Computational Random Multiscale Problems

Project Information

RandomMultiScales

Grant agreement ID: 865751

DOI

10.3030/865751

Project closed

EC signature date 18 December 2019

Start date 1 August 2020

End date 31 July 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 796 926,00

EU contribution

€ 1 796 926,00

Coordinated by

UNIVERSITAET AUGSBURG
Germany

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (26)

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Author(s): Philip Freese, Dietmar Gallistl, Daniel Peterseim, Timo Sprekeler
Published in: Computational Methods in Applied Mathematics, 2022, ISSN 1609-4840
Publisher: Walter de Gruyter and Co.
DOI: 10.48550/arxiv.2211.13731

Multi-resolution Localized Orthogonal Decomposition for Helmholtz problems

Author(s): Moritz Hauck, Daniel Peterseim
Published in: Multiscale Modeling & Simulation, Issue 15403459, 2022, Page(s) 657-684, ISSN 1540-3459
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/21m1414607

Super-localization of elliptic multiscale problems

Author(s): Moritz Hauck, Daniel Peterseim
Published in: Mathematics of Computation, 2022, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3798

A Priori Error Analysis of a Numerical Stochastic Homogenization Method

Author(s): Julian Fischer, Dietmar Gallistl, Daniel Peterseim
Published in: SIAM Journal on Numerical Analysis, Issue 59/2, 2021, Page(s) 660-674, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m1308992

Uncertainty quantification in timber-like beams using sparse grids: theory and examples with off-the-shelf software utilization

Author(s): Giuseppe Balduzzi, Francesca Bonizzoni, Lorenzo Tamellini
Published in: Construction and Building Materials, Issue 406, 2023, ISSN 0950-0618
Publisher: Elsevier BV
DOI: 10.1016/j.conbuildmat.2023.132730

Super-localised wave function approximation of Bose-Einstein condensates

Author(s): Daniel Peterseim, Johan Wärnegård, Christoph Zimmer
Published in: Journal of Computational Physics, 2024, ISSN 0021-9991
Publisher: Academic Press
DOI: 10.1016/j.jcp.2024.113097

Operator Compression with Deep Neural Networks

Author(s): Kröpfl, Fabian; Maier, Roland; Peterseim, Daniel
Published in: Advances in Continuous and Discrete Models, Issue 2022, 2022, ISSN 2731-4235
Publisher: Springer
DOI: 10.1186/s13662-022-03702-y

Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots

Author(s): Francesca Bonizzoni, Davide Pradovera, Michele Ruggeri
Published in: Mathematics in Engineering, Issue 5/4, 2023, Page(s) 1-38, ISSN 2640-3501
Publisher: AIMS Press
DOI: 10.3934/mine.2023074

Numerical homogenization beyond scale separation

Author(s): Robert Altmann, Patrick Henning, Daniel Peterseim
Published in: Acta Numerica, Issue 30, 2021, Page(s) 1-86, ISSN 0962-4929
Publisher: Cambridge University Press
DOI: 10.1017/s0962492921000015

Localization and delocalization of ground states of Bose-Einstein condensates under disorder

Author(s): Altmann, Robert; Henning, Patrick; Peterseim, Daniel
Published in: SIAM Journal on Applied Mathematics, Issue 82/1, 2022, Page(s) 330-358, ISSN 0036-1399
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1342434

Riemannian optimization methods for ground states of multicomponent Bose–Einstein condensates

Author(s): Robert Altmann, Martin Hermann, Daniel Peterseim, Tatjana Stykel
Published in: IMA Journal of Numerical Analysis, 2025, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/draf046

Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds

Author(s): Carsten Carstensen, Benedikt Gräßle, Ngoc Tien Tran
Published in: Numerische Mathematik, Issue 156, 2024, Page(s) 813-851, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-024-01407-w

The J-method for the Gross–Pitaevskii eigenvalue problem

Author(s): Robert Altmann, Patrick Henning, Daniel Peterseim
Published in: Numerische Mathematik, Issue 148/3, 2021, Page(s) 575-610, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-021-01216-5

