Markus Bachmayr

According to our database, Markus Bachmayr authored at least 30 papers between 2013 and 2024.

Collaborative distances:

• Dijkstra number of five.
• Erdős number of four.

2024

A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations.

Markus Bachmayr, Manfred Faldum

J. Complex., 2024

An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities.

Markus Bachmayr, Simon Boisserée

CoRR, 2024

Variationally Correct Neural Residual Regression for Parametric PDEs: On the Viability of Controlled Accuracy.

Markus Bachmayr, Wolfgang Dahmen, Mathias Oster

CoRR, 2024

Low-rank tensor product Richardson iteration for radiative transfer in plane-parallel geometry.

Markus Bachmayr, Riccardo Bardin, Matthias Schlottbom

CoRR, 2024

A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields.

Markus Bachmayr, Martin Eigel, Henrik Eisenmann, Igor Voulis

CoRR, 2024

2023

Polynomial approximation of symmetric functions.

Markus Bachmayr, Geneviève Dusson, Christoph Ortner, Jack Thomas

Math. Comput., June, 2023

Low-rank tensor methods for partial differential equations.

Markus Bachmayr

Acta Numer., May, 2023

Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations.

Markus Bachmayr, Henrik Eisenmann, André Uschmajew

CoRR, 2023

2022

Atomic cluster expansion: Completeness, efficiency and stability.

Geneviève Dusson, Markus Bachmayr, Gábor Csányi, Ralf Drautz, Simon Etter, Cas van der Oord, Christoph Ortner

J. Comput. Phys., 2022

2021

Existence of dynamical low-rank approximations to parabolic problems.

Markus Bachmayr, Henrik Eisenmann, Emil Kieri, André Uschmajew

Math. Comput., 2021

Approximation by tree tensor networks in high dimensions: Sobolev and compositional functions.

Markus Bachmayr, Anthony Nouy, Reinhold Schneider

CoRR, 2021

Polynomial Approximation of Symmetric Functions.

Markus Bachmayr, Geneviève Dusson, Christoph Ortner

CoRR, 2021

An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality.

Markus Bachmayr, Igor Voulis

CoRR, 2021

Particle Number Conservation and Block Structures in Matrix Product States.

Markus Bachmayr, Michael Götte, Max Pfeffer

CoRR, 2021

2020

Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances.

Markus Bachmayr, Ivan G. Graham, Van Kien Nguyen, Robert Scheichl

SIAM J. Numer. Anal., 2020

Stability of Low-Rank Tensor Representations and Structured Multilevel Preconditioning for Elliptic PDEs.

Markus Bachmayr, Vladimir A. Kazeev

Found. Comput. Math., 2020

Multilevel Representations of Isotropic Gaussian Random Fields on the Sphere.

Markus Bachmayr, Ana Djurdjevac

CoRR, 2020

Existence of dynamical low-rank approximations to parabolic problems.

Markus Bachmayr, Emil Kieri, André Uschmajew

CoRR, 2020

Adaptive low-rank approximations for operator equations: Accuracy control and computational complexity.

Markus Bachmayr, Wolfgang Dahmen

Proceedings of the 75 Years of Mathematics of Computation, 2020

2019

Sequential Sampling for Optimal Weighted Least Squares Approximations in Hierarchical Spaces.

Benjamin Arras, Markus Bachmayr, Albert Cohen

SIAM J. Math. Data Sci., 2019

Approximation of Potential Energy Surfaces with Spherical Harmonics.

Markus Bachmayr, Gábor Csányi, Geneviève Dusson, Simon Etter, Cas van der Oord, Christoph Ortner

CoRR, 2019

Adaptive Low-Rank Approximations for Operator Equations: Accuracy Control and Computational Complexity.

Markus Bachmayr, Wolfgang Dahmen

CoRR, 2019

2017

Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs.

Markus Bachmayr, Albert Cohen, Dinh Dung, Christoph Schwab

SIAM J. Numer. Anal., 2017

Kolmogorov widths and low-rank approximations of parametric elliptic PDEs.

Markus Bachmayr, Albert Cohen

Math. Comput., 2017

Iterative Methods Based on Soft Thresholding of Hierarchical Tensors.

Markus Bachmayr, Reinhold Schneider

Found. Comput. Math., 2017

2016

Adaptive Low-Rank Methods: Problems on Sobolev Spaces.

Markus Bachmayr, Wolfgang Dahmen

SIAM J. Numer. Anal., 2016

Tensor Networks and Hierarchical Tensors for the Solution of High-Dimensional Partial Differential Equations.

Markus Bachmayr, Reinhold Schneider, André Uschmajew

Found. Comput. Math., 2016

2015

Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations.

Markus Bachmayr, Wolfgang Dahmen

Found. Comput. Math., 2015

2014

Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry.

Markus Bachmayr, Huajie Chen, Reinhold Schneider

Numerische Mathematik, 2014

2013

Integration of Products of Gaussians and Wavelets with Applications to Electronic Structure Calculations.

Markus Bachmayr

SIAM J. Numer. Anal., 2013