Zobrazeno 1 - 10
of 92
pro vyhledávání: '"Holger Wendland"'
Autor:
Holger Wendland
Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial ba
Publikováno v:
Mathematics of Computation. 90:2137-2160
Motivated by the desire to compute complete Lyapunov functions for nonlinear dynamical systems, we develop a general theory of discretizing a certain type of continuous minimization problems with differential inequality constraints. The resulting dis
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c98588ef29f3eb48ad29d9b80bf0f2a0
https://doi.org/10.1090/mcom/3629
https://doi.org/10.1090/mcom/3629
Autor:
Tino Franz, Holger Wendland
Publikováno v:
SIAM Journal on Mathematical Analysis. 53:1239-1262
The smoothed particle hydrodynamics (SPH) method is a popular, kernel-based discretization method for fluid-flow problems. Despite its frequent use, mathematical understanding is still limited. In ...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::757e2b46a77ad4dda5440832cae32d9e
https://doi.org/10.1137/19m1308293
https://doi.org/10.1137/19m1308293
Autor:
Daniel Hoff, Holger Wendland
Publikováno v:
SIAM Journal on Numerical Analysis. 59:1896-1917
We describe a new approximation method for solving a PDE-constrained optimization problem numerically. Our method is based on the adjoint formulation of the optimization problem, leading to a syste...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9dce349f6e8b77c607928010a302c2d8
https://doi.org/10.1137/20m1363510
https://doi.org/10.1137/20m1363510
Publikováno v:
Numerische Mathematik. 142:383-419
We describe a novel meshless Galerkin method for numerically solving semilinear parabolic equations on spheres. The new approximation method is based upon a discretization in space using spherical basis functions in a Galerkin approximation. As our s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::35b231c5c6ac95dd5a40a95ed520a6b5
https://doi.org/10.1007/s00211-018-01021-7
https://doi.org/10.1007/s00211-018-01021-7
Autor:
Christian Rieger, Holger Wendland
Publikováno v:
IMA Journal of Numerical Analysis. 40:285-321
We derive sampling inequalities for discrete point sets that are of anisotropic tensor product form. Such sampling inequalities can be used to prove convergence for arbitrary stable reconstruction processes. As usual in the context of high-dimensiona
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::95cd3cab1bcb3df4a5d6f066f7690ffd
https://doi.org/10.1093/imanum/dry080
https://doi.org/10.1093/imanum/dry080
Autor:
Peter Giesl, Holger Wendland
Publikováno v:
Discrete & Continuous Dynamical Systems - B. 24:3843-3863
A contraction metric for an autonomous ordinary differential equation is a Riemannian metric such that the distance between adjacent solutions contracts over time. A contraction metric can be used to determine the basin of attraction of an equilibriu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1fff2959fb18120b030fc2cfe68efbdd
https://doi.org/10.3934/dcdsb.2018333
https://doi.org/10.3934/dcdsb.2018333
Autor:
Jens Künemund, Holger Wendland
Publikováno v:
Advances in Computational Mathematics. 46
Meshfree, kernel-based spatial discretisations are recent tools to discretise partial differential equations on surfaces. The goals of this paper are to analyse and compare three different meshfree kernel-based methods for the spatial discretisation
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9b192989d1962c38718a28afc46ccff9
https://doi.org/10.1007/s10444-020-09803-0
https://doi.org/10.1007/s10444-020-09803-0
Autor:
Tino Franz, Holger Wendland
Publikováno v:
SIAM Journal on Mathematical Analysis. 50:4752-4784
Smoothed particle hydrodynamics (SPH) is a popular particle- and kernel-based method for numerically computing solutions to fluid-flow problems. In this paper, we study the convergence of SPH for t...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3e1e5a957e3f23aecb5f7a80503ce1f3
https://doi.org/10.1137/17m1157696
https://doi.org/10.1137/17m1157696
Autor:
Holger Wendland, Tobias Ramming
Publikováno v:
Mathematics of Computation. 87:1757-1781
We derive a new discretisation method for first order PDEs of arbitrary spatial dimension, which is based upon a meshfree spatial approximation. This spatial approximation is similar to the SPH (smoothed particle hydrodynamics) technique and is a typ
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c8dc67e00578eb403194ca1b9e62a5de
https://doi.org/10.1090/mcom/3265
https://doi.org/10.1090/mcom/3265