A Super-Localized Generalized Finite Element Method

Author(s): Philip Freese, Moritz Hauck, Tim Keil, Daniel Peterseim
Published in: Numerische Mathematik, Issue 156, 2024, ISSN 0945-3245
Publisher: Springer
DOI: 10.1007/s00211-023-01386-4

Energy-adaptive Riemannian optimization on the Stiefel manifold

Author(s): Altmann, Robert; Peterseim, Daniel; Stykel, Tatjana
Published in: ESAIM. Mathematical Modelling and Numerical Analysis, Issue 28227840, 2022, Page(s) 1629 - 1653, ISSN 2822-7840
Publisher: EDP Sciences
DOI: 10.1051/m2an/2022036

Finite element approximation for uniformly elliptic linear PDE of second order in nondivergence form

Author(s): Ngoc Tien Tran
Published in: Mathematics of Computation, 2024, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3966

Quantum Realization of the Finite Element Method

Author(s): Matthias Deiml, Daniel Peterseim
Published in: Mathematics of Computation, 2025, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/4137

Discrete Weak Duality of Hybrid High-Order Methods for Convex Minimization Problems

Author(s): Ngoc Tien Tran
Published in: SIAM Journal on Numerical Analysis, Issue 62, 2024, Page(s) 1492-1514, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/23m1594534

Super-localization of spatial network models

Author(s): Moritz Hauck, Axel Målqvist
Published in: Numerische Mathematik, Issue 156, 2024, ISSN 0945-3245
Publisher: Springer
DOI: 10.1007/s00211-024-01410-1

Metamaterial applications of T<scp>matsolver</scp>, an easy-to-use software for simulating multiple wave scattering in two dimensions

Author(s): Stuart C. Hawkins, Luke G. Bennetts, Matthew A. Nethercote, Malte A. Peter, Daniel Peterseim, Henry J. Putley, Barbara Verfürth
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Issue 480, 2024, ISSN 1364-5021
Publisher: Royal Society of London
DOI: 10.1098/rspa.2023.0934

Stability and guaranteed error control of approximations to the Monge–Ampère equation

Author(s): Dietmar Gallistl, Ngoc Tien Tran
Published in: Numerische Mathematik, Issue 156, 2024, Page(s) 107-131, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-023-01385-5

A reduced basis super-localized orthogonal decomposition for reaction-convection-diffusion problems

Author(s): Francesca Bonizzoni, Moritz Hauck, Daniel Peterseim
Published in: Journal of Computational Physics, Issue 499, 2024, ISSN 0021-9991
Publisher: Academic Press
DOI: 10.1016/j.jcp.2023.112698

Minimal residual discretization of a class of fully nonlinear elliptic PDE

Author(s): Dietmar Gallistl, Ngoc Tien Tran
Published in: IMA Journal of Numerical Analysis, 2025, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/draf075

The Heterogeneous Multiscale Method for dispersive Maxwell systems

Author(s): Philip Freese
Published in: Multiscale Modeling & Simulation, Issue 20/2, 2022, Page(s) 769-797, ISSN 1540-3459
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/21m1443960

An improved high-order method for elliptic multiscale problems

Author(s): Zhaonan Dong, Moritz Hauck, Roland Maier
Published in: SIAM Journal on Numerical Analysis, Issue 61(4), 2023, Page(s) 1918-1937, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.48550/arxiv.2211.02484

Super-Localized Orthogonal Decomposition Method for Heterogeneous Linear Elasticity

Author(s): Camilla Belponer, José C. Garay, Peter Munch, Daniel Peterseim
Published in: Computational Methods in Applied Mathematics, Issue 25, 2025, Page(s) 561-579, ISSN 1609-4840
Publisher: Walter de Gruyter and Co.
DOI: 10.1515/cmam-2025-0005

Other (15)

Neural Network Acceleration of Iterative Methods for Nonlinear Schrödinger Eigenvalue Problems

Author(s): Daniel Peterseim, Jan-F. Pietschmann, Jonas Püschel, Kilian Ruess
Published in: ArXiv e-prints, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2507.16349

Positivity preserving finite element method for the Gross-Pitaevskii ground state: discrete uniqueness and global convergence

