Bengt Fornberg - Publications

Affiliations: 
Applied Mathematics University of Colorado, Boulder, Boulder, CO, United States 
Area:
Astronomy and Astrophysics

109 high-probability publications. We are testing a new system for linking publications to authors. You can help! If you notice any inaccuracies, please sign in and mark papers as correct or incorrect matches. If you identify any major omissions or other inaccuracies in the publication list, please let us know.

Year Citation  Score
2020 Fornberg B. Contour integrals of analytic functions given on a grid in the complex plane Ima Journal of Numerical Analysis. DOI: 10.1093/Imanum/Draa024  0.356
2020 Gunderman D, Flyer N, Fornberg B. Transport schemes in spherical geometries using spline-based RBF-FD with polynomials Journal of Computational Physics. 408: 109256. DOI: 10.1016/J.Jcp.2020.109256  0.414
2020 Fornberg B. Generalizing the trapezoidal rule in the complex plane Numerical Algorithms. 1-16. DOI: 10.1007/S11075-020-00963-0  0.394
2019 Reeger JA, Fornberg B, Watts ML. Numerical quadrature over smooth, closed surfaces. Proceedings. Mathematical, Physical, and Engineering Sciences. 472: 20160401. PMID 27843402 DOI: 10.1098/Rspa.2016.0401  0.798
2019 Bayona V, Flyer N, Fornberg B. On the role of polynomials in RBF-FD approximations: III. Behavior near domain boundaries Journal of Computational Physics. 380: 378-399. DOI: 10.1016/J.Jcp.2018.12.013  0.407
2019 Piret C, Dissanayake N, Gierke JS, Fornberg B. The Radial Basis Functions Method for Improved Numerical Approximations of Geological Processes in Heterogeneous Systems Mathematical Geosciences. 52: 477-497. DOI: 10.1007/S11004-019-09820-W  0.486
2019 Abrahamsen D, Fornberg B. Explicit Time Stepping of PDEs with Local Refinement in Space-Time Journal of Scientific Computing. 81: 1945-1962. DOI: 10.1007/S10915-019-01065-3  0.399
2018 Fasondini M, Fornberg B, Weideman J. A computational exploration of the McCoy–Tracy–Wu solutions of the third Painlevé equation Physica D: Nonlinear Phenomena. 363: 18-43. DOI: 10.1016/J.Physd.2017.10.011  0.386
2018 Colbrook MJ, Flyer N, Fornberg B. On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains Journal of Computational Physics. 374: 996-1016. DOI: 10.1016/J.Jcp.2018.08.005  0.418
2018 Reeger JA, Fornberg B. Numerical quadrature over smooth surfaces with boundaries Journal of Computational Physics. 355: 176-190. DOI: 10.1016/J.Jcp.2017.11.010  0.779
2018 Vlasiuk O, Michaels T, Flyer N, Fornberg B. Fast high-dimensional node generation with variable density Computers & Mathematics With Applications. 76: 1739-1757. DOI: 10.1016/J.Camwa.2018.07.026  0.367
2018 Fornberg B, Reeger JA. An improved Gregory-like method for 1-D quadrature Numerische Mathematik. 141: 1-19. DOI: 10.1007/S00211-018-0992-0  0.774
2017 Fasondini M, Fornberg B, Weideman J. Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces Journal of Computational Physics. 344: 36-50. DOI: 10.1016/J.Jcp.2017.04.071  0.426
2017 Martin B, Fornberg B. Seismic modeling with radial basis function-generated finite differences (RBF-FD) – a simplified treatment of interfaces Journal of Computational Physics. 335: 828-845. DOI: 10.1016/J.Jcp.2017.01.065  0.506
2017 Bayona V, Flyer N, Fornberg B, Barnett GA. On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs Journal of Computational Physics. 332: 257-273. DOI: 10.1016/J.Jcp.2016.12.008  0.445
2017 Wright GB, Fornberg B. Stable computations with flat radial basis functions using vector-valued rational approximations Journal of Computational Physics. 331: 137-156. DOI: 10.1016/J.Jcp.2016.11.030  0.69
