Select publications

• T. Hangelbroek, C. Rieger, and G. B. Wright. Spectral stability and perturbation results for kernel differentiation matrices on the sphere. Submitted (2023), arXiv:2311.06982.
• A. M. Jones, P. A. Bosler, P. A. Kuberry, and G. B. Wright. Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives. Comput. Math. Appl. 147, 1--13 (2023) (arxiv, journal).
• G. B. Wright, A. M. Jones, and V. Shankar. MGM: A meshfree geometric multilevel method for systems arising from elliptic equations on point cloud surfaces. SIAM J. Sci. Comput. 45, A312-A337 (2023) (arxiv, journal).
• K. P. Drake, E. J. Fuselier, and G. B. Wright. Implicit Surface Reconstruction with a Curl-free Radial Basis Function Partition of Unity Method. SIAM J. Sci. Comput. 42, A3018-A3040 (2022) (arxiv, journal).
• V. Shankar, G. B. Wright, and A. L. Fogelson. An Efficient High-Order Meshless Method for Advection-Diffusion Equations on Time-Varying Irregular Domains. J. Comput. Phys., 445, 110663 (2021) (arxiv).
• K. P. Drake, E. J. Fuselier, and G. B. Wright. A Partition of Unity Method for Divergence-free or Curl-free Radial Basis Function Approximation. SIAM J. Sci. Comput. 43(3), A1950-A1974 (2021) (arxiv, journal).
• V. Shankar, G. B. Wright, and A. Narayan. A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds. SIAM J. Sci. Comput., 42(4), A2371-A2401 (2020) (arxiv).
• K. P. Drake and G. B. Wright. A stable algorithm for divergence-free radial basis functions in the flat limit. J. Comput. Phys., 417, 109595 (2020) (arxiv).
• K. P. Drake and G. B. Wright. A Fast and Accurate Algorithm for Spherical Harmonic Analysis on HEALPix Grids with Applications to the Cosmic Microwave Background Radiation. J. Comput. Phys., 416, 109544 (2020) (arxiv).
• V. Shankar and G. B. Wright. Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions. J. Comput. Phys., 366, 170-190 (2018). (pdf, bibtex).
• E. Lehto, V. Shankar, and G. B. Wright. A radial basis function (RBF) compact finite difference (FD) scheme for reaction-diffusion equations on surfaces. SIAM. J. Sci. Comput., 39-5 (2017), A2129-A2151 (pdf).
• H. Wilber, A. Townsend, and G. B. Wright. Computing with functions in spherical and polar geometries II. The disk. SIAM. J. Sci. Comput., 39-4 (2017), C238-C262 (pdf).
• E. J. Fuselier and G. B. Wright. A radial basis function method for computing Helmholtz-Hodge decompositions. IMA J. Numer. Anal., 37-2 (2017), 774-797 (arxiv or journal).
• G. B. Wright and B. Fornberg. Stable computations with flat radial basis functions using vector-valued rational approximations. J. Comput. Phys., 331 (2017), 137-156 (pdf).
• A. Townsend, H. Wilber, and G. B. Wright. Computing with functions in spherical and polar geometries I. The sphere. SIAM. J. Sci. Comput., 38-4 (2016), C403-C425 (pdf).
• E. J. Fuselier, V. Shankar, and G. B. Wright. A high-order radial basis function (RBF) Leray projection method for the solution of the incompressible unsteady Stokes equations. Comput. Fluids, 128, (2016), 41-52. (arxiv, code).
• G. B. Wright, M. Javed, H. Montanelli, and L. N. Trefethen. Extension of Chebfun to periodic functions. SIAM. J. Sci. Comput., 37 (2015), C554-C573 (pdf).
• V. Shankar, G. B. Wright, A. L. Fogelson, and R. M. Kirby. Augmenting the immersed boundary method with radial basis functions (RBFs) for the modeling of platelets in hemodynamic flows. Int. J. Numer. Meth. Fluids, 79 (2015), 536-557 (arxiv).
