Holger Wendland's
Publications

Check out my citation index.

Books

Numerical Linear Algebra
 
scattered data approximation
 
numerische Mathematik

Papers

    Preprints

  1. (with S. De Marchi) On the Convergence of the Rescaled Localized Radial Basis Function Method, Preprint Bayreuth/Padova 2019.
  2. (with J. Künemund) Solving partial differential equations on (evolving) surfaces, Preprint Bayreuth 2019.
  3. (with C. Rieger) Sampling inequalities for anisotropic tensor product grids, Preprint Bayreuth/Bonn 2018, to appear in IMA Journal of Numerical Analysis

    4. 2019

  4. (with R. Kempf, C. Rieger) Kernel-based reconstruction for parametric PDEs, in: M. Griebel, M. A. Schweitzer (eds.) Meshfree Methods for Partial Differential Equations IX , Springer, Cham, 2019, 53 - 71.
  5. (with P. Giesl), Construction of a contraction metric by meshless collocation, Discrete & Continuous Dynamical Systems - B 24 (2019), 3843-3863.
  6. (with J. Künemund, F. Narcowich, J. Ward) A high-order meshless Galerkin method for semilinear parabolic equations on spheres, Numerische Mathematik 142 (2019), 383-419.

    7. 2018

  7. (with P. Giesl), Kernel-based discretisation for solving matrix-valued PDEs, SIAM Journal on Numerical Analysis 56 (2018), 3386-3406.
  8. (with C. Argaez, S. Hafstein and P. Giesl) Construction of a complete Lyapunov function using quadratic programming, in: K. Madani, O. Gusikhin (eds.) Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1, SciTePress, 2018, 560-568.
  9. (with T. Franz), Convergence of the smoothed particle hydrodynamics method for a specific barotropic fluid flow: Constructive kernel theory, SIAM Journal on Mathematical Analysis 50 (2018), 4752-4784.
  10. Solving partial differential equations with multiscale radial basis functions, in: J. Dick, F. Kuo, H. Wozniakowski (eds.) Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, Springer, Cham 2018, 1191-1213.
  11. (with T. Ramming), A kernel-based discretisation method for first order partial differential equations, Mathematics of Computation 87 (2018), 1757-1781.

    12. 2017

  12. Multiscale radial basis functions, in: I. Pesenson et al. (eds.), Frames and Other Bases in Abstract and Function Spaces - Novel Methods in Harmonic Analysis, Volume 1, Birkhäuser, Cham, 2017, 265-299.
  13. (with C. Rieger), Sampling inequalities for sparse grids, Numer. Math. 136 (2017), 439 - 466.
  14. (with Q. T. Le Gia, I. H. Sloan), Zooming from Global to Local: A Multiscale RBF Approach, Adv. Comput. Math. 43 (2017), 581-606.
  15. (with P. Farrell, K. Gillow), Multilevel Interpolation of Divergence-Free Vector Fields, IMA Journal of Numerical Analysis 37 (2017), 332-353.

    16. 2016

  16. (with C. Keim), A High-order, analytically divergence-free approximation method for the time-dependent Stokes problem, SIAM Journal on Numerical Analysis 54 (2016), 1288-1312.

    17. 2014

  17. (with Q. T. Le Gia), Data compression on the sphere using multiscale radial basis functions, Advances in Computational Mathematics 40 (2014), 923-943.

    18. 2013

  18. (with P. Farrell), RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems, SIAM Journal on Numerical Analysis, 51 (2013), 2403-2425.
  19. (with A. Townsend), Multiscale analysis in Sobolev spaces on bounded domains with zero boundary values, IMA Journal of Numerical Analysis 33 (2013), 1095-1114.
  20. A high-order approximation method for semilinear parabolic equations on spheres, Mathematics of Computation 82 (2013), 227 - 245.

    21. 2012

  21. (with D. Schräder), An extended error analysis for a meshfree discretization method of Darcy's problem, SIAM Journal on Numerical Analysis 50 (2012), 838-857.
  22. (with Q. T. Le Gia, I. H. Sloan), Multiscale approximation for functions in arbitrary Sobolev spaces by scaled radial basis functions on the unit sphere, Applied and Computational Harmonic Analysis 32 (2012), 401-412.
  23. (with Q. T. Le Gia, I. H. Sloan), Multiscale RBF collocation for solving PDEs on spheres, Numerische Mathematik 121 (2012), 99-125.
  24. (with P. Giesl), Numerical determination of the basin of attraction of asymptotically autonomous dynamical systems, Nonlinear Analysis 75 (2012), 2823-2840.
  25. with (M. Rütten), Performance Enhancement of Auxiliary Air Intakes by Using Vortex Generators, 50th AIAA Aerospace Science Meeting Fluid Dynamics Conference, 09. - 12. Jan. 2012, Nashville, Tennesee, USA, 2012.