2017 Martin B, Fornberg B. Using radial basis function-generated finite differences (RBF-FD) to solve heat transfer equilibrium problems in domains with interfaces Engineering Analysis With Boundary Elements. 79: 38-48. DOI: 10.1016/J.Enganabound.2017.03.005  0.407
2016 Driscoll T, Townsend A, Berrut J, Fornberg B, Greenbaum A, Higham NJ, LeVeque R, Sloan IH. New Directions in Numerical Computation Notices of the American Mathematical Society. 63: 398-400. DOI: 10.1090/Noti1363  0.387
2016 Fornberg B. Fast calculation of Laurent expansions for matrix inverses Journal of Computational Physics. 326: 722-732. DOI: 10.1016/J.Jcp.2016.09.028  0.325
2016 Flyer N, Fornberg B, Bayona V, Barnett GA. On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy Journal of Computational Physics. 321: 21-38. DOI: 10.1016/J.Jcp.2016.05.026  0.469
2015 Martin B, Fornberg B, St-Cyr A. Seismic modeling with radial-basis-function-generated finite differences Geophysics. 80: T137-T146. DOI: 10.1190/Geo2014-0492.1  0.474
2015 Reeger JA, Fornberg B. Numerical Quadrature over the Surface of a Sphere Studies in Applied Mathematics. 137: 174-188. DOI: 10.1111/Sapm.12106  0.77
2015 Fornberg B, Flyer N. Solving PDEs with radial basis functions Acta Numerica. 24: 215-258. DOI: 10.1017/S0962492914000130  0.399
2015 Fornberg B, Weideman JAC. A computational overview of the solution space of the imaginary Painlevé II equation Physica D: Nonlinear Phenomena. 309: 108-118. DOI: 10.1016/J.Physd.2015.07.008  0.438
2015 Fornberg B, Flyer N. Fast generation of 2-D node distributions for mesh-free PDE discretizations Computers and Mathematics With Applications. 69: 531-544. DOI: 10.1016/J.Camwa.2015.01.009  0.376
2015 Ghrist ML, Fornberg B, Reeger JA. Stability ordinates of Adams predictor-corrector methods Bit Numerical Mathematics. 55: 733-750. DOI: 10.1007/S10543-014-0528-7  0.774
2015 Flyer N, Wright GB, Fornberg B. Radial basis function-generated finite differences: Amesh-free method for computational geosciences Handbook of Geomathematics: Second Edition. 2635-2669. DOI: 10.1007/978-3-642-54551-1_61  0.687
2014 Martin B, Fornberg B, St-Cyr A, Flyer N. Seismic modeling with radial basis function-generated finite differences (RBF-FD) Seg Technical Program Expanded Abstracts. DOI: 10.1190/Segam2014-0917.1  0.321
2014 Davis CIR, Fornberg B. A spectrally accurate numerical implementation of the Fokas transform method for Helmholtz-type PDEs Complex Variables and Elliptic Equations. 59: 564-577. DOI: 10.1080/17476933.2013.766883  0.459
2014 Reeger JA, Fornberg B. Painlevé IV: A numerical study of the fundamental domain and beyond Physica D: Nonlinear Phenomena. 280: 1-13. DOI: 10.1016/J.Physd.2014.04.006  0.8
2014 Monnig ND, Fornberg B, Meyer FG. Inverting nonlinear dimensionality reduction with scale-free radial basis function interpolation Applied and Computational Harmonic Analysis. 37: 162-170. DOI: 10.1016/J.Acha.2013.10.004  0.331
2014 Fornberg B, Martel JM. On spherical harmonics based numerical quadrature over the surface of a sphere Advances in Computational Mathematics. DOI: 10.1007/S10444-014-9346-3  0.363
2013 Larsson E, Lehto E, Heryudono A, Fornberg B. Stable computation of differentiation matrices and scattered node stencils based on gaussian radial basis functions Siam Journal On Scientific Computing. 35: A2096-A2119. DOI: 10.1137/120899108  0.509
