEM), polygonal and polyhedral meshes, adaptive mesh refinement.

Mathematical modelling and numerical simulation of biochemical processes: Cellular signal transduction, membrane modeling, transport phenomena.

Codes

Supervision

Postdoctorate students:

G. Diwan (2014-16)

PhD students:

Mohammad A. Sabawi, Oliver Sutton

Former PhD students

  • Samuel P. Cox
  • Zhaonan (Peter) Dong
  • Stephen Metcalfe
  • Younis A. Sabawi

Former MMath students

  • Usman Ali
  • Oliver Sutton
  • Christopher Wallis

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