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Fakultät für Mathematik, Physik und Informatik

Lehrstuhl für Angewandte und Numerische Analysis - Prof. Dr. Holger Wendland

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Publikationen

Buch/Monografien

Holger Wendland: Numerical Linear Algebra : An Introduction. - Cambridge : Cambridge University Press, 2017. - X, 408 S.
doi:10.1017/9781316544938

Holger Wendland: Scattered Data Approximation. - Cambridge : Cambridge University Press, 2010. - X, 336 S.

Holger Wendland: Scattered data approximation. - Cambridge : Cambridge University Press, 2005. - X, 336 S.

Robert Schaback, Holger Wendland: Numerische Mathematik. - Berlin : Springer, 2005.
doi:10.1007/b137970

Artikel in einer Zeitschrift (begutachtet)

Jens Künemund, Francis J. Narcowich, Joseph D. Ward, Holger Wendland: A high-order meshless Galerkin method for semilinear parabolic equations on spheres. In: Numerische Mathematik, 142 (2019). - S. 383-419.
doi:10.1007/s00211-018-01021-7

Peter Giesl, Holger Wendland: Construction of a contraction metric by meshless collocation. In: Discrete and Continuous Dynamical Systems. Series B, 24 (2019). - S. 3843-3863.
doi:10.3934/dcdsb.2018333

Tino Franz, Holger Wendland: Convergence of the smoothed particle hydrodynamics method for a specific barotropic fluid flow : Constructive kernel theory. In: SIAM Journal on Mathematical Analysis, 50 (2018). - S. 4752-4784.
doi:10.1137/17M1157696

Peter Giesl, Holger Wendland: Kernel-based discretization for solving matrix-valued PDEs. In: SIAM Journal on Numerical Analysis, 56 (2018). - S. 3386-3406.
doi:10.1137/16M1092842

Tobias Ramming, Holger Wendland: A kernel-based discretisation method for first order partial differential equations. In: Mathematics of Computation, 87 (2018). - S. 1757-1781.
doi:10.1090/mcom/3265

Christian Rieger, Holger Wendland: Sampling inequalities for sparse grids. In: Numerische Mathematik, 136 (2017). - S. 439-466.
doi:10.1007/s00211-016-0845-7

Q. T. Le Gia, I. H. Sloan, Holger Wendland: Zooming from Global to Local : A Multiscale RBF Approach. In: Advances in Computational Mathematics, 43 (2017). - S. 581-606.
doi:10.1007/s10444-016-9498-4

Patricio Farrell, Kathryn Gillow, Holger Wendland: Multilevel Interpolation of Divergence-Free Vector Fields. In: IMA Journal of Numerical Analysis, 37 (2017). - S. 332-353.
doi:10.1093/imanum/drw006

Christopher Keim, Holger Wendland: A High-order, analytically divergence-free approximation method for the time-dependent Stokes problem. In: SIAM Journal on Numerical Analysis, 54 (2016). - S. 1288-1312.
doi:10.1137/151006196

Q. T. Le Gia, Holger Wendland: Data compression on the sphere using multiscale radial basis function approximation. In: Advances in Computational Mathematics, 40 (2014). - S. 923-943.
doi:10.1007/s10444-013-9334-z

Patricio Farrell, Holger Wendland: RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems. In: SIAM Journal on Numerical Analysis, 51 (2013). - S. 2403-2425.
doi:10.1137/120898383

Alex Townsend, Holger Wendland: Multiscale analysis in Sobolev spaces on bounded domains with zero boundary values. In: IMA Journal of Numerical Analysis, 33 (2013). - S. 1095-1114.
doi:10.1093/imanum/drs036

Holger Wendland: A high-order approximation method for semilinear parabolic equations on spheres. In: Mathematics of Computation, 82 (2013). - S. 227-245.
doi:10.1090/S0025-5718-2012-02623-8

Q. T. Le Gia, I. H. Sloan, Holger Wendland: Multiscale RBF collocation for solving PDEs on spheres. In: Numerische Mathematik, 121 (2012). - S. 99-125.
doi:10.1007/s00211-011-0428-6

