# Publications

### International refereed publications

M.J. Picklo and J.K. Ryan, "LSIAC-MRA for nonuniform meshes and applications to mesh adaptivity", Journal of Computational and Applied Mathematics, in press (2024).

M.J. Picklo, Q. Tang, Y. Zhang, J.K. Ryan. X.-Z. Tang,``Denoising Particle-In-Cell Data via Smoothness-Increasing Accuracy-Conserving (SIAC) Filters with Application to Bohm Speed Computation", Journal of Computational Physics, vol 501 (2024).

A. Galindo-Olarte, J. Huang, J. Ryan, and Y. Ching, ``Superconvergence and accuracy enhancement of discontinuous Galerkin solutions for Vlasov-Maxwell equations”, BIT Numerical Mathematics, vol. 62 (2023)

Q. Tao, L. Ji, J.K. Ryan, and Y. Xu, "Accuracy-enhancement of discontinuous Galerkin methods for PDEs containing high order spatial derivatives", Journal of Scientific Computing, vol. 93 (2022).

M.J. Picklo and J.K. Ryan, "Enhanced Multi-Resolution Analysis for Multi-Dimensional Data Utilizing Line Filtering Techniques", SIAM Journal on Scientific Computing, vol. 44 (2022), A2628-A2650.

J.K. Ryan, "Capitalizing on Superconvergence for more accurate Multi-Resolution discontinuous Galerkin Methods", Communications on Applied Mathematics and Computation, vol. 4 (2022).

A. Dedner, J. Giesselmann, T. Pryer, and J.K. Ryan, "Residual estimates for post-processors in elliptic problems", Journal of Scientific Computing, vol. 88 (2021).

J. Docampo Sánchez, G. Jacobs, X. Li, and J.K. Ryan, "Enhancing Accuracy with a Convolution Filter: What Works and Why!" Computers and Fluids, vol. 213 (2020).

D.J. Frean and J.K. Ryan, “Superconvergence and the numerical flux: A study using the upwind-biased flux in discontinuous Galerkin methods.” Communications on Applied Mathematics and Computation, vol. 2 (2020), pp 461-486.

G. Kesserwani, J. Shaw, M. Sharifian, D. Bau, C Keylock, P. Bates and J. Ryan, “(Multi)wavelets increase both accuracy and efficiency of standard Godunov-type hydrodynamic models.” Advances in Water Resources, vol. 129 (2019), pp 31–55.

X. Li, J.K. Ryan, R.M. Kirby and C. Vuik, “Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Discontinuous Galerkin Solutions over Nonuniform Meshes: Superconvergence and Optimal Accuracy.” Journal of Scientific Computing, vol. 81 (2019), pp 1150–1180.

B.W. Wissink, G.B. Jacobs, J.K. Ryan, W.S. Don and E.T.A. van der Weide, “Shock Regularization with Smoothness-Increasing Accuracy-Conserving Dirac-Delta Polynomial Kernels”. Journal of Scientific Computing, vol. 77(1) (2018), pp 579–596.

A. Jallepalli, J. Docampo Sánchez, J.K. Ryan, R. Haimes, and R.M. Kirby, “On the Treatment of Field Quantities and Elemental Continuity in FEM Solutions.” IEEE TVCG, vol. 24(1) (2018), pp 903 – 912.

M. Mirzargar, A. Jallepalli, J.K. Ryan, and R.M. Kirby, “Hexagonal Smoothness-Increasing Accuracy- Conserving Filtering.” Journal of Scientific Computing, vol. 73(2-3) (2017), pp 1072 – 1093,

J. Docampo Sánchez, J.K. Ryan, M. Mirzargar, and R.M. Kirby, “Multi-dimensional Filtering: Reducing the dimension through rotation.” SIAM Journal on Scientific Computing, vol. 39(5) (2017), pp A2179–A2200.

X. Meng and J.K. Ryan, “Divided difference estimates and accuracy enhancement of discontinuous Galerkin methods for nonlinear symmetric systems of hyperbolic conservation laws.” IMA Journal of Numerical Analysis, vol. 38 (2018), pp 125–155.

X. Meng and J.K. Ryan, “Discontinuous Galerkin methods for nonlinear scalar hyperbolic conservation laws: divided difference estimates and accuracy enhancement.” Numerische Mathematik, vol. 136(1)(2017), pp 27–73.

