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Publications
B. Adcock, D. Huybrechs, and C. Piret, Stable and accurate least squares radial basis function approximations on bounded domains, submitted (2023).
B. Fornberg and C. Piret, Computation of Fractional Derivatives of Analytic Functions. J Sci Comput 96, 79, 2023.
N. Dissanayake, J. Blazejewski, C. Piret, B. Ong, Parareal - Radial Basis Function-Finite Difference (RBF-FD) Framework for Solving Time-Dependent Partial Differential Equations. Dolomites Research Notes on Approximation, 15(5), 2022, pp. 8–23.
C. Piret, N. Dissanayake, J.Gierke, and B. Fornberg, The Radial Basis Functions Method for Improved Numerical Approximations of Geological Processes in Heterogeneous Systems, Mathematical Geosciences, 2020.
B.Fornberg and C.Piret, Complex Variables and Analytic Functions: An Illustrated Introduction, SIAM, 2020. (BOOK)
S. Kumar and C. Piret, Numerical Solution of Space-Time fractional PDEs using RBF-QR and Chebyshev Polynomials, Applied Numerical Mathematics, Volume 143, 2019, 300–315.
A.Petras, L.Ling, C. Piret, S. Ruuth, A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces, Journal of Computational Physics, Volume 381, 2019, 146–161.
C. Piret, and J. Dunn (2016). Fast RBF OGr for solving PDEs on arbitrary surfaces. AIP Conference Proceedings, 1776(1), 070005. doi:10.1063/1.4965351
C. Piret, A RBF-Based Frames Strategy for Bypassing the Runge Phenomenon, SIAM J. Sci. Comput., 38(4) (2016), A2262–A2282.
E. Hanert and C. Piret, A Chebyshev pseudo-spectral method to solve the space-time tempered fractional diffusion equation, SIAM J. Sci. Comput., 36(4) (2014).
C. Piret and E. Hanert, A Radial Basis Functions method for fractional diffusion equations, Journal of Computational Physics 238 (2013) pp. 71-81 (pdf)
E.Hanert and C. Piret, Numerical solution of the space-time fractional diffusion equation: Alternatives to finite differences, 5th IFAC Symposium on Fractional Differentiation and Its Applications-FDA2012, Hohai University, Nanjing, China, 14-17 May 2012. (pdf)
E. Marchandise, C.Piret and J.-F. Remacle, CAD and mesh repair with Radial Basis Functions, Journal of Computational Physics 231 (2012) pp. 2376-2387. (pdf)
C. Piret, J.-F. Remacle and E. Marchandise, Mesh and CAD Repair Based on Parametrizations with Radial Basis Functions, Proceedings of the 20th International Meshing Roundtable 2012, Part 6, 419-436, DOI: 10.1007/978-3-642-24734-7 23. (pdf)
C. Piret, The Orthogonal Gradients Method: a Radial Basis Functions Method for Solving Partial Differential Equations on Arbitrary Surfaces, Journal of Computational Physics (2012), In Press. http://dx.doi.org/10.1016/j.jcp.2012.03.007 (pdf)
J. Schmidt, C. Piret, B. Kadlec, D. Yuen, E. Sevre, N. Zhang, Y. Liu, “Simulating tsunami Shallow-Water Equations with Graphics Accelerated Hardware (GPU) and Radial Basis Functions (RBF)”, in proceedings of the South China Sea Tsunami Workshop 2008, SCSTW 2008. Shanghai, China, December 2008.
J. Schmidt, C. Piret, N. Zhang, B. Kadlec, Y. Liu, D. Yuen, G. B. Wright, and E. Sevre, Modeling of Tsunami Equations and Atmospheric Swirling Flows with Graphics Accelerated Hardware (GPU) and Radial Basis Functions (RBF), Concurrency and Computation: Practice and Experience,Volume 22, Issue 12, pages 1813 - 1835, 2010. (pdf)
B. Fornberg and C. Piret, On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere, Journal of Computational Physics, 227 (2008), 2758- 2780. (pdf)
B. Fornberg, N. Flyer, S. Hovde and C. Piret, Locality properties of radial basis function expansion coefficients for equispaced interpolation, IMA Journal of Numerical Analysis 28 (2008), 121-142. (pdf)
B. Fornberg and C. Piret, A stable algorithm for flat radial basis functions on a sphere, SIAM J. Sci. Comp. 30 (2007), 60-80. (pdf)
B. Fornberg and C. Piret, Computation of Fractional Derivatives of Analytic Functions. J Sci Comput 96, 79, 2023.
N. Dissanayake, J. Blazejewski, C. Piret, B. Ong, Parareal - Radial Basis Function-Finite Difference (RBF-FD) Framework for Solving Time-Dependent Partial Differential Equations. Dolomites Research Notes on Approximation, 15(5), 2022, pp. 8–23.
