Bengt Fornberg

Publication Activity (10 Years)

Years Active: 1981-2024
Publications (10 Years): 31

Top Topics

Image Denoising

Mlp Neural Networks

Partial Differential Equations

Smooth Surfaces

Top Venues

J. Comput. Phys.

Comput. Math. Appl.

Numer. Algorithms

Publications

Morten E. Nielsen, Bengt Fornberg
High-order numerical method for solving elliptic partial differential equations on unfitted node sets. CoRR (2024)
Andrew P. Lawrence, Morten E. Nielsen, Bengt Fornberg
Node subsampling for multilevel meshfree elliptic PDE solvers. Comput. Math. Appl. 164 (2024)
Bengt Fornberg, Andrew P. Lawrence
Enhanced trapezoidal rule for discontinuous functions. J. Comput. Phys. 491 (2023)
Bengt Fornberg, Cécile Piret
Computation of Fractional Derivatives of Analytic Functions. J. Sci. Comput. 96 (3) (2023)
Kiera van der Sande, Natasha Flyer, Bengt Fornberg
Accelerating Explicit Time-Stepping with Spatially Variable Time Steps Through Machine Learning. J. Sci. Comput. 96 (1) (2023)
Andrew P. Lawrence, Morten E. Nielsen, Bengt Fornberg
Node Subsampling for Multilevel Meshfree Elliptic PDE Solvers. CoRR (2023)
J. A. C. Weideman, Bengt Fornberg
Fully numerical Laplace transform methods. Numer. Algorithms 92 (1) (2023)
Bengt Fornberg
Finite difference formulas in the complex plane. Numer. Algorithms 90 (3) (2022)
Bengt Fornberg
Improving the Accuracy of the Trapezoidal Rule. SIAM Rev. 63 (1) (2021)
Bengt Fornberg
Generalizing the trapezoidal rule in the complex plane. Numer. Algorithms 87 (1) (2021)
Dylan Abrahamsen, Bengt Fornberg
On the Infinite Order Limit of Hermite-based Finite Difference Schemes. SIAM J. Numer. Anal. 59 (4) (2021)
Abe C. Ellison, Bengt Fornberg
A parallel-in-time approach for wave-type PDEs. Numerische Mathematik 148 (1) (2021)
Dylan Abrahamsen, Bengt Fornberg
Solving the Korteweg-de Vries equation with Hermite-based finite differences. Appl. Math. Comput. 401 (2021)
Kiera van der Sande, Bengt Fornberg
Fast Variable Density 3-D Node Generation. SIAM J. Sci. Comput. 43 (1) (2021)
David Gunderman, Natasha Flyer, Bengt Fornberg
Transport schemes in spherical geometries using spline-based RBF-FD with polynomials. J. Comput. Phys. 408 (2020)
Dylan Abrahamsen, Bengt Fornberg
Explicit Time Stepping of PDEs with Local Refinement in Space-Time. J. Sci. Comput. 81 (3) (2019)
Bengt Fornberg, Jonah A. Reeger
An improved Gregory-like method for 1-D quadrature. Numerische Mathematik 141 (1) (2019)
Abe C. Ellison, Bengt Fornberg
A parallel-in-time approach for wave-type PDEs. CoRR (2019)
Victor Bayona, Natasha Flyer, Bengt Fornberg
On the role of polynomials in RBF-FD approximations: III. Behavior near domain boundaries. J. Comput. Phys. 380 (2019)
Kiera van der Sande, Bengt Fornberg
Fast variable density 3-D node generation. CoRR (2019)
O. Vlasiuk, Timothy Michaels, Natasha Flyer, Bengt Fornberg
Fast high-dimensional node generation with variable density. Comput. Math. Appl. 76 (7) (2018)
Jonah A. Reeger, Bengt Fornberg
Numerical quadrature over smooth surfaces with boundaries. J. Comput. Phys. 355 (2018)
Matthew J. Colbrook, Natasha Flyer, Bengt Fornberg
On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains. J. Comput. Phys. 374 (2018)
Victor Bayona, Natasha Flyer, Bengt Fornberg, Gregory A. Barnett
On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs. J. Comput. Phys. 332 (2017)
Bradley Martin, Bengt Fornberg
Seismic modeling with radial basis function-generated finite differences (RBF-FD) - a simplified treatment of interfaces. J. Comput. Phys. 335 (2017)
Marco Fasondini, Bengt Fornberg, J. A. C. Weideman
Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces. J. Comput. Phys. 344 (2017)
Grady B. Wright, Bengt Fornberg
Stable computations with flat radial basis functions using vector-valued rational approximations. J. Comput. Phys. 331 (2017)
Bengt Fornberg
Fast calculation of Laurent expansions for matrix inverses. J. Comput. Phys. 326 (2016)
Natasha Flyer, Bengt Fornberg, Victor Bayona, Gregory A. Barnett