2013 Reeger JA, Fornberg B. Painlevé IV with both Parameters Zero: A Numerical Study Studies in Applied Mathematics. 130: 108-133. DOI: 10.1111/J.1467-9590.2012.00564.X  0.797
2013 Fornberg B, Lehto E, Powell C. Stable calculation of Gaussian-based RBF-FD stencils Computers and Mathematics With Applications. 65: 627-637. DOI: 10.1016/J.Camwa.2012.11.006  0.474
2013 Fornberg B, Weideman JAC. A Computational Exploration of the Second Painlevé Equation Foundations of Computational Mathematics. 1-32. DOI: 10.1007/S10208-013-9156-X  0.441
2012 Ghrist M, Fornberg B. Two results concerning the stability of staggered multistep methods Siam Journal On Numerical Analysis. 50: 1849-1860. DOI: 10.1137/110837541  0.813
2011 Fornberg B. Finite difference method Scholarpedia. 6: 9685. DOI: 10.4249/Scholarpedia.9685  0.365
2011 Fornberg B, Larsson E, Flyer N. Stable computations with gaussian radial basis functions Siam Journal On Scientific Computing. 33: 869-892. DOI: 10.1137/09076756X  0.452
2011 Fornberg B, Flyer N. 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. 467: 2983-3003. DOI: 10.1098/Rspa.2011.0032  0.411
2011 Fornberg B, Weideman JAC. A numerical methodology for the Painlevé equations Journal of Computational Physics. 230: 5957-5973. DOI: 10.1016/J.Jcp.2011.04.007  0.44
2011 Fornberg B, Lehto E. Stabilization of RBF-generated finite difference methods for convective PDEs Journal of Computational Physics. 230: 2270-2285. DOI: 10.1016/J.Jcp.2010.12.014  0.411
2011 Flyer N, Fornberg B. Radial basis functions: Developments and applications to planetary scale flows Computers and Fluids. 46: 23-32. DOI: 10.1016/J.Compfluid.2010.08.005  0.44
2010 Fornberg B, Flyer N, Russell JM. Comparisons between pseudospectral and radial basis function derivative approximations Ima Journal of Numerical Analysis. 30: 149-172. DOI: 10.1093/Imanum/Drn064  0.507
2010 Nitsche M, Weidman PD, Grimshaw R, Ghrist M, Fornberg B. Evolution of solitary waves in a two-pycnocline system Journal of Fluid Mechanics. 642: 235-277. DOI: 10.1017/S0022112009991819  0.773
2010 Fornberg B. A finite difference method for free boundary problems Journal of Computational and Applied Mathematics. 233: 2831-2840. DOI: 10.1016/J.Cam.2009.11.028  0.355
2008 Fornberg B, Flyer N, Hovde S, Piret C. Locality properties of radial basis function expansion coefficients for equispaced interpolation Ima Journal of Numerical Analysis. 28: 121-142. DOI: 10.1093/Imanum/Drm014  0.775
2008 Elcrat AR, Fornberg B, Miller KG. Steady axisymmetric vortex flows with swirl and shear Journal of Fluid Mechanics. 613: 395-410. DOI: 10.1017/S002211200800342X  0.361
2008 Fornberg B, Piret C. On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere Journal of Computational Physics. 227: 2758-2780. DOI: 10.1016/J.Jcp.2007.11.016  0.799
2008 Xiong J, Colice M, Schlottau F, Wagner K, Fornberg B. Numerical solutions to 2D Maxwell-Bloch equations Optical and Quantum Electronics. 40: 447-453. DOI: 10.1007/S11082-008-9227-4  0.426
2007 Fornberg B, Piret C. A stable algorithm for flat radial basis functions on a sphere Siam Journal On Scientific Computing. 30: 60-80. DOI: 10.1137/060671991  0.794
2007 Fornberg B, Zuev J. The Runge phenomenon and spatially variable shape parameters in RBF interpolation Computers and Mathematics With Applications. 54: 379-398. DOI: 10.1016/J.Camwa.2007.01.028  0.763
2007 Fornberg B, Zuev J, Lee J. Stability and accuracy of time-extrapolated ADI-FDTD methods for solving wave equations Journal of Computational and Applied Mathematics. 200: 178-192. DOI: 10.1016/J.Cam.2005.12.012  0.78