Q. T. Le Gia, I. H. Sloan, Holger Wendland: Multiscale approximation for functions in arbitrary Sobolev spaces by scaled radial basis functions on the unit sphere. In: Applied and Computational Harmonic Analysis, 32 (2012). - S. 401-412.
doi:10.1016/j.acha.2011.07.007

Holger Wendland, Peter Giesl: Numerical determination of the basin of attraction of asymptotically autonomous dynamical systems. In: Nonlinear Analysis : Theory, Methods & Applications, 75 (2012). - S. 2823-2840.
doi:10.1016/j.na.2011.11.027

Daniela Schräder, Holger Wendland: An extended error analysis for a meshfree discretization method of Darcy's problem. In: SIAM Journal on Numerical Analysis, 50 (2012). - S. 838-857.
doi:10.1137/100806461

Holger Wendland, Peter Giesl: Numerical determination of the basin of attraction for exponentially asymptotically autonomous dynamical systems. In: Nonlinear Analysis : Theory, Methods & Applications, 74 (2011). - S. 3191-3202.
doi:10.1016/j.na.2011.01.032

Daniela Schräder, Holger Wendland: A high-order, analytically divergence-free discretization method for Darcy's problem. In: Mathematics of Computation, 80 (2011). - S. 263-277.
doi:10.1090/S0025-5718-2010-02388-9

Holger Wendland: Multiscale analysis of Sobolev spaces on bounded domains. In: Numerische Mathematik, 116 (2010). - S. 493-517.
doi:10.1007/s00211-010-0313-8

Holger Wendland, Quoc T. Le Gia, Ian H. Sloan: Multiscale analysis in Sobolev spaces on the sphere. In: SIAM Journal on Numerical Analysis, 48 (2010). - S. 2065-2090.
doi:10.1137/090774550

Peter Giesl, Holger Wendland: Approximating the basin of attraction of time-periodic ODEs by meshless collocation. In: Discrete and Continuous Dynamical Systems. Series A, 25 (2009). - S. 1249-1274.
doi:10.3934/dcds.2009.25.1249

Peter Giesl, Holger Wendland: Approximating the basin of attraction of time-periodic ODEs by meshless collocation of a Cauchy problem. In: Discrete and Continuous Dynamical Systems. Series A, (2009). - S. 259-268.

Holger Wendland, Jochen Krebs, Alfred K. Louis: Sobolev error estimates and a priori parameter selection for semi-discrete Tikhonov regularization. In: Journal of Inverse and ILL-Posed Problems, 17 (2009). - S. 845-869.
doi:10.1515/JIIP.2009.050

Ian H. Sloan, Holger Wendland: Inf-sup condition for spherical polynomials and radial basis functions on spheres. In: Mathematics of Computation, 78 (2009). - S. 1319-1331.
doi:10.1090/S0025-5718-09-02207-8

Holger Wendland: Divergence-free kernel methods for approximating the Stokes problem. In: SIAM Journal on Numerical Analysis, 47 (2009). - S. 3158-3179.
doi:10.1137/080730299

Markus Rütten, Thomas Alrutz, Holger Wendland: A Vortex axis and vortex core border grid adaptation algorithm. In: International Journal for Numerical Methods in Fluids, 58 (2008). - S. 1379-1405.
doi:10.1002/fld.1792

Nira Dyn, Armin Iske, Holger Wendland: Meshfree thinning of 3D point clouds. In: Foundations of Computational Mathematics, 8 (2008). - S. 409-425.
doi:10.1007/s10208-007-9008-7

Regina Ahrem, Armin Beckert, Holger Wendland: Recovering rotations in aeroelasticity. In: Journal of Fluids and Structures, 23 (2007). - S. 874-884.
doi:10.1016/j.jfluidstructs.2007.02.003

Holger Wendland: On the stability of meshless symmetric collocation for boundary value problems. In: BIT Numerical Mathematics, 47 (2007). - S. 455-468.
doi:10.1007/s10543-007-0121-4

Peter Giesl, Holger Wendland: Meshless collocation : error estimates with application to dynamical systems. In: SIAM Journal Numerical Analysis, 45 (2007). - S. 1723-1741.
doi:10.1137/060658813

Francis J. Narcowich, Xingping Sun, Joseph D. Ward, Holger Wendland: Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions. In: Foundations of Computational Mathematics, 7 (2007). - S. 369-390.
doi:10.1007/s10208-005-0197-7