On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy. J. Comput. Phys. 321 (2016)
Bengt Fornberg, Natasha Flyer
Fast generation of 2-D node distributions for mesh-free PDE discretizations. Comput. Math. Appl. 69 (7) (2015)
Bengt Fornberg, Natasha Flyer
Solving PDEs with radial basis functions. Acta Numer. 24 (2015)
Bengt Fornberg, Jordan M. Martel
On spherical harmonics based numerical quadrature over the surface of a sphere. Adv. Comput. Math. 40 (5-6) (2014)
Bengt Fornberg, J. A. C. Weideman
A Computational Exploration of the Second Painlevé Equation. Found. Comput. Math. 14 (5) (2014)
Nathan D. Monnig, Bengt Fornberg, François G. Meyer
Inverting Non-Linear Dimensionality Reduction with Scale-Free Radial Basis Interpolation CoRR (2013)
Bengt Fornberg, Erik Lehto, Collin Powell
Stable calculation of Gaussian-based RBF-FD stencils. Comput. Math. Appl. 65 (4) (2013)
Elisabeth Larsson, Erik Lehto, Alfa R. H. Heryudono, Bengt Fornberg
Stable Computation of Differentiation Matrices and Scattered Node Stencils Based on Gaussian Radial Basis Functions. SIAM J. Sci. Comput. 35 (4) (2013)
Michelle Ghrist, Bengt Fornberg
Two Results Concerning the Stability of Staggered Multistep Methods. SIAM J. Numer. Anal. 50 (4) (2012)
Bengt Fornberg, J. A. C. Weideman
A numerical methodology for the Painlevé equations. J. Comput. Phys. 230 (15) (2011)
Bengt Fornberg, Elisabeth Larsson, Natasha Flyer
Stable Computations with Gaussian Radial Basis Functions. SIAM J. Sci. Comput. 33 (2) (2011)
Bengt Fornberg
Finite difference method. Scholarpedia 6 (10) (2011)
Bengt Fornberg, Erik Lehto
Stabilization of RBF-generated finite difference methods for convective PDEs. J. Comput. Phys. 230 (6) (2011)
Bengt Fornberg
A finite difference method for free boundary problems. J. Comput. Appl. Math. 233 (11) (2010)
Bengt Fornberg, Cécile Piret
On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere. J. Comput. Phys. 227 (5) (2008)
Bengt Fornberg, Julia Zuev
The Runge phenomenon and spatially variable shape parameters in RBF interpolation. Comput. Math. Appl. 54 (3) (2007)
Bengt Fornberg, Cécile Piret
A Stable Algorithm for Flat Radial Basis Functions on a Sphere. SIAM J. Sci. Comput. 30 (1) (2007)
Bengt Fornberg, Elisabeth Larsson, Grady B. Wright
A new class of oscillatory radial basis functions. Comput. Math. Appl. 51 (8) (2006)
Bengt Fornberg
A Pseudospectral Fictitious Point Method for High Order Initial-Boundary Value Problems. SIAM J. Sci. Comput. 28 (5) (2006)
Grady B. Wright, Bengt Fornberg
Scattered node compact finite difference-type formulas generated from radial basis functions. J. Comput. Phys. 212 (1) (2006)
Bengt Fornberg, Natasha Flyer
Accuracy of radial basis function interpolation and derivative approximations on 1-D infinite grids. Adv. Comput. Math. 23 (1-2) (2005)
Bengt Fornberg, Natasha Flyer
On the Nature of Initial-Boundary Value Solutions for Dispersive Equations. SIAM J. Appl. Math. 64 (2) (2004)
Tobin A. Driscoll, Bengt Fornberg
A Padé-based algorithm for overcoming the Gibbs phenomenon. Numer. Algorithms 26 (1) (2001)
Michelle Ghrist, Bengt Fornberg, Tobin A. Driscoll
Staggered Time Integrators for Wave Equations. SIAM J. Numer. Anal. 38 (3) (2000)
Bengt Fornberg, Michelle Ghrist
Spatial Finite Difference Approximations for Wave-Type Equations. SIAM J. Numer. Anal. 37 (1) (1999)
Tobin A. Driscoll, Bengt Fornberg
Block Pseudospectral Methods for Maxwell's Equations II: Two-Dimensional, Discontinuous-Coefficient Case. SIAM J. Sci. Comput. 21 (3) (1999)
Bengt Fornberg
Classroom Note: Calculation of Weights in Finite Difference Formulas. SIAM Rev. 40 (3) (1998)
Bengt Fornberg
The Prospect for Parallel Computing in the Oil Industry. PARA (1996)
Bengt Fornberg
A Pseudospectral Approach for Polar and Spherical Geometries. SIAM J. Sci. Comput. 16 (5) (1995)
Bengt Fornberg
Numerical Differentiation of Analytic Functions. ACM Trans. Math. Softw. 7 (4) (1981)
Bengt Fornberg
Algorithm 579: CPSC: Complex Power Series Coefficients [D4]. ACM Trans. Math. Softw. 7 (4) (1981)