Publications in VIVO

Co-author Network

Fornberg, Bengt Professor

Positions

Professor, Applied Mathematics

Research Areas

Research

research overview

Prof. Fornberg's work is focused on radial basis function (RBF) based numerical methods, applicable to a wide range of PDEs, arising for example in the geosciences and for wave propagation. He has also recently developed methods for numerical quadrature and for solving the Painlevé equations.

keywords

numerical methods for ODEs and PDEs, quadrature, complex variables, finite differences, spectral methods, radial basis function methods, computational fluid dynamics, Painlevé equations

Publications

selected publications

book
chapter
- STEADY VORTEX FLOW PAST A CYLINDER OR SPHERE. 146-+. 2008
- Some numerical techniques for Maxwell's equations in different types of geometries. Lecture Notes in Computational Science and Engineering. 265-299. 2003
- Steady vortex flows obtained from a nonlinear eigenvalue problem. ESAIM : Proceedings. 130-136. 1999
- A review of pseudospectral methods for solving partial differential equations. 203-267. 1994
- COMPUTING STEADY INCOMPRESSIBLE FLOWS PAST BLUNT BODIES - A HISTORICAL OVERVIEW. 115-133. 1993
- Rapid generation of weights in finite difference formulas. 105-121. 1990
- Numerical computation of nonlinear waves. 157-184. 1981
- Pseudospectral calculations on $2$-d turbulence and nonlinear waves. 1--18. SIAM-AMS Proc.-Vol. XI. 1978
conference proceeding
- Simulations of 2D Maxwell-Bloch equations. Proceedings of the International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD. 5-+. 2007
- Scattered node compact finite difference-type formulas generated from radial basis functions. 1391-+. 2004
- Pseudospectral methods for large-scale bioacoustic models. 1501-1506. 1997
journal article
- On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains. Journal of Computational Physics. 996-1016. 2018
- Fast high-dimensional node generation with variable density. Computers and Mathematics with Applications. 1739-1757. 2018
- Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals. Physical Review E. 2018
- Numerical quadrature over smooth surfaces with boundaries. Journal of Computational Physics. 176-190. 2018
- A computational exploration of the McCoy-Tracy-Wu solutions of the third Painleve equation. Physica D: Nonlinear Phenomena. 18-43. 2018
- Methods for the computation of the multivalued Painleve transcendents on their Riemann surfaces. Journal of Computational Physics. 36-50. 2017
- Using radial basis function-generated finite differences (RBF-FD) to solve heat transfer equilibrium problems in domains with interfaces. Engineering Analysis with Boundary Elements. 38-48. 2017
- Seismic modeling with radial basis function-generated finite differences (RBF-FD) - a simplified treatment of interfaces. Journal of Computational Physics. 828-845. 2017
- On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs. Journal of Computational Physics. 257-273. 2017
- Stable computations with flat radial basis functions using vector-valued rational approximations. Journal of Computational Physics. 137-156. 2017
- Fast calculation of Laurent expansions for matrix inverses. Journal of Computational Physics. 722-732. 2016
- Numerical quadrature over smooth, closed surfaces. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2016
- On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy. Journal of Computational Physics. 21-38. 2016
- Numerical Quadrature over the Surface of a Sphere. Studies in Applied Mathematics. 174-188. 2016
- Stability ordinates of Adams predictor-corrector methods. BIT Numerical Mathematics. 733-750. 2015
- A computational overview of the solution space of the imaginary Painleve II equation. Physica D: Nonlinear Phenomena. 108-118. 2015
- Seismic modeling with radial-basis-function-generated finite differences. Geophysics. T137-T146. 2015
- Fast generation of 2-D node distributions for mesh-free PDE discretizations. Computers and Mathematics with Applications. 531-544. 2015
- Solving PDEs with radial basis functions. Acta Numerica. 215-258. 2015
- On spherical harmonics based numerical quadrature over the surface of a sphere. Advances in Computational Mathematics. 1169-1184. 2014
- A Computational Exploration of the Second Painlev, Equation. Foundations of Computational Mathematics. 985-1016. 2014
- Some observations regarding steady laminar flows past bluff bodies. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences. 2014
- Inverting nonlinear dimensionality reduction with scale-free radial basis function interpolation. Applied and Computational Harmonic Analysis. 162-170. 2014
- Painleve IV: A numerical study of the fundamental domain and beyond. Physica D: Nonlinear Phenomena. 1-13. 2014
- A spectrally accurate numerical implementation of the Fokas transform method for Helmholtz-type PDEs. Complex Variables. 564-577. 2014