Quoc T. Le Gia, Francis J. Narcowich, Joseph D. Ward, Holger Wendland: Continuous and discrete least-squares approximation by basis functions on spheres. In: Journal of Approximation Theory, 143 (2006). - S. 124-133.
doi:10.1016/j.jat.2006.03.007

Francis J. Narcowich, Joseph D. Ward, Holger Wendland: Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions. In: Constructive Approximation, 24 (2006). - S. 175-186.
doi:10.1007/s00365-005-0624-7

Regine Ahrem, Armin Beckert, Holger Wendland: A meshless spatial coupling scheme for large-scale fluid-structure-interaction problems. In: Computer Modeling in Engineering and Sciences, 12 (2006). - S. 121-136.
doi:10.3970/cmes.2006.012.121

Robert Schaback, Holger Wendland: Kernel techniques : from machine learning to meshless methods. In: Acta Numerica, 15 (2006). - S. 543-639.
doi:10.1017/S0962492906270016

Stefano de Marchi, Robert Schaback, Holger Wendland: Near-optimal data-independent point locations for radial basis function interpolation. In: Advances in Computational Mathematics, 23 (2005). - S. 317-330.
doi:10.1007/s10444-004-1829-1

Holger Wendland, Christian Rieger: Approximate interpolation with applications to selecting smoothing parameters. In: Numerische Mathematik, 101 (2005). - S. 729-748.
doi:10.1007/s00211-005-0637-y

Francis J. Narcowich, Joseph D. Ward, Holger Wendland: Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting. In: Mathematics of Computation, 74 (2005). - S. 743-763.
doi:10.1090/S0025-5718-04-01708-9

Holger Wendland: On the convergence of a general class of finite volume methods. In: SIAM Journal on Numerical Analysis, 43 (2005). - S. 987-1002.
doi:10.1137/040612993

Francis J. Narcowich, Joseph D. Ward, Holger Wendland: Refined error estimates for radial basis function interpolation. In: Constructive Approximation, 19 (2003). - S. 541-564.
doi:10.1007/s00365-002-0529-7

Robert Schaback, Holger Wendland: Inverse and saturation theorems for radial basis function interpolation. In: Mathematics of Computation, 71 (2002). - S. 669-681.
doi:10.1090/S0025-5718-01-01383-7

Armin Beckert, Holger Wendland: Multivariate interpolation for fluid-structure-interaction problems using radial basis functions. In: Aerospace Science and Technology, 5 (2001). - S. 125-134.
doi:10.1016/S1270-9638(00)01087-7

Holger Wendland: Local polynomial reproduction and moving least squares approximation. In: IMA Journal of Numerical Analysis, 21 (2001). - S. 285-300.
doi:10.1093/imanum/21.1.285

Robert Schaback, Holger Wendland: Adaptive greedy techniques for approximate solution of large RBF systems. In: Numerical Algorithms, 24 (2000). - S. 239-254.
doi:10.1023/A:1019105612985

Holger Wendland: Optimal approximation orders in Lp for radial basis functions. In: East Journal on Approximations, 6 (2000). - S. 87-102.

Holger Wendland: On the smoothness of positive definite and radial functions. In: Journal of Computational and Applied Mathematics, 101 (1999). - S. 177-188.
doi:10.1016/S0377-0427(98)00218-0

Holger Wendland: Meshless Galerkin methods using radial basis functions. In: Mathematics of Computation, 68 (1999). - S. 1521-1531.
doi:10.1090/S0025-5718-99-01102-3

Holger Wendland: Error estimates for interpolation by compactly supported radial basis functions of minimal degree. In: Journal of Approximation Theory, 93 (1998). - S. 258-272.
doi:10.1006/jath.1997.3137

Holger Wendland: Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree. In: Advances in Computational Mathematics, 4 (1995). - S. 389-396.
doi:10.1007/BF02123482

Aufsätze in einem Buch (begutachtet)

Rüdiger Kempf, Holger Wendland, Christian Rieger: Kernel-based reconstructions for parametric PDEs. In: Michael Griebel, Marc Alexander Schweitzer (Hrsg.): Meshfree Methods for Partial Differential Equations IX. - Cham : Springer, 2019. - S. 53-71.
doi:10.1007/978-3-030-15119-5_4

Peter Giesl, Carlos Argáez, Sigurdur Hafstein, Holger Wendland: Construction of a complete Lyapunov function using quadratic programming. In: Kurosh Madani, Oleg Gusikhin (Hrsg.): ICINCO 2018 : Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics. Volume 1. - Setúbal : SciTePress, 2018. - S. 560-568.

