Markus Bachmayr

39 papers Journal 38

Year	Rank	Type	Title / Venue / Authors
2026	J	`jnl`	Low-Rank Tensor Product Richardson Iteration for Radiative Transfer in Plane-Parallel Geometry. SIAM J. Numer. Anal. Markus Bachmayr, Riccardo Bardin, Matthias Schlottbom
2026	J	`jnl`	Preconditioning and Numerical Stability in Neural Network Training for Parametric PDEs. CoRR Markus Bachmayr, Wolfgang Dahmen, Chenguang Duan, Mathias Oster
2025	J	`jnl`	A Convergent Adaptive Finite Element Stochastic Galerkin Method Based on Multilevel Expansions of Random Fields. SIAM J. Numer. Anal. Markus Bachmayr, Martin Eigel, Henrik Eisenmann, Igor Voulis
2025	J	`jnl`	Adaptive stochastic Galerkin finite element methods: Optimality and non-affine coefficients. CoRR Markus Bachmayr, Henrik Eisenmann, Igor Voulis
2025	J	`jnl`	Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations. Numerische Mathematik Markus Bachmayr, Henrik Eisenmann, André Uschmajew
2025	J	`jnl`	Iterative thresholding low-rank time integration. CoRR Markus Bachmayr, Matthieu Dolbeault, Polina Sachsenmaier
2025	J	`jnl`	Preface. Found. Comput. Math. Markus Bachmayr, Albert Cohen, Evelyne Hubert, Teresa Krick
2025	J	`jnl`	Sparse and low-rank approximations of parametric elliptic PDEs: the best of both worlds. CoRR Markus Bachmayr, Huqing Yang
2024	J	`jnl`	A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields. CoRR Markus Bachmayr, Martin Eigel, Henrik Eisenmann, Igor Voulis
2024	J	`jnl`	A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations. J. Complex. Markus Bachmayr, Manfred Faldum
2024	J	`jnl`	An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities. CoRR Markus Bachmayr, Simon Boisserée
2024	J	`jnl`	Low-rank tensor product Richardson iteration for radiative transfer in plane-parallel geometry. CoRR Markus Bachmayr, Riccardo Bardin, Matthias Schlottbom
2024	J	`jnl`	Variationally Correct Neural Residual Regression for Parametric PDEs: On the Viability of Controlled Accuracy. CoRR Markus Bachmayr, Wolfgang Dahmen, Mathias Oster
2023	J	`jnl`	A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations. CoRR Markus Bachmayr, Manfred Faldum
2023	J	`jnl`	Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations. CoRR Markus Bachmayr, Henrik Eisenmann, André Uschmajew
2023	J	`jnl`	Low-rank tensor methods for partial differential equations. Acta Numer. Markus Bachmayr
2023	J	`jnl`	Polynomial approximation of symmetric functions. Math. Comput. Markus Bachmayr, Geneviève Dusson, Christoph Ortner, Jack Thomas
2022	J	`jnl`	Atomic cluster expansion: Completeness, efficiency and stability. J. Comput. Phys. Geneviève Dusson, Markus Bachmayr, Gábor Csányi, Ralf Drautz, Simon Etter, Cas van der Oord, Christoph Ortner
2021	J	`jnl`	An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality. CoRR Markus Bachmayr, Igor Voulis
2021	J	`jnl`	Approximation by tree tensor networks in high dimensions: Sobolev and compositional functions. CoRR Markus Bachmayr, Anthony Nouy, Reinhold Schneider
2021	J	`jnl`	Existence of dynamical low-rank approximations to parabolic problems. Math. Comput. Markus Bachmayr, Henrik Eisenmann, Emil Kieri, André Uschmajew
2021	J	`jnl`	Particle Number Conservation and Block Structures in Matrix Product States. CoRR Markus Bachmayr, Michael Götte, Max Pfeffer
2021	J	`jnl`	Polynomial Approximation of Symmetric Functions. CoRR Markus Bachmayr, Geneviève Dusson, Christoph Ortner
2020	—	`ch.`	Adaptive low-rank approximations for operator equations: Accuracy control and computational complexity. 75 Years of Mathematics of Computation Markus Bachmayr, Wolfgang Dahmen
2020	J	`jnl`	Existence of dynamical low-rank approximations to parabolic problems. CoRR Markus Bachmayr, Emil Kieri, André Uschmajew
2020	J	`jnl`	Multilevel Representations of Isotropic Gaussian Random Fields on the Sphere. CoRR Markus Bachmayr, Ana Djurdjevac
2020	J	`jnl`	Stability of Low-Rank Tensor Representations and Structured Multilevel Preconditioning for Elliptic PDEs. Found. Comput. Math. Markus Bachmayr, Vladimir A. Kazeev
2020	J	`jnl`	Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances. SIAM J. Numer. Anal. Markus Bachmayr, Ivan G. Graham, Van Kien Nguyen, Robert Scheichl
2019	J	`jnl`	Adaptive Low-Rank Approximations for Operator Equations: Accuracy Control and Computational Complexity. CoRR Markus Bachmayr, Wolfgang Dahmen
2019	J	`jnl`	Approximation of Potential Energy Surfaces with Spherical Harmonics. CoRR Markus Bachmayr, Gábor Csányi, Geneviève Dusson, Simon Etter, Cas van der Oord, Christoph Ortner
2019	J	`jnl`	Sequential Sampling for Optimal Weighted Least Squares Approximations in Hierarchical Spaces. SIAM J. Math. Data Sci. Benjamin Arras, Markus Bachmayr, Albert Cohen
2017	J	`jnl`	Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs. SIAM J. Numer. Anal. Markus Bachmayr, Albert Cohen, Dinh Dung, Christoph Schwab
2017	J	`jnl`	Iterative Methods Based on Soft Thresholding of Hierarchical Tensors. Found. Comput. Math. Markus Bachmayr, Reinhold Schneider
2017	J	`jnl`	Kolmogorov widths and low-rank approximations of parametric elliptic PDEs. Math. Comput. Markus Bachmayr, Albert Cohen
2016	J	`jnl`	Adaptive Low-Rank Methods: Problems on Sobolev Spaces. SIAM J. Numer. Anal. Markus Bachmayr, Wolfgang Dahmen
2016	J	`jnl`	Tensor Networks and Hierarchical Tensors for the Solution of High-Dimensional Partial Differential Equations. Found. Comput. Math. Markus Bachmayr, Reinhold Schneider, André Uschmajew
2015	J	`jnl`	Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations. Found. Comput. Math. Markus Bachmayr, Wolfgang Dahmen
2014	J	`jnl`	Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry. Numerische Mathematik Markus Bachmayr, Huajie Chen, Reinhold Schneider
2013	J	`jnl`	Integration of Products of Gaussians and Wavelets with Applications to Electronic Structure Calculations. SIAM J. Numer. Anal. Markus Bachmayr