M.J. Vuik and J.K. Ryan, “Automated parameters for troubled-cell indicators using outlier detection.” SIAM Journal on Scientific Computing, vol. 38(1) (2016), pp. A84–A104.

X. Li, J.K. Ryan, R.M. Kirby and C. Vuik, “Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Derivative Approximations of discontinuous Galerkin (DG) Solutions over Nonuniform Meshes and Near Boundaries.” Journal of Computational and Applied Mathematics, vol. 294 (2016), pp. 275–296.

M. Mirzargar, J.K. Ryan and R.M. Kirby, “Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering and Quasi-Interpolation: A Unified View.” Journal of Scientific Computing, vol. 67 (2016) pp 237–261.

J.K. Ryan, X. Li, R.M. Kirby, and C. Vuik, “One-Sided Position-Dependent Smoothness-Increasing Accuracy- Conserving (SIAC) Filtering Over Uniform and Non-Uniform Meshes.” Journal of Scientific Computing, vol. 64 (2015), pp 773–817.

L. Ji, P. van Slingerland, J.K. Ryan, and C.W. Vuik, “Superconvergent Error Estimates for a Position- Dependent Smoothness-Increasing Accuracy-Conserving Filter for DG Solutions.” Mathematics of Computation, vol. 83 (2014), pp.2239–2262.

M.J. Vuik and J.K. Ryan, “Multiwavelet troubled-cell indicator for discontinuity detection of discontinuous Galerkin schemes.” Journal of Computational Physics, vol. 270 (2014), pp. 138–170.

H. Mirzaee, J. King, J.K. Ryan, and R.M. Kirby, “Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Discontinuous Galerkin Solutions: Application to Structured Tetrahedral Meshes.” Journal of Scientific Computing, vol. 58 (2014), pp. 690–704.

H. Mirzaee, J. King, J.K. Ryan, and R.M. Kirby, “Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Discontinuous Galerkin Solutions Over Unstructured Triangular Meshes.” SIAM Journal on Scientific Computing, vol. 35 (2013), pp. A212–A230.

K. Mustapha and J.K. Ryan, “Post-processing discontinuous Galerkin solutions to Volterra equations integro-differential equations: Analysis and Simulations.” Journal of Computational and Applied Mathe- matics, vol. 253 (2013), pp. 89–103.

L. Ji, Y. Xu, and J.K. Ryan, “Negative-order norm estimates for nonlinear hyperbolic conservation laws.” Journal of Scientific Computing, vol. 54 (2013), pp. 269–310.

J. King, H. Mirzaee, J.K. Ryan, and R.M. Kirby, “Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for discontinuous Galerkin Solutions: Improved Errors Versus Higher-Order Accuracy.” Journal of Scientific Computing, vol. 53 (2012), pp. 129–149.

H. Mirzaee, J.K. Ryan, and R.M. Kirby, “Efficient Implementation of Smoothness-Increasing Accuracy- Conserving (SIAC) Filters for Discontinuous Galerkin Solutions.” Journal of Scientific Computing, vol. 52 (2012), pp. 85–112.

L. Ji, Y. Xu, and J.K. Ryan, “Accuracy enhancement of the linear convection-diffusion equation in multiple dimensions.” Mathematics of Computation, vol. 81 (2012), pp. 1929–1950.

H. Mirzaee, L. Ji, J.K. Ryan, and R.M. Kirby, “Smoothness-increasing accuracy-conserving (SIAC) post- processing for discontinuous Galerkin solutions over structured triangular meshes.” SIAM Journal on Nu- merical Analysis, vol. 49 (2011), pp. 1899–1920.

P. van Slingerland, J.K.Ryan, and C. Vuik, “Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Accuracy for Improving discontinuous Galerkin solutions.” SIAM Journal on Scientific Computing, vol. 33 (2011), pp. 802–825.

H. Mirzaee, R.M. Kirby, and J.K. Ryan, “Quantification of Errors introduced in the Numerical Approximation of SIAC Filtering.” Journal of Scientific Computing, vol. 45 (2010), pp. 447–470.

J.K. Ryan and B. Cockburn, “Local Derivative Post-processing for Discontinuous Galerkin Method.” Journal of Computational Physics, vol. 228 (2009), pp. 8642–8664.

D.Walfisch, J.K.Ryan, R.M.Kirby, and R.Haimes, “One-Sided Smoothness-Increasing Accuracy-Conserving Filtering for Enhanced Streamline Integration through Discontinuous Fields.” Journal of Scientific Computing, vol. 38 (2009), pp. 164–184.