2006 Fornberg B. A pseudospectral fictitious point method for high order initial-boundary value problems Siam Journal On Scientific Computing. 28: 1716-1729. DOI: 10.1137/040611252  0.449
2006 Wright GB, Fornberg B. Scattered node compact finite difference-type formulas generated from radial basis functions Journal of Computational Physics. 212: 99-123. DOI: 10.1016/J.Jcp.2005.05.030  0.65
2006 Fornberg B, Larsson E, Wright G. A new class of oscillatory radial basis functions Computers and Mathematics With Applications. 51: 1209-1222. DOI: 10.1016/J.Camwa.2006.04.004  0.66
2005 Elcrat AR, Fornberg B, Miller KG. Stability of vortices in equilibrium with a cylinder Journal of Fluid Mechanics. 544: 53-68. DOI: 10.1017/S0022112005006579  0.313
2005 Larsson E, Fornberg B. Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions Computers and Mathematics With Applications. 49: 103-130. DOI: 10.1016/J.Camwa.2005.01.010  0.413
2005 Åhlander K, Allen E, Aptekarev AI, Arioli M, Arnold M, Asadzadeh M, Baglama J, Bailly C, Baker C, Bartels S, Bendali A, Benzi M, Berntsson F, Breda D, Brunner H, ... ... Fornberg B, et al. BIT Numerical Mathematics: Editorial Bit Numerical Mathematics. 45: v-vi. DOI: 10.1007/S10543-005-0037-9  0.331
2005 Fornberg B, Flyer N. Accuracy of radial basis function interpolation and derivative approximations on 1-D infinite grids Advances in Computational Mathematics. 23: 5-20. DOI: 10.1007/S10444-004-1812-X  0.461
2004 Flyer N, Fornberg B. On the nature of initial-boundary value solutions for dispersive equations Siam Journal On Applied Mathematics. 64: 546-564. DOI: 10.1137/S0036139902415853  0.421
2004 Fornberg B, Wright G, Larsson E. Some Observations Regarding Interpolants in the Limit of Flat Radial Basis Functions Computers and Mathematics With Applications. 47: 37-55. DOI: 10.1016/S0898-1221(04)90004-1  0.65
2004 Fornberg B, Wright G. Stable computation of multiquadric interpolants for all values of the shape parameter Computers and Mathematics With Applications. 48: 853-867. DOI: 10.1016/J.Camwa.2003.08.010  0.674
2004 Lee J, Fornberg B. Some unconditionally stable time stepping methods for the 3D Maxwell's equations Journal of Computational and Applied Mathematics. 166: 497-523. DOI: 10.1016/J.Cam.2003.09.001  0.464
2003 Larsson E, Fornberg B. A numerical study of some radial basis function based solution methods for elliptic PDEs Computers and Mathematics With Applications. 46: 891-902. DOI: 10.1016/S0898-1221(03)90151-9  0.487
2003 Lee J, Fornberg B. A split step approach for the 3-D Maxwell's equations Journal of Computational and Applied Mathematics. 158: 485-505. DOI: 10.1016/S0377-0427(03)00484-9  0.448
2003 Flyer N, Fornberg B. Accurate numerical resolution of transients in initial-boundary value problems for the heat equation Journal of Computational Physics. 184: 526-539. DOI: 10.1016/S0021-9991(02)00034-7  0.448
2002 Fornberg B, Driscoll TA, Wright G, Charles R. Observations on the behavior of radial basis function approximations near boundaries Computers and Mathematics With Applications. 43: 473-490. DOI: 10.1016/S0898-1221(01)00299-1  0.666
2002 Driscoll TA, Fornberg B. Interpolation in the limit of increasingly flat radial basis functions Computers and Mathematics With Applications. 43: 413-422. DOI: 10.1016/S0898-1221(01)00295-4  0.444
2001 Ghrist M, Fornberg B, Driscoll TA. Staggered time integrators for wave equations Siam Journal On Numerical Analysis. 38: 718-741. DOI: 10.1137/S0036142999351777  0.805
