List of publications

S. Takacs and S. Tyoler.
Multi-resolution isogeometric analysis – efficient adaptivity utilizing the multi-patch structure.
Computers & Mathematics with Applications, vol. 179, p. 103 – 125, 2025.
arXiv:2405.08904
J. Sogn and S. Takacs.
Isogeometric Tearing and Interconnecting Solvers for Linearized Elasticity in multi-patch Isogeometric Analysis with theory for two dimensional domains.
Computer Methods in Applied Mechanics and Engineering, vol. 418 (Article 116482), 2024.
arXiv:2305.04975
M. Montardini, G. Sangalli, R. Schneckenleitner, S. Takacs, and M. Tani.
A IETI-DP method for discontinuous Galerkin discretizations in Isogeometric Analysis with inexact local solvers.
Mathematical Models and Methods in Applied Sciences, vol. 33 (10), p. 2085 – 2111, 2023.
arXiv:2206.08416
J. Sogn and S. Takacs.
Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch Isogeometric Analysis.
ESAIM: Mathematical Modelling and Numerical Analysis, vol. 57 (2), p. 921 – 925, 2023.
arXiv:2202.13707
J. Sogn and S. Takacs.
Multigrid solvers for isogeometric discretizations of the second biharmonic problem.
Mathematical Models and Methods in Applied Sciences, vol. 33 (9), p. 1803 – 1828, 2023.
NuMa-Report 2021-10 arXiv:2112.12559
J. Sogn and S. Takacs.
Dual-Primal Isogeometric Tearing and Interconnecting methods for the Stokes problem.
In J. M. Melenk, I. Perugia, J. Schöberl, and C. Schwab (eds): Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1, p. 469 – 481, 2023.
NuMa-Report 2021-09 arXiv:2112.12163
R. Schneckenleitner and S. Takacs.
Inexact IETI-DP for conforming isogeometric multi-patch discretizations.
In J. M. Melenk, I. Perugia, J. Schöberl, and C. Schwab (eds): Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1, p. 399 – 410, 2023.
RICAM-Report 29/2021 arXiv:2110.06087
R. Schneckenleitner and S. Takacs.
IETI-DP methods for discontinuous Galerkin multi-patch Isogeometric Analysis with T-junctions.
Computer Methods in Applied Mechanics and Engineering, vol. 393 (Article 114694), 2022.
RICAM-Report 28/2021 arXiv:2109.13147
R. Schneckenleitner and S. Takacs.
IETI-DP for conforming multi-patch Isogeometric Analysis in three dimensions.
In S.C. Brenner, W. Chung, A. Klawonn, F. Kwok, J. Xu, and J. Zou (eds): Domain Decomposition Methods in Science and Engineering XXVI, p. 555 – 562, 2023.
RICAM-Report 14/2021 arXiv:2103.04801
R. Schneckenleitner and S. Takacs.
Towards a IETI-DP Solver on Non-Matching Multi-Patch Domains.
In S.C. Brenner, W. Chung, A. Klawonn, F. Kwok, J. Xu, and J. Zou (eds): Domain Decomposition Methods in Science and Engineering XXVI, p. 523 – 530, 2023.
RICAM-Report 12/2021 arXiv:2103.02536
K.-A. Mardal, J. Sogn, and S. Takacs.
Robust preconditioning and error estimates for optimal control of the convection-diffusion-reaction equation with limited observation in Isogeometric analysis.
SIAM Journal on Numerical Analysis, vol. 60 (1), p. 195 – 221, 2022.
RICAM-Report 46/2020 arXiv:2012.13003
R. Schneckenleitner and S. Takacs.
Convergence theory for IETI-DP solvers for discontinuous Galerkin Isogeometric Analysis that is explicit in p and h.
Computational Methods in Applied Mathematics, vol. 22 (1), p. 199 – 225, 2022.
RICAM-Report 29/2020 arXiv:2005.09546
R. Schneckenleitner and S. Takacs.
Condition number bounds for IETI-DP methods that are explicit in p and h.
Mathematical Models and Methods in Applied Sciences, vol. 30 (11), p. 2067 – 2103, 2020.
RICAM-Report 31/2019 arXiv:1912.07909 Comment
S. Takacs.
Fast multigrid solvers for conforming and non-conforming multi-patch Isogeometric Analysis.
Computer Methods in Applied Mechanics and Engineering, vol. 371 (Article 113301), 2020.
RICAM-Report 15/2019 arXiv:1902.01818
S. Takacs.
Discretization error estimates for discontinuous Galerkin Isogeometric Analysis.
Applicable Analysis, vol. 102 (5), p. 1439 – 1462, 2023.
RICAM-Report 02/2019 arXiv:1901.03263
A. Bressan and S. Takacs.
Sum-factorization techniques in Isogeometric Analysis.
Computer Methods in Applied Mechanics and Engineering, vol. 352, p. 437 – 460, 2019.
arXiv:1809.05471
C. Hofer and S. Takacs.
A parallel multigrid solver for multi-patch Isogeometric Analysis.
