Dr. Pravin Madhavan

Ph.D. in Mathematics (MASDOC) at University of Warwick (October 2010 - September 2014)

M.Sc. in Mathematical Modelling and Scientific Computing at University of Oxford (October 2009 - September 2010)

B.Sc. in Mathematics at University of Warwick (October 2006 - July 2009)

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Research Interests: Numerical analysis; scientific computing.

PhD Research: My PhD thesis extended the discontinuous Galerkin (DG) method onto surfaces, which involved deriving both a priori and a posteriori error estimates for various DG approximations to surface PDEs. Numerical simulations were performed using the Distributed and Unified Numerics Environment (DUNE) software package. Applications include efficient simulation of a wide range of problems arising in continuum mechanics.

Publications:

Journals

- A. Dedner, P. Madhavan. Discontinuous Galerkin methods for hyperbolic and advection-dominated problems on surfaces. Submitted to IMA Journal of Numerical Analysis, (2015) (preprint).

- P. Antonietti, A. Dedner, P. Madhavan, S. Stangalino, B. Stinner and M. Verani. High order discontinuous Galerkin methods for elliptic problems on surfaces. SIAM Journal on Numerical Analysis 53 (2), (2015), 1145-1171 (preprint).

- A. Dedner, P. Madhavan. Adaptive discontinuous Galerkin methods on surfaces. Numerische Mathematik, DOI: 10.1007/s00211-015-0719-4, (2015) (preprint).

- A. Dedner, P. Madhavan, and B. Stinner. Analysis of the discontinuous Galerkin method for elliptic problems on surfaces. IMA Journal of Numerical Analysis, 33 (3), (2013), 952-973 (preprint).

Theses

- P. Madhavan. Analysis of discontinuous Galerkin methods on surfaces. Ph.D. Thesis, University of Warwick, 2014.

- P. Madhavan. Numerical integration in meshfree methods. M.Sc. Thesis, University of Oxford, 2010.

Selected Reports/Posters/Presentations:

- P. Madhavan. Adaptive refinement for PDEs on surfaces. CSC (Centre for Scientific Computing) Seminar, Warwick, 2014 (presentation).

- P. Madhavan. On a discontinuous Galerkin method for surface PDEs. Applied PDEs Seminar, Warwick, 2013 (presentation).

- A. Aylwin, P. Madhavan. Brake pad modelling and simulation. Example based mini-course on mathematical modelling, Warwick, 2012 (report and presentation).

- P. Madhavan. Discontinuous Galerkin methods for surface PDEs. Annual SIAM UKIE meeting, Leicester, 2012 (poster).

- D.P. Amarasinghe, A. Aylwin, P. Madhavan, and C. Pettitt. Biomembranes report. MASDOC Research Study Group, Warwick, 2011 (report, poster and presentation).