Holger Wendland: Solving partial differential equations with multiscale radial basis functions. In: Josef Dick, Frances Y. Kuo, Henryk Wozniakowski (Hrsg.): Contemporary Computational Mathematics : A Celebration of the 80th Birthday of Ian Sloan. - Cham : Springer, 2018. - S. 1191-1213.
doi:10.1007/978-3-319-72456-0_55

Holger Wendland: Multiscale radial basis functions. In: Isaac Pesenson (Hrsg.): Frames and Other Bases in Abstract and Function Spaces : Novel Methods in Harmonic Analysis. Volume 1. - Cham : Birkhäuser, 2017. - S. 265-299.
doi:10.1007/978-3-319-55550-8_12

Holger Wendland, Markus Rütten: Performance Enhancement of Auxiliary Air Intakes by Using Vortex Generators. In: 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. - S.l. : 2012.
doi:10.2514/6.2012-57

Holger Wendland: Hybrid methods for fluid-structure-interaction problems in Aeroelasticity. In: Michael Griebel, Marc A. Schweitzer (Hrsg.): Meshfree Methods for Partial Differential Equations IV. - Berlin : Springer, 2008. - S. 335-358.

Holger Wendland: Spatial coupling in Aeroelasticity by meshless kernel-based methods. In: Peter Wesseling, Eugenio Oñate, Jacques. Périaux (Hrsg.): Proceedings ECCOMAS CFD 2006 : European Conference on Computational Fluid Dynamics. - Delft : Univ. of Technology, 2006.

Holger Wendland: Computational aspects of radial basis function approximation. In: Kurt Jetter (Hrsg.): Topics in multivariate approximation and interpolation. - Amsterdam : Elsevier, 2006. - S. 231-256.
doi:10.1016/S1570-579X(06)80010-8

R. Ahrem, Armin Beckert, Holger Wendland: A new multivariate interpolation method for large-scale spatial coupling problems in aeroelasticity. In: Conference Proceedings : Vorträge ; [München, June 28 - July 1, 2005]. - Bonn : DGLR, 2005.

Holger Wendland: Spatial coupling in Aeroelasticity by meshless kernel-based methods. In: Marian Neamtu, Edward B. Saff (Hrsg.): Advances in Constructive Approximation : Vanderbilt 2003. - Brentwood, USA : Nashboro Press, 2004.

Holger Wendland: Reconstructing multivariate functions from large data sets. In: Werner Haußmann (Hrsg.): Modern developments in multivariate approximation : 5th International Conference, Witten-Bommerholz (Germany), September, 2002. - Basel : Birkhäuser, 2003. - S. 295-308.

Holger Wendland: Fast evaluation of radial basis functions : methods based on partition of unity. In: Charles K. Chui (Hrsg.): Approximation theory X : [selections of papers that were presented at the Tenth International Conference on Approximation Theory, held in St. Louis, Missouri, in March 2001]. - Nashville, Tn : Vanderbilt Univ. Press, 2002. - S. 473-483.

Holger Wendland, Robert Schaback: Approximation by positive definite kernels. In: Martin D. Buhmann, Detlef H. Mache (Hrsg.): Advanced Problems in Constructive Approximation. - Basel : Birkhäuser, 2002. - S. 203-221.

Holger Wendland: Moving least squares approximation on the sphere. In: Tom Lyche, Larry L. Schumaker (Hrsg.): Mathematical methods for curves and surfaces : Oslo 2000. - Nashville : Vanderbilt Univ. Press, 2001. - S. 517-526.

Holger Wendland: Gaussian interpolation revisited. In: Trends in approximation theory 2000 : Vanderbild University, Nashville. - Nashville : Vanderbilt Univ. Press, Nashville, TN, 2001. - S. 417-426.

