Meshless Finite Difference Method
Finite Element Method
Scattered Data Fitting
Approximation Theory: Splines, Radial Basis Functions
Recent Research Publications
(with C. Bracco, C. Giannelli and A. Sestini) A positive meshless finite difference scheme for scalar conservation laws with
adaptive artificial viscosity driven by fault detection Preprint, arXiv:2409.15544 https://arxiv.org/abs/2409.15544
(with B. Degli Esposti) Meshless quadrature formulas arising from numerical differentiation.
Preprint, arXiv:2409.03567 https://arxiv.org/abs/2409.03567
Overlap splines and meshless finite difference methods.
Preprint, arXiv:2306.02391 https://arxiv.org/abs/2306.02391
(with A. Westermann,
A. Sokolov and
S. Turek)
Numerical study of the RBF-FD method for the Stokes equations.
Preprint,
Eldorado - Repository of the TU Dortmund, Ergebnisbericht Nr. 662, 2023,
https://eldorado.tu-dortmund.de/handle/2003/41366
Error bounds for a least squares meshless finite difference method on closed manifolds,
Advances in Computational Mathematics, 49 (2023), 48,
https://doi.org/10.1007/s10444-023-10044-0 (open access)
Preprints (2019-2023): arXiv:1910.03359 http://arxiv.org/abs/1910.03359
(with D. T. Oanh and N. M. Tuong) Improved stencil selection for meshless finite difference methods in 3D,
Journal of Computational and Applied Mathematics, 425 (2023), 115031.
https://doi.org/10.1016/j.cam.2022.115031
Preprint: arXiv:2202.06426 http://arxiv.org/abs/2202.06426
(with P. Suchde and T. Jacquemin) Point cloud generation for meshfree methods: An overview,
Archives of Computational Methods in Engineering, 30 (2023), 889-915.
https://doi.org/10.1007/s11831-022-09820-w (open access)
(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
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
(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
(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
Selection of sparse sets of influence for meshless finite difference methods.
Preprint, arXiv:1908.01567 http://arxiv.org/abs/1908.01567
(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.
https://doi.org/10.1515/jnma-2018-0097. Preprint version:
Eldorado - Repository of the TU Dortmund, Ergebnisbericht Nr. 587, 2018,
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. https://doi.org/10.1007/978-3-030-15119-5_7
Preprint version: Eldorado - Repository of the TU Dortmund, Ergebnisbericht Nr. 579,
2017, https://eldorado.tu-dortmund.de/handle/2003/36231
(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.