C. Piret, N. Dissanayake, J.Gierke, and B. Fornberg, The Radial Basis Functions Method for Improved Numerical Approximations of Geological Processes in Heterogeneous Systems, Mathematical Geosciences, 2020.
B.Fornberg and C.Piret, Complex Variables and Analytic Functions: An Illustrated Introduction, SIAM, 2020. (BOOK)
S. Kumar and C. Piret, Numerical Solution of Space-Time fractional PDEs using RBF-QR and Chebyshev Polynomials, Applied Numerical Mathematics, Volume 143, 2019, 300–315.
A.Petras, L.Ling, C. Piret, S. Ruuth, A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces, Journal of Computational Physics, Volume 381, 2019, 146–161.
C. Piret, and J. Dunn (2016). Fast RBF OGr for solving PDEs on arbitrary surfaces. AIP Conference Proceedings, 1776(1), 070005. doi:10.1063/1.4965351
C. Piret, A RBF-Based Frames Strategy for Bypassing the Runge Phenomenon, SIAM J. Sci. Comput., 38(4) (2016), A2262–A2282.
E. Hanert and C. Piret, A Chebyshev pseudo-spectral method to solve the space-time tempered fractional diffusion equation, SIAM J. Sci. Comput., 36(4) (2014).
C. Piret and E. Hanert, A Radial Basis Functions method for fractional diffusion equations, Journal of Computational Physics 238 (2013) pp. 71-81 (pdf)
E.Hanert and C. Piret, Numerical solution of the space-time fractional diffusion equation: Alternatives to finite differences, 5th IFAC Symposium on Fractional Differentiation and Its Applications-FDA2012, Hohai University, Nanjing, China, 14-17 May 2012. (pdf)
E. Marchandise, C.Piret and J.-F. Remacle, CAD and mesh repair with Radial Basis Functions, Journal of Computational Physics 231 (2012) pp. 2376-2387. (pdf)
C. Piret, J.-F. Remacle and E. Marchandise, Mesh and CAD Repair Based on Parametrizations with Radial Basis Functions, Proceedings of the 20th International Meshing Roundtable 2012, Part 6, 419-436, DOI: 10.1007/978-3-642-24734-7 23. (pdf)
C. Piret, The Orthogonal Gradients Method: a Radial Basis Functions Method for Solving Partial Differential Equations on Arbitrary Surfaces, Journal of Computational Physics (2012), In Press. http://dx.doi.org/10.1016/j.jcp.2012.03.007 (pdf)
J. Schmidt, C. Piret, B. Kadlec, D. Yuen, E. Sevre, N. Zhang, Y. Liu, “Simulating tsunami Shallow-Water Equations with Graphics Accelerated Hardware (GPU) and Radial Basis Functions (RBF)”, in proceedings of the South China Sea Tsunami Workshop 2008, SCSTW 2008. Shanghai, China, December 2008.
J. Schmidt, C. Piret, N. Zhang, B. Kadlec, Y. Liu, D. Yuen, G. B. Wright, and E. Sevre, Modeling of Tsunami Equations and Atmospheric Swirling Flows with Graphics Accelerated Hardware (GPU) and Radial Basis Functions (RBF), Concurrency and Computation: Practice and Experience,Volume 22, Issue 12, pages 1813 - 1835, 2010. (pdf)
B. Fornberg and C. Piret, On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere, Journal of Computational Physics, 227 (2008), 2758- 2780. (pdf)
B. Fornberg, N. Flyer, S. Hovde and C. Piret, Locality properties of radial basis function expansion coefficients for equispaced interpolation, IMA Journal of Numerical Analysis 28 (2008), 121-142. (pdf)
B. Fornberg and C. Piret, A stable algorithm for flat radial basis functions on a sphere, SIAM J. Sci. Comp. 30 (2007), 60-80. (pdf)