In T. Apel, U. Langer, A. Meyer, and O. Steinbach (eds.): Advanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz Finite Element Symposium 2017, p. 205 – 219, 2019.
RICAM-Report 10/2018 arXiv:1804.02539
J. Sogn and S. Takacs.
Robust multigrid solvers for the biharmonic problem in Isogeometric Analysis.
Computers and Mathematics with Applications, vol. 77 (1), p. 105 – 124, 2019.
RICAM-Report 03/2018 arXiv:1802.00220
S. Takacs.
Robust approximation error estimates and multigrid solvers for isogeometric multi-patch discretizations.
Mathematical Models and Methods in Applied Sciences, vol. 28 (10), p. 1899 – 1928, 2018.
RICAM-Report 32/2017 arXiv:1709.05375
C. Hofer, U. Langer, and S. Takacs.
Inexact dual-primal isogeometric tearing and interconnecting methods.
In P. E. Bjørstad, S. C. Brenner, L. Halpern, R. Kornhuber, H. H. Kim, T. Rahman, and O. B. Widlund (eds.): Domain Decomposition Methods in Science and Engineering XXIV, p. 397 – 406, 2019.
RICAM-Report 16/2017 arXiv:1705.04531
S. Takacs.
Robust multigrid methods for isogeometric discretizations of the Stokes equation.
In P. E. Bjørstad, S. C. Brenner, L. Halpern, R. Kornhuber, H. H. Kim, T. Rahman, and O. B. Widlund (eds.): Domain Decomposition Methods in Science and Engineering XXIV, p. 513 – 522, 2019.
RICAM-Report 15/2017 arXiv:1705.04481
C. Hofreither and S. Takacs.
Robust multigrid for Isogeometric Analysis based on stable splittings of spline spaces.
SIAM Journal on Numerical Analysis, vol. 55 (4), p. 2004 – 2024, 2017.
G+S-Report 45/2016 arXiv:1607.05035
C. Hofreither, S. Takacs, and W. Zulehner.
A robust multigrid method for Isogeometric Analysis in two dimensions using boundary correction.
Computer Methods in Applied Mechanics and Engineering, vol. 316, p. 22 – 42, 2017.
G+S-Report 33/2015 arXiv:1512.07091
S. Takacs and T. Takacs.
Approximation error estimates and inverse inequalities for B-splines of maximum smoothness.
Mathematical Models and Methods in Applied Sciences, vol. 26 (7), p. 1411 – 1445, 2016.
NuMa-Report 2015-02 arXiv:1502.03733
S. Takacs.
A robust all-at-once multigrid method for the Stokes control problem.
Numerische Mathematik, vol. 130 (3), p. 517 – 540, 2015.
arXiv:1502.04121
S. Takacs.
A robust multigrid method for the time-dependent Stokes problem.
SIAM Journal on Numerical Analysis, vol. 53 (6), p. 2634 – 2654, 2015.
arXiv:1502.04070
S. Takacs.
Using cylindrical algebraic decomposition and local Fourier analysis to study numerical methods: Two examples.
In F. Winkler, V. Negru, T. Ida, T. Jebelean, D. Petcu, S. Watt, and D. Zaharie (eds.): 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), p. 42 – 49, 2014.
Technical Report arXiv:1502.03926 Supplemental material
S. Takacs.
Efficient smoothers for all-at-once multigrid methods for Poisson and Stokes control problems.
In C. Pötzsche, C. Heuberger, B. Kaltenbacher, and F. Rendl (eds.): System Modeling and Optimization, p. 337 – 347, 2014.
arXiv:1502.03917
V. Pillwein and S. Takacs.
A local Fourier convergence analysis of a multigrid method using symbolic computation.
Journal of Symbolic Computation, vol. 63, p. 1 – 20, 2014.
DK-Report 2012-04 Supplemental material
S. Takacs and W. Zulehner.
Convergence analysis of all-at-once multigrid methods for elliptic control problems under partial elliptic regularity.
SIAM Journal on Numerical Analysis, vol. 51 (3), p. 1853 – 1874, 2013.
DK-Report 2012-08
S. Takacs and W. Zulehner.
Convergence analysis of multigrid methods with collective point smoothers for optimal control problems.
Computing and Visualization in Science, vol. 14 (3), p. 131 – 141, 2011.
DK-Report 2011-01
V. Pillwein and S. Takacs.
Smoothing analysis of an all-at-once multigrid approach for optimal control problems using symbolic computation.
In U. Langer and P. Paule (eds.): Numerical and Symbolic Scientific Computing: Progress and Prospects, p. 175 – 191, 2011.
DK-Report 2010-09
S. Takacs and W. Zulehner.
Multigrid methods for elliptic optimal control problems with Neumann boundary control.
In G. Kreiss, P. Lötstedt, A. Malqvist, and M. Neytcheva (eds.): Numerical Mathematics and Advanced Applications 2009, p. 855 – 863, 2010.
DK-Report 2009-01