• V. Shankar, G. B. Wright, A. L. Fogelson, and R. M. Kirby. A radial basis function (RBF)-finite difference (FD) method for diffusion and reaction-diffusion equations on surfaces. J. Sci. Comput., 63 (2015), 745-768 (arxiv, bibtex).
• N. Flyer, G. B. Wright, and B. Fornberg. Radial basis function-generated finite differences: A mesh-free method for computational geosciences. Handbook of Geomathematics, 2nd Edition, W. Freeden, Z. Nashed, T. Sonar (eds.), Springer, 2015. doi: 10.1007/978-3-642-27793-1_61-1 (pdf, bibtex).
• E. J. Fuselier and G. B. Wright. Order-preserving derivative approximation with periodic radial basis functions. Adv. Comput. Math., 41 (2015), 23-53 (pdf, bibtex).
• P-A. Arrial, N. Flyer, G. B. Wright, and L. H. Kellogg. On the sensitivity of 3D thermal convection codes to numerical discretization: A model intercomparison. Geosci. Model Dev., 7 (2014), 2065-2076 (pdf, bibtex).
• V. Shankar, G. B. Wright, A. L. Fogelson, and R. M. Kirby. A radial basis function (RBF)-finite difference method for the simulation of reaction-diffusion equations on stationary platelets within the augmented forcing method. Int. J. Numer. Meth. Fluids, 75 (2014), 1-22 (arxiv).
• E. J. Fuselier, T. Hangelbroek, F. J. Narcowich, J. D. Ward, and G. B. Wright. Kernel based quadrature on spheres and other homogeneous spaces. Numer. Math., 127 (2014), 57-92 (pdf), bibtex).
• U. Harlander, Th. von Larcher, G.B. Wright, M. Hoff, K. Alexandrov, C. Egbers. Orthogonal Decomposition Methods to Analyze PIV, LDV, and Thermography Data of Thermally Driven Rotating Annulus Laboratory Experiments. Modeling Atmospheric and Oceanic flows: Insights from Laboratory Experiments and Numerical Simulations. T. von Larcher and P. D. Williams, eds. American Geophysical Union (AGU) Book Series, Wiley, 2014 (doi:10.1002/9781118856024.ch17, pdf).
• E. J. Fuselier, T. Hangelbroek, F. J. Narcowich, J. D. Ward, and G. B. Wright. Localized bases for kernel spaces on the unit sphere. SIAM J. Numer. Anal., 15 (2013), 2538-2562 (pdf, bibtex).
• J. Du, R. D. Guy, A. L. Fogelson, G. B. Wright, and J. P. Keener. An interface-capturing regularization method for solving the equations for two-fluid mixtures. Commun. Comput. Phys., 14 (2013), 1322-1346 (pdf).
• E. J. Fuselier and G. B. Wright. A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces. J. Sci. Comput., 56 (2013), 535-565 (pdf, bibtex, me63.4096, m code).
• V. Shankar, G. B. Wright, A. L. Fogelson, and R. M. Kirby. A Study of Different Modeling Choices For Simulating Platelets Within the Immersed Boundary Method. Appl. Numer. Math. 63 (2013), 58-77 (arxiv, bibtex).
• E. J. Fuselier and G. B. Wright. Scattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates. SIAM J. Numer. Anal., 50 (2012), 1753-1776 (pdf, bibtex).
• N. Flyer, E. Lehto, S. Blaise, G. B. Wright, and A. St-Cyr. A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere. J. Comput. Phys., 231 (2012), 4078-4095 (pdf, bibtex).
• U. Harlander, G. B. Wright, and C. Egbers. Reconstruction of the 3D flow field in a differentially heated rotating annulus by synchronized particle image velocimetry and infrared thermography measurements. In: 16th International symposium on applied laser techniques to fluid mechanics, Lisbon, Portugal, 2012 (pdf).
• G. B. Wright, R. D. Guy, J. Du, and A. L. Fogelson. A high-resolution finite-difference method for simulating two-fluid, viscoelastic gel dynamics. J. Non-Newton. Fluid Mech., 166 (2011), 1137-1157 (pdf, bibtex).