M. Steffan, S.Curtis, R.M. Kirby, and J.K. Ryan, “Investigation of Smoothness Enhancing Accuracy- Conserving Filters for Improving Streamline Integration Through Discontinuous Fields.” IEEE Transactions on Visualization and Computer Graphics, vol. 14 (2008), pp. 680–692.

S.Curtis, R.M. Kirby, J.K. Ryan, C.-W. Shu, “Post-processing for the discontinuous Galerkin method over nonuniform meshes.” SIAM Journal on Scientific Computing, vol. 30 (2007), pp. 272–289.

R.Archibald, A.Gelb, S.Gottlieb, and J.K.Ryan, “One-sided post-processing for the discontinuous Galerkin method using ENO type stencil choosing and the local edge detection method". Journal of Scientific Computing, vol. 28 (2006), pp. 167–190.

J.K. Ryan, C.-W. Shu, and H.L. Atkins, “Extension of a Post-Processing technique for discontinuous Galerkin Methods for hyperbolic equations with application to an aeroacoustic problem.” SIAM Journal on Scientific Computing, vol. 26 (2004), pp. 821–843.

J.K. Ryan and C.-W. Shu, “One-sided post-processing for the discontinuous Galerkin methods.” Methods and Applications of Analysis, vol. 10 (2003), pp. 295–307.

### Refereed Proceedings Articles

J. Docampo Sánchez and J.K. Ryan, ``Magic SIAC Toolbox: A Codebase of Effective, Efficient, and Flexible Filters", Editors: Emmanuel Franck,and Jügen Fuhrmann, Victor Michel-Dansac, Laurent Navoret, Proceedings in Mathematics & Statistics, Springer vol. 433 (2023).

.K. Ryan and J. Docampo Sánchez, ``One-dimensional Line SIAC filtering for multi-dimensions: Applications to Streamline Visualization". Editors: E.H. van Brummelen, A. Corsini, S. Perotto, G. Rozza, Lecture Notes in Computational Science and Engineering (LNCSE), Springer ({\it to appear}).

M.J. Vuik and J.K. Ryan, “Detecting discontinuities over triangular meshes using multiwavelets". Proceedings of the 2016 Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, Rio de Janeiro, Brazil. Lecture Notes in Computational Science and Engineering, Springer, vol. 119 (2015), pp 383–395.

L.Ji and J.K. Ryan, “Smoothness-Increasing Accuracy-Conserving (SIAC) Filters in Fourier Space". Proceedings of the 2014 Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014, Salt Lake City, Utah. Lecture Notes in Computational Science and Engineering, Springer, vol. 106 (2015), pp 415–423.

J.K. Ryan, “Exploiting Superconvergence through Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering”. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014, Salt Lake City, Utah. Lecture Notes in Computational Science and Engineering, Springer, vol. 106 (2015), pp 87–102.

M.J. Vuik and J.K. Ryan, “Multiwavelets and jumps in DG approximations”. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014, Salt Lake City, Utah. Lecture Notes in Computational Science and Engineering, Springer, vol. 106 (2015), pp 503–511.

X.Li and J.K. Ryan, “SIAC Filtering for Nonlinear Hyperbolic Equations” Proceedings of the 2013 conference on Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science, Waterloo, Canada. Springer Proceedings in Mathematics & Statistics, Springer, vol. 117 (2015), pp 285–291.

Invited Book Chapters

F. Vermolen, L.Y.D. Crapts, J.K. Ryan, “A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes: Application to stem cell injection after a myocardial infarction”. Editors: Miguel Cerrolaza, Sandra Shefelbine, Diego Garz ́on-Alvarado, Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes, Elsevier, 2017.

Technical Reports

P. van Slingerland, J.K. Ryan, and C. Vuik, “Smoothness Increasing Accuracy Conserving Filtering Applied to Streamline Visualisation of DG Solutions.” Delft University of Technology Technical Report, Delft, Netherlands, Report no. 09-06, 2009.

V. Cheruvu and J.K. Ryan, “A Multi-wavelet type limiter for discontinuous Galerkin Approximations.” Delft University of Technology Technical Report, Delft, Netherlands, Report no. 10-17, 2010.

J.K. Ryan, “Local Derivative Post-Processing: Challenges for a Non-Uniform Mesh,” Delft University of Technology Technical Report, Delft, Netherlands, Report no. 10-18, 2010.