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ORCIDMarkus Bachmayr
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2020 – today
- 2024
[j16]Markus Bachmayr, Manfred Faldum:
A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations. J. Complex. 82: 101839 (2024)- [i14]Markus Bachmayr, Martin Eigel, Henrik Eisenmann, Igor Voulis:
A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields. CoRR abs/2403.13770 (2024) - [i13]Markus Bachmayr, Riccardo Bardin, Matthias Schlottbom:
Low-rank tensor product Richardson iteration for radiative transfer in plane-parallel geometry. CoRR abs/2403.14229 (2024) - [i12]Markus Bachmayr, Wolfgang Dahmen, Mathias Oster:
Variationally Correct Neural Residual Regression for Parametric PDEs: On the Viability of Controlled Accuracy. CoRR abs/2405.20065 (2024) - [i11]Markus Bachmayr, Simon Boisserée:
An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities. CoRR abs/2409.13420 (2024) - 2023
- [j15]Markus Bachmayr
:
Low-rank tensor methods for partial differential equations. Acta Numer. 32: 1-121 (2023) - [j14]Markus Bachmayr, Geneviève Dusson, Christoph Ortner, Jack Thomas:
Polynomial approximation of symmetric functions. Math. Comput. 93(346): 811-839 (2023) - [i10]Markus Bachmayr, Manfred Faldum:
A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations. CoRR abs/2302.01658 (2023) - [i9]Markus Bachmayr, Henrik Eisenmann, André Uschmajew:
Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations. CoRR abs/2308.16720 (2023) - 2022
- [j13]Geneviève Dusson, Markus Bachmayr, Gábor Csányi, Ralf Drautz, Simon Etter, Cas van der Oord, Christoph Ortner:
Atomic cluster expansion: Completeness, efficiency and stability. J. Comput. Phys. 454: 110946 (2022) - 2021
- [j12]Markus Bachmayr, Henrik Eisenmann, Emil Kieri, André Uschmajew:
Existence of dynamical low-rank approximations to parabolic problems. Math. Comput. 90(330): 1799-1830 (2021) - [i8]Markus Bachmayr, Michael Götte, Max Pfeffer:
Particle Number Conservation and Block Structures in Matrix Product States. CoRR abs/2104.13483 (2021) - [i7]Markus Bachmayr, Igor Voulis:
An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality. CoRR abs/2109.09136 (2021) - [i6]Markus Bachmayr, Geneviève Dusson, Christoph Ortner:
Polynomial Approximation of Symmetric Functions. CoRR abs/2109.14771 (2021) - [i5]Markus Bachmayr, Anthony Nouy, Reinhold Schneider:
Approximation by tree tensor networks in high dimensions: Sobolev and compositional functions. CoRR abs/2112.01474 (2021) - 2020
- [j11]Markus Bachmayr, Vladimir A. Kazeev:
Stability of Low-Rank Tensor Representations and Structured Multilevel Preconditioning for Elliptic PDEs. Found. Comput. Math. 20(5): 1175-1236 (2020) - [j10]Markus Bachmayr, Ivan G. Graham, Van Kien Nguyen, Robert Scheichl:
Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances. SIAM J. Numer. Anal. 58(5): 2953-2980 (2020) - [p1]Markus Bachmayr, Wolfgang Dahmen:
Adaptive low-rank approximations for operator equations: Accuracy control and computational complexity. 75 Years of Mathematics of Computation 2020 - [i4]Markus Bachmayr, Emil Kieri, André Uschmajew:
Existence of dynamical low-rank approximations to parabolic problems. CoRR abs/2002.12197 (2020) - [i3]Markus Bachmayr, Ana Djurdjevac:
Multilevel Representations of Isotropic Gaussian Random Fields on the Sphere. CoRR abs/2011.06987 (2020)
2010 – 2019
- 2019
- [j9]Benjamin Arras, Markus Bachmayr, Albert Cohen:
Sequential Sampling for Optimal Weighted Least Squares Approximations in Hierarchical Spaces. SIAM J. Math. Data Sci. 1(1): 189-207 (2019) - [i2]Markus Bachmayr, Wolfgang Dahmen:
Adaptive Low-Rank Approximations for Operator Equations: Accuracy Control and Computational Complexity. CoRR abs/1910.07052 (2019) - [i1]Markus Bachmayr, Gábor Csányi, Geneviève Dusson, Simon Etter, Cas van der Oord, Christoph Ortner:
Approximation of Potential Energy Surfaces with Spherical Harmonics. CoRR abs/1911.03550 (2019) - 2017
- [j8]Markus Bachmayr, Reinhold Schneider:
Iterative Methods Based on Soft Thresholding of Hierarchical Tensors. Found. Comput. Math. 17(4): 1037-1083 (2017) - [j7]Markus Bachmayr, Albert Cohen:
Kolmogorov widths and low-rank approximations of parametric elliptic PDEs. Math. Comput. 86(304): 701-724 (2017) - [j6]Markus Bachmayr, Albert Cohen, Dinh Dung, Christoph Schwab:
Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs. SIAM J. Numer. Anal. 55(5): 2151-2186 (2017) - 2016
- [j5]Markus Bachmayr, Reinhold Schneider, André Uschmajew:
Tensor Networks and Hierarchical Tensors for the Solution of High-Dimensional Partial Differential Equations. Found. Comput. Math. 16(6): 1423-1472 (2016) - [j4]Markus Bachmayr, Wolfgang Dahmen:
Adaptive Low-Rank Methods: Problems on Sobolev Spaces. SIAM J. Numer. Anal. 54(2): 744-796 (2016) - 2015
- [j3]Markus Bachmayr, Wolfgang Dahmen:
Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations. Found. Comput. Math. 15(4): 839-898 (2015) - 2014
- [j2]Markus Bachmayr, Huajie Chen, Reinhold Schneider:
Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry. Numerische Mathematik 128(1): 137-165 (2014) - 2013
- [j1]Markus Bachmayr:
Integration of Products of Gaussians and Wavelets with Applications to Electronic Structure Calculations. SIAM J. Numer. Anal. 51(5): 2491-2513 (2013)
Coauthor Index
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