- Painleve IV with both Parameters Zero: A Numerical Study. Studies in Applied Mathematics. 108-133. 2013
- Stable calculation of Gaussian-based RBF-FD stencils. Computers and Mathematics with Applications. 627-637. 2013
- STABLE COMPUTATION OF DIFFERENTIATION MATRICES AND SCATTERED NODE STENCILS BASED ON GAUSSIAN RADIAL BASIS FUNCTIONS. SIAM Journal on Scientific Computing. A2096-A2119. 2013
- TWO RESULTS CONCERNING THE STABILITY OF STAGGERED MULTISTEP METHODS. SIAM Journal on Numerical Analysis. 1849-1860. 2012
- A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2983-3003. 2011
- A numerical methodology for the Painleve equations. Journal of Computational Physics. 5957-5973. 2011
- Radial basis functions: Developments and applications to planetary scale flows. Computers and Fluids. 23-32. 2011
- Stabilization of RBF-generated finite difference methods for convective PDEs. Journal of Computational Physics. 2270-2285. 2011
- STABLE COMPUTATIONS WITH GAUSSIAN RADIAL BASIS FUNCTIONS. SIAM Journal on Scientific Computing. 869-892. 2011
- A finite difference method for free boundary problems. Journal of Computational and Applied Mathematics. 2831-2840. 2010
- Evolution of solitary waves in a two-pycnocline system. Journal of Fluid Mechanics. 235-277. 2010
- Comparisons between pseudospectral and radial basis function derivative approximations. IMA Journal of Numerical Analysis. 149-172. 2010
- MAGNETIC RELAXATION IN THE SOLAR CORONA. Astrophysical Journal. 720-733. 2009
- Steady axisymmetric vortex flows with swirl and shear. Journal of Fluid Mechanics. 395-410. 2008
- Numerical solutions to 2D Maxwell-Bloch equations. Optical and Quantum Electronics. 447-453. 2008
- On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere. Journal of Computational Physics. 2758-2780. 2008
- Locality properties of radial basis function expansion coefficients for equispaced interpolation. IMA Journal of Numerical Analysis. 121-142. 2008
- The Runge phenomenon and spatially variable shape parameters in RBF interpolation. Computers and Mathematics with Applications. 379-398. 2007
- Stability and accuracy of time-extrapolated ADI-FDTD methods for solving wave equations. Journal of Computational and Applied Mathematics. 178-192. 2007
- A stable algorithm for flat radial basis functions on a sphere. SIAM Journal on Scientific Computing. 60-80. 2007
- A new class of oscillatory radial basis functions. Computers and Mathematics with Applications. 1209-1222. 2006
- Scattered node compact finite difference-type formulas generated from radial basis functions. Journal of Computational Physics. 99-123. 2006
- A pseudospectral fictitious point method for high order initial-boundary value problems. SIAM Journal on Scientific Computing. 1716-1729. 2006
- Stability of vortices in equilibrium with a cylinder. Journal of Fluid Mechanics. 53-68. 2005
- Magnetic field confinement in the solar corona. II. Field-plasma interaction. Astrophysical Journal. 1239-1259. 2005
- Accuracy of radial basis function interpolation and derivative approximations on 1-D infinite grids. Advances in Computational Mathematics. 5-20. 2005
- Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions. Computers and Mathematics with Applications. 103-130. 2005
- Stable computation of multiquadric interpolants for all values of the shape parameter. Computers and Mathematics with Applications. 853-867. 2004
- Magnetic field confinement in the solar corona. I. Force-free magnetic fields. Astrophysical Journal. 1210-1222. 2004
- Some unconditionally stable time stepping methods for the 3D Maxwell's equations. Journal of Computational and Applied Mathematics. 497-523. 2004
- Some observations regarding interpolants in the limit of flat radial basis functions. Computers and Mathematics with Applications. 37-55. 2004
- Some observations regarding interpolants in the limit of flat radial basis functions. Computers and Mathematics with Applications. 37-55. 2004
- A split step approach for the 3-D Maxwell's equations. Journal of Computational and Applied Mathematics. 485-505. 2003
- A numerical study of some radial basis function based solution methods for elliptic PDEs. Computers and Mathematics with Applications. 891-902. 2003
- A numerical study of some radial basis function based solution methods for elliptic PDEs. Computers and Mathematics with Applications. 891-902. 2003
- Accurate numerical resolution of transients in initial-boundary value problems for the heat equation. Journal of Computational Physics. 526-539. 2003
- On the nature of initial-boundary value solutions for dispersive equations. SIAM Journal on Applied Mathematics. 546-564. 2003
- Interpolation in the limit of increasingly flat radial basis functions. Computers and Mathematics with Applications. 413-422. 2002
