Biography

I am an applied mathematician specializing in the numerical solution to hyperbolic partial differential equations.

 

Follow this link for details of current PhD opportunities in Mathematics. But feel free to email me to discuss projects outside these areas and alternative sources of funding.

Career History

  • 8/2015-current, Senior Lecturer in Applied Mathematics, University of East Anglia (UK).
  • 2012-8/2015, Lecturer in Applied Mathematics, University of East Anglia (UK).
  • 2008-2012, Assistant Professor, Numerical Analysis, Delft University of Technology (Netherlands).
  • 2005-2007, Assistant Professor, Mathematics, Virginia Tech (USA).
  • 2003-2005, Householder Postdoctoral Fellow, Oak Ridge National Lab (USA).
  • 2003, PhD in Applied Mathematics from Brown University (USA).

All Publications

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Mirzargar, M., Jallepalli, A., Ryan, J. K., Kirby, R. M.

(2017)

Hexagonal Smoothness-Increasing Accuracy-Conserving Filtering,

in Journal of Scientific Computing

73

(2-3)

pp. 1072–1093

Full Text UEA Repository

(Article)

(Published)


Docampo-Sánchez, J., Ryan, J. K., Mirzargar, M., Kirby, R. M.

(2017)

Multi-dimensional filtering: Reducing the dimension through rotation,

in SIAM Journal on Scientific Computing

39

(5)

pp. A2179–A2200

Full Text UEA Repository

(Article)

(Published)


Jallepalli, A., Docampo-Sánchez, J., Ryan, J. K., Haimes, R., Kirby, R. M.

(2017)

On the Treatment of Field Quantities and Elemental Continuity in FEM Solutions,

in IEEE Transactions on Visualization and Computer Graphics.

IEEE Press

Full Text

(Conference contribution)

(E-pub ahead of print)


Meng, X., Ryan, J.

(2017)

Discontinuous Galerkin methods for nonlinear scalar hyperbolic conservation laws: divided difference estimates and accuracy enhancement,

in Numerische Mathematik

136

(1)

pp. 27–73

Full Text UEA Repository

(Article)

(Published)


Meng, X., Ryan, J. K.

(2017)

Divided difference estimates and accuracy enhancement of discontinuous Galerkin methods for nonlinear symmetric systems of hyperbolic conservation laws,

in IMA Journal of Numerical Analysis

Full Text UEA Repository

(Article)

(E-pub ahead of print)


Vuik, M., Ryan, J.

(2017)

Detecting Discontinuities Over Triangular Meshes Using Multiwavelets,

in Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016.

Springer

pp. 383-395

ISBN 978-3-319-65869-8

Full Text

(Conference contribution)

(Published)


Mirzargar, M., Ryan, J., Kirby, R.

(2016)

Smoothness-Increasing Accuracy-Conserving (SIAC) filtering and quasi interpolation: A unified view,

in Journal of Scientific Computing

67

(1)

pp. 237-261

Full Text UEA Repository

(Article)

(Published)


Li, X., Ryan, J. K., Kirby, R. M., Vuik, C.

(2016)

Smoothness-Increasing Accuracy-Conserving (SIAC) filters for derivative approximations of discontinuous Galerkin (DG) solutions over nonuniform meshes and near boundaries,

in Journal of Computational and Applied Mathematics

294

pp. 275-296

Full Text UEA Repository

(Article)

(Published)


Vuik, M., Ryan, J.

(2016)

Automated parameters for troubled-cell indicators using outlier detection,

in SIAM Journal on Scientific Computing

38

(1)

pp. A84–A104

Full Text UEA Repository

(Article)

(Published)


Vuik, M., Ryan, J.

(2015)

Multiwavelets and Jumps in DG Approximations,

in Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014.

Springer

pp. 503-511

ISBN 978-3-319-19799-9

(Conference contribution)

(Published)


Ji, L., Ryan, J.

(2015)

Smoothness-Increasing Accuracy-Conserving (SIAC) Filters in Fourier Space,

in Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014.

Springer

pp. 415-423

ISBN 978-3-319-19799-9

(Conference contribution)

(Published)


Ryan, J., Li, X., Kirby, M., Vuik, K.

(2015)

One-Sided Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering Over Uniform and Non-Uniform Meshes,

in Journal of Scientific Computing

64

(3)

pp. 773-817

Full Text UEA Repository

(Article)

(Published)


Li, X., Ryan, J.

(2015)

SIAC Filtering for Nonlinear Hyperbolic Equations,

in Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science.

Springer

pp. 285-291

(Conference contribution)

(Published)


Ryan, J.

(2015)

Exploiting Superconvergence Through Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering,

in Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014.

Springer

pp. 87-102

ISBN 978-3-319-19799-9

(Conference contribution)

(Published)


Vuik, M., Ryan, J.

(2014)

Multiwavelet troubled-cell indicator for discontinuity detection of discontinuous Galerkin schemes,

in Journal of Computational Physics

270

pp. 138–160

Full Text UEA Repository

(Article)

(Published)


Mirzaee, H., King, J., Ryan, J., Kirby, R.

(2014)

Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Discontinuous Galerkin Solutions: Application to Structured Tetrahedral Meshes,

in Journal of Scientific Computing

58

pp. 690-704

UEA Repository

(Article)

(Published)


Ji, L., van Slingerland, P., Ryan, J., Vuik, K.

(2014)

Superconvergent error estimates for position-dependent smoothness-increasing accuracy-conserving (SIAC) post-processing of discontinuous Galerkin solutions,

UEA Repository

(Article)

(Published)


Mirzaee, H., King, J., Ryan, J., Kirby, R.

(2013)

Smootheness-Increasing Accuracy-Conserving (SIAC) filters for discontinuous Galerkin solutions over unstructured triangular meshes,

in SIAM Journal on Scientific Computing

35

pp. A212-A230

UEA Repository

(Article)

(Published)


Mustapha, K., Ryan, J.

(2013)

Post-processing discontinuous Galerkin solutions to Volterra intergro-differential equations: Analysis and simulations,

in Journal of Computational and Applied Mathematics

253

pp. 89-103

UEA Repository

(Article)

(Published)


Ji, L., Xu, Y., Ryan, J.

(2013)

Negative-order norm estimates for nonlinear hyperbolic conservation laws,

in Journal of Scientific Computing

54

pp. 269-310

UEA Repository

(Article)

(Published)


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Key Research Interests

My background is in designing and developing higher-order methods for numerical partial differential equations.  I investigate the underlying theory,  not only to improve the method itself, but also to improve its computational efficiency.  I do this by using the inherent properties of the method.  The techniques that I develop can be exploited for use in imaging, data extraction, detection of discontinuous phenomenon, visualisation of fluids, and more.   To apply these ideas to such a challenging area one must examine the mathematical properties of the simulation as well as the computational viability.

Higher Order Methods

Superconvergence

Numerical Hyperbolic PDEs

Visualization

Spectral Methods

Limiting

Discontinuous Galerkin methods

Shock Detection

Finite Volume methods

 Multi-Wavelets

Teaching Interests

I have taught a variety of subjects including single- and multi-variable Calculus, Linear Algebra, Differential Equations, Introduction to Fluids, Scientific Computing, Spectral Methods and Finite Volume methods.