• R. D. Guy, T. Nakagaki, and G. B. Wright. Flow-induced channel formation in the cytoplasm of motile cells. Phys. Rev. E, 84:016310 (2011) (pdf, bibtex).
• G. B. Wright, N. Flyer, and D. A. Yuen. A hybrid radial basis function - pseudospectral method for thermal convection in a 3D spherical shell. Geochem. Geophys. Geosyst., 11 (2010), Q07003 (pdf, bibtex).
• E. J. Fuselier and G. B. Wright. Stability and error estimates for vector field interpolation and decomposition on the sphere with RBFs. SIAM J. Numer. Anal., 47 (2009), 3213-3239 (pdf, bibtex).
• N. Flyer and G. B. Wright. A radial basis function method for the shallow water equations on a sphere. Proc. R. Soc. A, 465 (2009), 1949-1976 (pdf, bibtex).
• E. J. Fuselier, F. J. Narcowich, J. D. Ward, and G. B. Wright. Error and stability estimates for surface-divergence free RBF interpolants on the sphere. Math. Comp., 78 (2009), 2157-2186 (link, bibtex)</a>
• J. Du, A. L. Fogelson, and G. B. Wright. A parallel computational method for simulating two-phase gel dynamics on a staggered grid. Int. J. Numer. Meth. Fluids, 60 (2009), 633-649 (pdf, bibtex).
• G. B. Wright, R. D. Guy, and A. L. Fogelson. An efficient and robust method for simulating two-phase gel dynamics. SIAM J. Sci. Comput., 30 (2008), 2535-2565 (pdf, bibtex).
• F. J. Narcowich, J. D. Ward, and G. B. Wright. Divergence-free RBFs on surfaces. J. Fourier Anal. Appl., 13 (2007), 643-663 (pdf, bibtex).
• N. Flyer and G. B. Wright. Transport schemes on a sphere using radial basis functions. J. Comp. Phys., 226 (2007), 1059-1084 (pdf, bibtex).
• O. E. Livne and G. B. Wright. Fast multilevel evaluation of 1-D piecewise smooth radial basis function expansions. Unpublished manuscript, 2007 (pdf).
• G. B. Wright and B. Fornberg. Scattered node mehrstellenverfahren-type formulas generated from radial basis functions. Book chapter: Computational Methods, G. Liu, V. Tan, and X. Han, eds., Springer (2006), 1391-1395 (pdf).
• O. E. Livne and G. B. Wright. Fast multilevel evaluation of smooth radial basis function expansions. ETNA, 23 (2006), 263-287 (pdf, bibtex).
• G. B. Wright and B. Fornberg. Scattered node compact finite difference-type formulas generated from radial basis functions, J. Comput. Phys., 212 (2006), 99-123 (pdf, bibtex).
• B. Fornberg, E. Larsson, and G. Wright. A new class of oscillatory radial basis functions, Computers and Mathematics with Applications, 51 (2006), 1209-1222 (pdf, bibtex).
• B. Fornberg and G. Wright. Stable computation of multiquadric interpolants for all values of the shape parameter, Computers and Mathematics with Applications 48 (2004) 853-867 (pdf, bibtex).
• B. Fornberg, G. Wright, and E. Larsson. Some observations regarding interpolants in the limit of flat radial basis functions, Computers and Mathematics with Applications 47 (2004) 37-55 (pdf, bibtex).
• B. Fornberg, T. A. Driscoll, G. Wright, and R. Charles. Observations on the behavior of radial basis functions near boundaries,Computers and Mathematics with Applications 43(2002), 473-490 (pdf, bibtex).
• G. B. Wright. Radial Basis Function Interpolation: Numerical and Analytical Developments. University of Colorado, Boulder. PhD Thesis, 2003 (pdf, bibtex).

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Conference/Seminar/Workshop talks

• Dolomites Research Week on Approximation (DRWA13), Sept. 8-13, 2013, published slides.
• Montestigliano workshop, April 13-19, 2014.

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Software contributions

• Chebfun
• SpherePts
• CFPU