- Observations on the behavior of radial basis function approximations near boundaries. Computers and Mathematics with Applications. 473-490. 2002
- Some steady axisymmetric vortex flows past a sphere. Journal of Fluid Mechanics. 315-328. 2001
- A Pade-based algorithm for overcoming the Gibbs phenomenon. Numerical Algorithms. 77-92. 2001
- Staggered time integrators for wave equations. SIAM Journal on Numerical Analysis. 718-741. 2000
- Note on nonsymmetric finite differences for Maxwell's equations. Journal of Computational Physics. 723-727. 2000
- Some steady vortex flows past a circular cylinder. Journal of Fluid Mechanics. 13-27. 2000
- Spatial finite difference approximations for wave-type equations. SIAM Journal on Numerical Analysis. 105-130. 1999
- Block pseudospectral methods for Maxwell's equations - II: Two-dimensional, discontinuous-coefficient case. SIAM Journal on Scientific Computing. 1146-1167. 1999
- A fast spectral algorithm for nonlinear wave equations with linear dispersion. Journal of Computational Physics. 456-467. 1999
- Calculation of weights in finite difference formulas. SIAM Review. 685-691. 1998
- A block pseudospectral method for Maxwell's equations - I. One-dimensional case. Journal of Computational Physics. 47-65. 1998
- On the chance of freak waves at sea. Journal of Fluid Mechanics. 113-138. 1998
- Comparison of finite difference- and pseudospectral methods for convective flow over a sphere. Geophysical Research Letters. 3245-3248. 1997
- A high-order finite-difference method applied to large Rayleigh number mantle convection. Geophysical and Astrophysical Fluid Dynamics. 53-83. 1997
- A new numerical algorithm for the analytic continuation of Green's functions. Journal of Computational Physics. 99-108. 1996
- A PSEUDOSPECTRAL APPROACH FOR POLAR AND SPHERICAL GEOMETRIES. SIAM Journal on Scientific Computing. 1071-1081. 1995
- A COMPACT 4TH-ORDER FINITE-DIFFERENCE SCHEME FOR THE STEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS. International Journal for Numerical Methods in Fluids. 1137-1151. 1995
- FLOW PAST A ROW OF FLAT PLATES AT LARGE REYNOLDS-NUMBERS. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 211-235. 1993
- A FINITE-DIFFERENCE PROCEDURE FOR A CLASS OF FREE-BOUNDARY PROBLEMS. Journal of Computational Physics. 72-77. 1992
- STEADY INCOMPRESSIBLE-FLOW PAST A ROW OF CIRCULAR-CYLINDERS. Journal of Fluid Mechanics. 655-671. 1991
- DISCRETIZATION ERRORS AT FREE BOUNDARIES OF THE GRAD-SCHLUTER-SHAFRANOV EQUATION. Numerische Mathematik. 683-710. 1991
- AN IMPROVED PSEUDOSPECTRAL METHOD FOR INITIAL-BOUNDARY VALUE-PROBLEMS. Journal of Computational Physics. 381-397. 1990
- HIGH-ORDER FINITE-DIFFERENCES AND THE PSEUDOSPECTRAL METHOD ON STAGGERED GRIDS. SIAM Journal on Numerical Analysis. 904-918. 1990
- GENERATION OF FINITE-DIFFERENCE FORMULAS ON ARBITRARILY SPACED GRIDS. Mathematics of Computation. 699-706. 1988
- STEADY VISCOUS-FLOW PAST A SPHERE AT HIGH REYNOLDS-NUMBERS. Journal of Fluid Mechanics. 471-489. 1988
- THE PSEUDOSPECTRAL METHOD - ACCURATE REPRESENTATION OF INTERFACES IN ELASTIC WAVE CALCULATIONS. Geophysics. 625-637. 1988
- THE PSEUDOSPECTRAL METHOD - COMPARISONS WITH FINITE-DIFFERENCES FOR THE ELASTIC WAVE-EQUATION. Geophysics. 483-501. 1987
- STEADY VISCOUS-FLOW PAST A CIRCULAR-CYLINDER UP TO REYNOLDS NUMBER-600. Journal of Computational Physics. 297-320. 1985
- A NUMERICAL-METHOD FOR CONFORMAL MAPPING OF DOUBLY CONNECTED REGIONS. SIAM Journal on Scientific Computing. 771-783. 1984
- CALCULATIONS OF LAMINAR VISCOUS-FLOW OVER A MOVING WAVY SURFACE. Journal of Fluid Mechanics. 347-362. 1982
- A VECTOR IMPLEMENTATION OF THE FAST FOURIER-TRANSFORM ALGORITHM. Mathematics of Computation. 189-191. 1981
- ALGORITHM-579 CPSC - COMPLEX POWER-SERIES COEFFICIENTS [D4]. ACM Transactions on Mathematical Software. 542-547. 1981
- NUMERICAL DIFFERENTIATION OF ANALYTIC-FUNCTIONS. ACM Transactions on Mathematical Software. 512-526. 1981
- A NUMERICAL STUDY OF STEADY VISCOUS-FLOW PAST A CIRCULAR-CYLINDER. Journal of Fluid Mechanics. 819-855. 1980
- A NUMERICAL-METHOD FOR CONFORMAL-MAPPINGS. SIAM Journal on Scientific Computing. 386-400. 1980
- NUMERICAL AND THEORETICAL-STUDY OF CERTAIN NON-LINEAR WAVE PHENOMENA. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences. 373-404. 1978
- NUMERICAL STUDY OF 2-D TURBULENCE. Journal of Computational Physics. 1-31. 1977
- COMPLEX ZEROS OF JONQUIERE OR POLYLOGARITHM FUNCTION. Mathematics of Computation. 582-599. 1975
- FOURIER METHOD FOR INTEGRATION OF HYPERBOLIC EQUATIONS. SIAM Journal on Numerical Analysis. 509-528. 1975
- INSTABILITY OF LEAP-FROG AND CRANK-NICOLSON APPROXIMATIONS OF A NONLINEAR PARTIAL DIFFERENTIAL EQUATION. Mathematics of Computation. 45-57. 1973
- A method for acceleration of the convergence of infinite series. BIT Numerical Mathematics. 78-80. 1969

