Meshless Finite Difference Method
Finite Element Method
Scattered Data Fitting
Approximation Theory: Splines, Radial Basis Functions
Recent Research Publications
(with W. P. Yeo) C1 Piecewise Quadratic Hierarchical Bases, Applied and Computational Harmonic Analysis,
54 (2021), 250-272. Available online 23 March 2021. https://doi.org/10.1016/j.acha.2021.03.002
Share Link by May 19, 2021: https://authors.elsevier.com/a/1cp%7EI_OBe362wr
Approximation with conditionally positive definite kernels on deficient sets,
in "Approximation Theory XVI: Nashville 2019"
(Gregory E. Fasshauer, Marian Neamtu and Larry L. Schumaker, Eds.),
pp.27-38, Springer Proceedings in Mathematics & Statistics, vol. 336,
Springer-Verlag, 2021. https://doi.org/10.1007/978-3-030-57464-2_3
Preprint version: arXiv:2006.13543 http://arxiv.org/abs/2006.13543
(with M. Safarpoor) A meshless finite difference method for elliptic interface problems based on pivoted QR decomposition,
Applied Numerical Mathematics, 161 (2021), 489-509. Available online 9 December 2020, https://doi.org/10.1016/j.apnum.2020.11.018
Share Link by January 30, 2021: https://authors.elsevier.com/a/1cDsGcQDwuKb8
(with M. Ainsworth and H. Wang), Some remarks on spectral convergence and stability of Iso-Geometric
Analysis, Computer Methods in Applied Mechanics and Engineering,372 (2020), 113408.
https://doi.org/10.1016/j.cma.2020.113408
Error bounds for a least squares meshless finite difference method on closed manifolds, preprint,
arXiv:1910.03359 http://arxiv.org/abs/1910.03359
Selection of sparse sets of influence for meshless finite difference methods, preprint, arXiv:1908.01567 http://arxiv.org/abs/1908.01567
(with O. Kozynenko and D. Skorokhodov) Optimal approximation order of piecewise constants on convex partitions,
Journal of Complexity,58 (2020), 101444. Published Online: 6 November 2019, https://doi.org/10.1016/j.jco.2019.101444,
Preprint version: arXiv:1904.09005 http://arxiv.org/abs/1904.09005
(with D. T. Oanh and N. M. Tuong) Octant-based stencil selection for meshless finite difference methods in 3D,
Vietnam Journal of Mathematics,48 (2020), 93-106. Published online 14 August 2019 http://link.springer.com/article/10.1007/s10013-019-00364-4
Springer Nature SharedIt view-only version: https://rdcu.be/bOTBL
(with A. Sokolov,
D. Kuzmin,
A. Westermann, and
S. Turek)
A flux-corrected RBF-FD method for convection dominated problems in domains and on manifolds,
Journal of Numerical Mathematics,27 (2019), 253-269.
| DOI: https://doi.org/10.1515/jnma-2018-0097. Preprint version:
Ergebnisberichte des Instituts für Angewandte Mathematik, 2018-06, 21 pages, https://eldorado.tu-dortmund.de/handle/2003/36905
(with C. Bracco, C. Giannelli and A. Sestini) Fault and gradient fault detection and reconstruction from scattered data,
CAGD,75 (2019), 101786. https://doi.org/10.1016/j.cagd.2019.101786
(with A. Sokolov and S. Turek) Numerical study of the RBF-FD level set based
method for partial differential equations on evolving-in-time surfaces,
in "Meshfree Methods for Partial Differential Equations IX"
(Michael Griebel and Marc Alexander Schweitzer, Eds.),
pp.117--134, Lecture Notes in Computational Science and Engineering, vol. 129,
Springer-Verlag, 2019.
(with C. Bracco, C. Giannelli, and A. Sestini) An application of numerical differentiation formulas to discontinuity
curve detection from irregularly sampled data,
Rend. Sem. Mat. Univ. Pol. Torino,76 (2018), 69--76.
http://www.seminariomatematico.polito.it/rendiconti/76-2/69.pdf Preprint version: arXiv:1812.07399
(with W. P. Yeo)
Approximation by C1 splines on piecewise conic domains,
in "Approximation Theory XV: San Antonio 2016"
(Gregory E. Fasshauer and Larry L. Schumaker, Eds.),
pp.21--37, Springer Proceedings in Mathematics & Statistics, vol. 201,
Springer-Verlag, 2017.
(with W. P. Yeo)
Macro-element hierarchical Riesz bases,
in "Mathematical Methods for Curves and Surfaces:
8th International Conference, Oslo, 2012"
(M. Floater et al, Eds.), pp.112--134, LNCS 8177, Springer-Verlag, 2014.