Author(s): Moritz Hauck, Yizhou Liang, Daniel Peterseim
Published in: Arxiv e-prints, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2405.17090

A greedy MOR method for the tracking of eigensolutions to parametric elliptic PDEs

Author(s): Moataz M. Alghamdi, Daniele Boffi, Francesca Bonizzoni
Published in: Arxiv e-prints, 2022
Publisher: arXiv
DOI: 10.48550/arxiv.2208.14054

Hierarchical Super-Localized Orthogonal Decomposition Method

Author(s): Jose C. Garay, Hannah Mohr, Daniel Peterseim, Christoph Zimmer
Published in: ArXiv e-prints, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2407.18671

Energy-Adaptive Riemannian Conjugate Gradient Method for Density Functional Theory

Author(s): Daniel Peterseim, Jonas Püschel, Tatjana Stykel
Published in: ArXiv e-prints, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2503.16225

Super-localized Orthogonal Decomposition for high-frequency Helmholtz problems

Author(s): Philip Freese, Moritz Hauck, Daniel Peterseim
Published in: Arxiv e-prints, 2021
Publisher: arXiv
DOI: 10.48550/arxiv.2112.11368

Neural Network Localized Orthogonal Decomposition for Numerical Homogenization of Diffusion Operators with Random Coefficients

Author(s): Fabian Kröpfl, Daniel Peterseim, Elisabeth Ullmann
Published in: ArXiv e-prints, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2509.12896

Discrete tensor product BGG sequences: splines and finite elements

Author(s): Francesca Bonizzoni, Kaibo Hu, Guido Kanschat, Duygu Sap
Published in: Arxiv e-prints, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2302.02434

Lower eigenvalue bounds with hybrid high-order methods

Author(s): Ngoc Tien Tran
Published in: ArXiv e-prints, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2406.06244

A simple collocation-type approach to numerical stochastic homogenization

Author(s): Moritz Hauck, Hannah Mohr, Daniel Peterseim
Published in: Arxiv e-prints, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2404.01732

Super-localized orthogonal decomposition for convection-dominated diffusion problems

Author(s): Francesca Bonizzoni, Philip Freese, Daniel Peterseim
Published in: Arxiv e-prints, 2022
Publisher: arXiv
DOI: 10.48550/arxiv.2206.01975

Riemannian Newton methods for energy minimization problems of Kohn-Sham type

Author(s): R. Altmann, D. Peterseim, T. Stykel
Published in: Arxiv e-prints, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2307.13820

Mixed finite elements for the Gross-Pitaevskii eigenvalue problem: a priori error analysis and guaranteed lower energy bound

Author(s): Dietmar Gallistl, Moritz Hauck, Yizhou Liang, Daniel Peterseim
Published in: Arxiv e-prints, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2402.06311

A hybrid high-order method for the biharmonic problem

Author(s): Yizhou Liang, Ngoc Tien Tran
Published in: ArXiv e-prints, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2504.16608

Nonlinear quantum computing by amplified encodings

Author(s): Matthias Deiml, Daniel Peterseim
Published in: ArXiv e-prints, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2411.16435

Conference proceedings (1)

A Tensor-Product Finite Element Cochain Complex with Arbitrary Continuity

Author(s): Bonizzoni, Francesca; Kanschat, Guido
Published in: The 8th European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS Congress 2022, 2022, Page(s) 12, ISBN 9788412322286
Publisher: Eccomas
DOI: 10.23967/eccomas.2022.134

Non-peer reviewed articles (1)

Locking-Free Hybrid High-Order Method for Linear Elasticity

Author(s): Carsten Carstensen, Ngoc Tien Tran
Published in: SIAM Journal on Numerical Analysis, Issue 63, 2025, Page(s) 827-853, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/24m1650363

Thesis and dissertations (2)

Deep-learning-based numerical homogenization of heterogeneous media

Author(s): Fabian Kröpfl
Published in: 2025
Publisher: Universität Augsburg

Numerical homogenization: multi-resolution and super-localization approaches

Author(s): Hauck, Moritz
Published in: Issue 1, 2023
Publisher: Universität Augsburg