Teaching

courses taught

APPM 5610 Numerical Analysis 2 (Spring 2019)
APPM 6950 Master's Thesis (Spring 2019)
APPM 7900 Independent Study (Spring 2019)
APPM 8990 Doctoral Dissertation (Spring 2019)
MATH 5610 Numerical Analysis 2 (Spring 2019)
APPM 2360 Introduction to Differential Equations with Linear Algebra (Fall 2018)
APPM 6950 Master's Thesis (Fall 2018)
APPM 8990 Doctoral Dissertation (Fall 2018)
APPM 6950 Master's Thesis (Spring 2018)
APPM 7400 Topics in Applied Mathematics (Spring 2018)
APPM 7900 Independent Study (Spring 2018)
APPM 8990 Doctoral Dissertation (Spring 2018)

Background

education and training

Ph.D., University of Uppsala (Sweden) 1972
B.S., University of Uppsala (Sweden) 1969

awards and honors

BFA Award for Excellence in Research, Scholarly and Creative Work (Boulder Faculty Assembly), conferred by Boulder Faculty Assembly, 2014
Fellow (Society for Industrial and Applied Mathematics), conferred by Society for Industrial and Applied Mathematics, 2014
Fellowship (John Simon Guggenheim Memorial Foundation), conferred by John Simon Guggenheim Memorial Foundation, 1981

International Activities

global connections related to teaching and scholarly work (in recent years)

Africa Continent
Europe Continent
South Africa Country
Spain Country
Sweden Country
United Kingdom Country

Other Profiles

ORCID iD

http://orcid.org/0000-0003-0014-6985

Google Scholar

http://scholar.google.com/citations?user=aL9gPCcAAAAJ&hl=en