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Hybrid explicit–implicit learning for multiscale problems with time dependent source
Yalchin Efendiev, Wing Tat Leung, Wenyuan Li and Zecheng Zhang Communications in Nonlinear Science and Numerical Simulation 120 107081 (2023) https://doi.org/10.1016/j.cnsns.2022.107081
Reduced order modeling for elliptic problems with high contrast diffusion coefficients
Albert Cohen, Wolfgang Dahmen, Matthieu Dolbeault and Agustin Somacal ESAIM: Mathematical Modelling and Numerical Analysis 57(5) 2775 (2023) https://doi.org/10.1051/m2an/2023013
Multiscale Sub-grid Correction Method for Time-Harmonic High-Frequency Elastodynamics with Wave Number Explicit Bounds
Contrast-independent partially explicit time discretizations for multiscale wave problems
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung and Petr N. Vabishchevich Journal of Computational Physics 466 111226 (2022) https://doi.org/10.1016/j.jcp.2022.111226
Computational multiscale method for parabolic wave approximations in heterogeneous media
Contrast-independent partially explicit time discretizations for multiscale flow problems
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung and Petr N. Vabishchevich Journal of Computational Physics 445 110578 (2021) https://doi.org/10.1016/j.jcp.2021.110578
Iterated Numerical Homogenization for MultiScale Elliptic Equations with Monotone Nonlinearity
A Priori Error Analysis of a Numerical Stochastic Homogenization Method
Julian Fischer, Dietmar Gallistl and Daniel Peterseim SIAM Journal on Numerical Analysis 59(2) 660 (2021) https://doi.org/10.1137/19M1308992
Computational multiscale methods for quasi-gas dynamic equations
Boris Chetverushkin, Eric Chung, Yalchin Efendiev, Sai-Mang Pun and Zecheng Zhang Journal of Computational Physics 440 110352 (2021) https://doi.org/10.1016/j.jcp.2021.110352
Contrast-Independent, Partially-Explicit Time Discretizations for Nonlinear Multiscale Problems
A diffuse modeling approach for embedded interfaces in linear elasticity
Paul Hennig, Roland Maier, Daniel Peterseim, Dominik Schillinger, Barbara Verfürth and Markus Kästner GAMM-Mitteilungen 43(1) (2020) https://doi.org/10.1002/gamm.202000001
Efficient implementation of the localized orthogonal decomposition method
Christian Engwer, Patrick Henning, Axel Målqvist and Daniel Peterseim Computer Methods in Applied Mechanics and Engineering 350 123 (2019) https://doi.org/10.1016/j.cma.2019.02.040
Generalized Multiscale Finite Element Methods with energy minimizing oversampling
Eric Chung, Yalchin Efendiev and Wing Tat Leung International Journal for Numerical Methods in Engineering 117(3) 316 (2019) https://doi.org/10.1002/nme.5958
A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities
Shape Optimization, Homogenization and Optimal Control
Mario Ohlberger, Michael Schaefer and Felix Schindler International Series of Numerical Mathematics, Shape Optimization, Homogenization and Optimal Control 169 143 (2018) https://doi.org/10.1007/978-3-319-90469-6_8
Localized harmonic characteristic basis functions for multiscale finite element methods
Domain Decomposition Methods in Science and Engineering XXIII
Ralf Kornhuber, Joscha Podlesny and Harry Yserentant Lecture Notes in Computational Science and Engineering, Domain Decomposition Methods in Science and Engineering XXIII 116 217 (2017) https://doi.org/10.1007/978-3-319-52389-7_21
A multiscale method for linear elasticity reducing Poisson locking
Fredrik Hellman, Patrick Henning and Axel Målqvist Discrete and Continuous Dynamical Systems - Series S 9(5) 1269 (2016) https://doi.org/10.3934/dcdss.2016051
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
Daniel Peterseim Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 343 (2016) https://doi.org/10.1007/978-3-319-41640-3_11