Holger Wendland, Robert Schaback: Characterization and construction of radial basis functions. In: Nira Dyn, D. Leviatan, D. Levin, A. Pinkus (Hrsg.): Multivariate Approximation and Applications. - Cambridge : Cambridge Univ. Press, 2001. - S. 1-24.

Robert Schaback, Holger Wendland: Numerical techniques based on radial basis functions. In: Albert Cohen, Christophe Rabut, Larry L. Schumaker (Hrsg.): Curve and surface fitting : Saint-Malo 99. - Nashville : Vanderbilt Univ. Press, 2000. - S. 359-374.

Robert Schaback, Holger Wendland: Using compactly supported radial basis functions to solve partial differential equations. In: C. S. Chen, C. A. Brebbia, D. W. Pepper (Hrsg.): Boundary Element Technology XIII : Incorporating Computational Methods and Testing for Engineering Integrity. - Southampton, USA : WIT Press, 1999. - S. 311-324.

Holger Wendland: Numerical solution of variational problems by radial basis functions. In: Charles K. Chui, Larry L. Schumaker (Hrsg.): Approximation Theory IX. Volume 2. Computational Aspects. - Nashville, USA : Vanderbilt Univ. Press, 1998. - S. 361-368.

Holger Wendland: Sobolev-type error estimates for interpolation by radial basis functions. In: Alan Le Méhauté, Christophe Rabut, Larry L. Schumaker (Hrsg.): Surface Fitting and Multiresolution Methods : Papers from the Third International Conference on Curves and Surfaces. Volume 2. - Nashville, USA : Vanderbilt Univ. Press, 1997. - S. 337-344.

Preprint

Holger Wendland, Jens Künemund: Solving partial differential equations on (evolving) surfaces.. - Bayreuth, 2019. -

Holger Wendland, S. de Marchi: On the Convergence of the Rescaled Localized Radial Basis Function Method.. - Bayreuth ; Padova, 2019. -

Holger Wendland, Christian Rieger: Sampling inequalities for anisotropic tensor product grids.. - Bayreuth ; Bonn, 2018. -

Dissertationen

Tino Franz:Convergence of the Smoothed Particle Hydrodynamics Method for Barotropic Flows : Constructive Kernel Theory. - Bayreuth: 2020. - 146 S.
(Dissertation, 2020, Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)
doi:10.15495/EPub_UBT_00004969

Jens Künemund:Numerische Lösung partieller Differentialgleichungen auf veränderlichen Oberflächen mit kernbasierten Verfahren. - Bayreuth: 2018.
(Dissertation, 2018, Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)

Christopher Keim:Collocation Methods for the Navier-Stokes Equations. - Bayreuth: 2016.
(Dissertation, 2016, Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)

Masterarbeiten

Daniel Peter Hoff: Ein gitterfreies Verfahren zur numerischen Lösung von Problemen der optimalen Steuerung partieller Differentialgleichungen. - Bayreuth, 2019.
(Masterarbeit, 2019, Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik, Lehrstuhl Angewandte und Numerische Analysis)

Rüdiger Kempf: Kernel-based reconstructions for parametric partial differential equations. - Bayreuth, 2017.
(Masterarbeit, 2017, Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik, Lehrstuhl Angewandte und Numerische Analysis)

Maximilian Bauer: Konvergenz und Stabilität adaptiver Multilevelverfahren. - Bayreuth, 2016.
(Masterarbeit, 2016, Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik, Lehrstuhl Angewandte und Numerische Analysis)

Tino Franz: Konvergenz des Hamiltonian Particle-Mesh Verfahrens. - Bayreuth, 2015.
(Masterarbeit, 2015, Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik, Lehrstuhl Angewandte und Numerische Analysis)

Bachelorarbeiten

Daniel Christoph Fischer: Über kernbasierte Lernverfahren und neuronale Netze. - Bayreuth, 2019.
(, 2019, Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik, Lehrstuhl Angewandte und Numerische Analysis)

Daniel Peter Hoff: Approximative Berechnung der Helmholtz-Hodge-Zerlegung mittels radialer Basisfunktionen. - Bayreuth, 2016.
(, 2016, Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik, Lehrstuhl Angewandte und Numerische Analysis)

Verantwortlich für die Redaktion: Univ.Prof.Dr. Holger Wendland

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