2001 Driscoll TA, Fornberg B. A Padé-based algorithm for overcoming the Gibbs phenomenon Numerical Algorithms. 26: 77-92. DOI: 10.1023/A:1016648530648  0.441
2001 Elcrat A, Fornberg B, Miller K. Some steady axisymmetric vortex flows past a sphere Journal of Fluid Mechanics. 433: 315-328. DOI: 10.1017/S0022112001003469  0.329
2000 Fornberg B, Ghrist M. Spatial finite difference approximations for wave-type equations Siam Journal On Numerical Analysis. 37: 105-130. DOI: 10.1137/S0036142998335881  0.799
2000 Elcrat A, Fornberg B, Horn M, Miller K. Some steady vortex flows past a circular cylinder Journal of Fluid Mechanics. 409: 13-27. DOI: 10.1017/S0022112099007715  0.415
2000 Driscoll TA, Fornberg B. Note on Nonsymmetric Finite Differences for Maxwell's Equations Journal of Computational Physics. 161: 723-727. DOI: 10.1006/Jcph.2000.6524  0.497
1999 Driscoll TA, Fornberg B. Block pseudospectral methods for Maxwell's equations II: two-dimensional, discontinuous-coefficient case Siam Journal On Scientific Computing. 21: 1146-1167. DOI: 10.1137/S106482759833320X  0.443
1999 Elcrat A, Fornberg B, Miller K. Steady vortex flows obtained from a nonlinear eigenvalue problem Esaim: Proceedings. 7: 130-136. DOI: 10.1051/Proc:1999012  0.345
1999 Fornberg B, Driscoll TA. A Fast Spectral Algorithm for Nonlinear Wave Equations with Linear Dispersion Journal of Computational Physics. 155: 456-467. DOI: 10.1006/Jcph.1999.6351  0.491
1998 Fornberg B. Classroom Note: Calculation of Weights in Finite Difference Formulas Siam Review. 40: 685-691. DOI: 10.1137/S0036144596322507  0.351
1998 Wojcik G, Mould J, Carcione L, Fornberg B, Waag R, Ayter S. Large‐scale modeling of ultrasound transducer pulses in lossy, nonlinear tissue The Journal of the Acoustical Society of America. 104: 1843-1843. DOI: 10.1121/1.424432  0.399
1998 White BS, Fornberg B. On the chance of freak waves at sea Journal of Fluid Mechanics. 355: 113-138. DOI: 10.1017/S0022112097007751  0.346
1998 Driscoll TA, Fornberg B. A Block Pseudospectral Method for Maxwell's Equations: I. One-Dimensional Case Journal of Computational Physics. 140: 47-65. DOI: 10.1006/Jcph.1998.5883  0.487
1997 Larsen TB, Yuen DA, Moser J, Fornberg B. A high-order finite-difference method applied to large rayleigh number mantle convection Geophysical and Astrophysical Fluid Dynamics. 84: 53-83. DOI: 10.1080/03091929708208973  0.402
1997 Fornberg B, Merrill D. Comparison of finite difference- And pseudospectral methods for convective flow over a sphere Geophysical Research Letters. 24: 3245-3248. DOI: 10.1029/97Gl03272  0.391
1996 Natoli VD, Cohen MH, Fornberg B. A new numerical algorithm for the analytic continuation of Green's functions Journal of Computational Physics. 126: 99-108. DOI: 10.1006/Jcph.1996.0123  0.369
1995 Fornberg B. A pseudospectral approach for polar and spherical geometries Siam Journal On Scientific Computing. 16: 1071-1081. DOI: 10.1137/0916061  0.413
1995 Ming Li, Tao Tang, Fornberg B. A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations International Journal For Numerical Methods in Fluids. 20: 1137-1151. DOI: 10.1002/Fld.1650201003  0.453
1994 Fornberg B, Sloan DM. A review of pseudospectral methods for solving partial differential equations Acta Numerica. 3: 203-267. DOI: 10.1017/S0962492900002440  0.373
1993 Natarajan R, Fornberg B, Acrivos A. Flow past a row of flat plates at large Reynolds numbers Proceedings - Royal Society of London, A. 441: 211-235. DOI: 10.1098/Rspa.1993.0058  0.386