    26. 2011

  26. (with Peter Giesl) Numerical determination of the basin of attraction for exponentially asymptotically autonomous dynamical systems, Nonlinear Analysis 74 (2011), 3191-3202.
  27. (with Daniela Schräder) A high-order, analytically divergence-free discretization method for Darcy's problem, Mathematics of Computation 80 (2011), 263-277.

    28. 2010

  28. (with Q. Thong Le Gia and Ian H. Sloan) Multiscale analysis in Sobolev spaces on the sphere, SIAM Journal on Numerical Analysis 48 (2010), 2065-2090.
  29. Multiscale analysis in Sobolev spaces on bounded domains, Numerische Mathematik 116 (2010), 493-517.

    30. 2009

  30. (with Jochen Krebs and Alfred K. Louis) Sobolev error estimates and a priori parameter selection for semi-discrete Tikhonov regularization, Journal of Inverse and Ill-Posed Problems 17 (2009), 845-869.
  31. (with Ian H. Sloan) Inf-sup conditions for spherical polynomials and radial basis functions on spheres, Math. Comp.78 (2009), 1319-1331.
  32. Divergence-free kernel methods for approximating the Stokes problem, SIAM Journal on Numerical Analysis 47 (2009), 3158-3179.
  33. (with Peter Giesl) Approximating the basin of attraction of time-periodic ODEs by meshless collocation, Discrete and Continuous Dynamical Systems, Series A, 25 (2009), 1249 - 1274.
  34. (with Peter Giesl) Approximating the basin of attraction of time-periodic ODEs by meshless collocation of a Cauchy problem, Discrete and Continuous Dynamical Systems, Supplements (2009), 259-268.

    35. 2008

  35. Hybrid methods for fluid-structure-interaction problems in Aeroelasticity, in: M. Griebel, M. A. Schweitzer (eds.) Meshfree Methods for Partial Differential Equations IV, 335-358, Springer, Berlin, 2008.
  36. (with Markus Rütten and Thomas Alrutz) A Vortex axis and vortex core border grid adaptation algorithm, International Journal for Numerical Methods in Fluids 58 (2008), 1379-1405.
  37. (with Nira Dyn and Armin Iske) Meshfree thinning of 3d point clouds, J. Foundations of Computational Mathematics 8 (2008), 409-425.

    38. 2007

  38. (with Peter Giesl) Meshless Collocation: Error estimates with application to dynamical systems, SIAM Journal on Numerical Analysis 45 (2007), 1723-1741.
  39. On the stability of meshless symmetric collocation for boundary value problems, BIT Numerical Mathematics 47 (2007), 455-468.
  40. (with Regine Ahrem and Armin Beckert) Recovering rotations in aeroelasticity, Journal of Fluid and Structures 23 (2007), 874-884.
  41. (with Francis J. Narcowich, Xinping Sun, and Joseph D. Ward) Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions, J. Foundations of Computational Mathematics 7 (2007), 369-390.

    42. 2006

  42. Spatial coupling in Aeroelasticity by meshless kernel-based methods, in: P. Wesseling, E. Onate, J. Periaux (eds.), Proceedings to ECCOMAS CFD 2006, Egmond aan Zee, The Netherlands.
  43. (with Quoc Le Gia, Francis J. Narcowich, and Joseph D. Ward) Continuous and discrete least-squares approximation by basis functions on spheres, Journal of Approximation Theory 143 (2006), 124-133.
  44. (with Robert Schaback) Kernel techniques: From machine learning to meshless methods, Acta Numerica 15 (2006), 543-639.
  45. (with Regine Ahrem and Armin Beckert) A meshless spatial coupling scheme for large-scale fluid-structure-interaction problems, Computer Modeling in Engineering and Sciences 12 (2006), 121-136.
  46. (with Francis J. Narcowich and Joseph D. Ward) Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions, Constructive Approximation 24 (2006), 175--186.

    47. 2005

  47. (with Regine Ahrem and Armin Beckert) A new multivariate interpolation method for large-scale spatial coupling problems in aeroelasticity, Conference Proceedings to the International Forum on Aeroelasticity and Structural Dynamics (IFASD), Munich 2005, DGLR-Bericht 2005-04, ISBN 3-932-182-43-X.
  48. (with Christian Rieger) Approximate interpolation with applications to selecting smoothing parameters, Numerische Mathematik 101 (2005), 643-662.
  49. Computational aspects of radial basis function approximation, in K. Jetter et al. (eds.) Topics in Multivariate Approximation and Interpolation , Elsevier B.V., 2005, 231-256.
  50. On the convergence of a general class of finite volume methods, SIAM J. Numerical Analysis 43 (2005), 987-1002,
  51. (with Stefano De Marchi and Robert Schaback) Near-optimal data-independent point locations for radial basis function interpolation, Advances in Computational Mathematics 23 (2005), 317-330.
  52. (with Francis J. Narcowich and Joseph D. Ward) Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting, Mathematics of Computation 74 (2005), 743-763.

    53. 2004

  53. Solving large generalized interpolation problems efficiently, in M. Neamtu, E. B. Saff (eds.), Advances in Constructive Approximation , Nashboro Press, Brentwood, TN, 2004.

    54. 2003

  54. Reconstructing multivariate functions from large data sets, in W. Haussmann, K. Jetter, M. Reimer, Modern Developments in Multivariate Approximation, ISNM 145, Birkhäuser Verlag, Basel, 2003, 295-308.
  55. (with Francis J. Narcowich and Joseph D. Ward) Refined error estimates for radial basis function interpolation, Constructive Approximation 19 (2003), 541-564.

    56. 2002

  56. (with Robert Schaback) Approximation by positive definite kernels, in: M. D. Buhmann and D. H. Mache, Advanced Problems in Constructive Approximation, Birkhäuser Verlag, Basel, 2002, 203-221.
  57. Fast evaluation of radial basis functions: Methods based on partition of unity, in: C. K. Chui, L. L. Schumaker, and J. Stöckler (eds), Approximation Theory X: Wavelets, Splines, and Applications, Vanderbilt University Press, Nashville, 2002, 473-483.
  58. (with Robert Schaback) Inverse and saturation theorems for radial basis function interpolation, Mathematics of Computation 71 (2002), 669-681.

    59. 2001

  59. Gaussian interpolation revisited, in: K. Kopotun, T. Lyche, and M. Neamtu (eds.), Trends in Approximation Theory , Vanderbilt University Press, Nashville, 2001, 427-436.
  60. Moving least squares approximation on the sphere, in: T. Lyche and L. L. Schumaker (eds.), Mathematical Methods in CAGD: Oslo 2000, Vanderbilt University Press, Nashville, 2001, 517-526.
  61. (with Armin Beckert) Multivariate interpolation for fluid-structure-interpolation problems using radial basis functions, Aerosp. Sci. Technol 5 (2001), 125-134.
  62. (with Robert Schaback) Characterization and construction of radial basis functions, in N. Dyn, D. Leviatan, D. Levin and A. Pinkus (eds), Multivariate Approximation and Applications , Cambridge University Press, Cambridge, 2001.
  63. Local polynomial reproduction and moving least squares approximation, IMA Journal of Numerical Analysis 21 (2001), 285-300.

    64. 2000

  64. (with Robert Schaback) Numerical Techniques based on radial basis functions, in A. Cohen, C. Rabut, and L. L. Schumaker (eds.), Curve and Surface Fitting: Saint-Malo 1999, 359-374, Vanderbilt University Press, Nashville, TN, 2000.
  65. (with Robert Schaback) Adaptive greedy techniques for approximate solution of large rbf systems, Numerical Algorithms 24 (2000), 239-254.
  66. Optimal approximation orders in Lp for radial basis functions, East Journal on Approximations 6 (2000), 87-102.

    67. before 2000

  67. (with Robert Schaback) Using compactly supported radial basis functions to solve partial differential equations, in: C.S. Chen, C.A. Brebbia and D.W. Pepper (eds.), Boundary Element Technology XIII, WitPress, Southampton, Boston, 1999, 311-324.
  68. On the smoothness of positive definite and radial functions, Journal of Computational and Applied Mathematics 101 (1999), 177-188.
  69. Meshless Galerkin methods using radial basis functions, Mathematics of Computation 68 (1999), 1521-1531.
  70. Numerical solution of variational problems by radial basis functions, C. K. Chui and L. L. Schumaker (eds.), Approximation Theory IX, Volume 2: Computational Aspects, Vanderbilt University Press, Nashville, TN, 1998, 361-368.
  71. Error estimates for interpolation by compactly supported radial basis functions of minimal degree, Journal of Approximation Theory 93 (1998), 258-272.
  72. Sobolev-type error estimates for interpolation by radial basis functions, in: A. LeMéhauté, C. Rabut, and L.L. Schumaker (eds.), Surface Fitting and Multiresolution Methods , 337-344, Vanderbilt University Press, Nashville, TN, 1997.
  73. Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree, Advances in Computational Mathematics 4 (1995), 389-396.