1992 Fornberg B, Meyer-Spasche R. A finite difference procedure for a class of free boundary problems Journal of Computational Physics. 102: 72-77. DOI: 10.1016/S0021-9991(05)80006-3  0.397
1991 Meyer-Spasche R, Fornberg B. Discretization errors at free boundaries of the Grad-Schlüter-Shafranov equation Numerische Mathematik. 59: 683-710. DOI: 10.1007/Bf01385804  0.4
1990 Fornberg B. High-Order Finite Differences and the Pseudospectral Method on Staggered Grids Siam Journal On Numerical Analysis. 27: 904-918. DOI: 10.1137/0727052  0.451
1990 Fornberg B. An improved pseudospectral method for initial-boundary value problems Journal of Computational Physics. 91: 381-397. DOI: 10.1016/0021-9991(90)90043-Z  0.421
1989 Fornberg B. Pseudospectral Approximation of the Elastic Wave Equation On a Staggered Grid Seg Technical Program Expanded Abstracts. 1047-1049. DOI: 10.1190/1.1889877  0.42
1988 Fornberg B. The pseudospectral method: Accurate representation of interfaces in elastic wave calculations Geophysics. 53: 625-637. DOI: 10.1190/1.1442497  0.418
1988 Fornberg B. Generation of finite difference formulas on arbitrarily spaced grids Mathematics of Computation. 51: 699-706. DOI: 10.1090/S0025-5718-1988-0935077-0  0.383
1987 Fornberg B. The pseudospectral method: Comparisons with finite differences for the elastic wave equation Geophysics. 52: 483-501. DOI: 10.1190/1.1892921  0.456
1985 Fornberg B. Steady viscous flow past a circular cylinder up to reynolds number 600 Journal of Computational Physics. 61: 297-320. DOI: 10.1016/0021-9991(85)90089-0  0.325
1984 Fornberg B. A Numerical Method for Conformal Mapping of Doubly Connected Regions Siam Journal On Scientific and Statistical Computing. 5: 771-783. DOI: 10.1137/0905055  0.318
1982 Caponi EA, McLean JW, Yuen HC, Fornberg B, Saffman PG, Knight DD. CALCULATIONS OF LAMINAR VISCOUS FLOW OVER A MOVING WAVY SURFACE Proceedings of the U.S. National Congress of Applied Mechanics. 465. DOI: 10.1017/S0022112082002535  0.377
1981 Fornberg B. Algorithm 579: CPSC: Complex Power Series Coefficients [D4] Acm Transactions On Mathematical Software (Toms). 7: 542-547. DOI: 10.1145/355972.355982  0.346
1981 Fornberg B. Numerical Differentiation of Analytic Functions Acm Transactions On Mathematical Software (Toms). 7: 512-526. DOI: 10.1145/355972.355979  0.343
1980 Fornberg B. A Numerical Method for Conformal Mappings Siam Journal On Scientific and Statistical Computing. 1: 386-400. DOI: 10.1137/0901027  0.372
1980 Fornberg B. A numerical study of steady viscous flow past a circular cylinder Journal of Fluid Mechanics. 98: 819-855. DOI: 10.1017/S0022112080000419  0.367
1978 Fornberg B, Whitham GB. A numerical and theoretical study of certain nonlinear wave phenomena Philos. Trans. R. Soc. A. 289: 373-404. DOI: 10.1098/Rsta.1978.0064  0.43
1977 Fornberg B. A numerical study of 2-D turbulence Journal of Computational Physics. 25: 1-31. DOI: 10.1016/0021-9991(77)90023-7  0.314
1975 Fornberg B. On a Fourier Method for the Integration of Hyperbolic Equations Siam Journal On Numerical Analysis. 12: 509-528. DOI: 10.1137/0712040  0.462
1973 Fornberg B. On the instability of leap-frog and crank-nicolson approximations of a nonlinear partial differential equation Mathematics of Computation. 27: 45-57. DOI: 10.1090/S0025-5718-1973-0395249-2  0.416
1969 Beckman A, Fornberg B, Tengvald A. A method for acceleration of the convergence of infinite series Bit. 9: 78-80. DOI: 10.1007/Bf01933541  0.396
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