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Keyword

multiscale problems

Description: Mathematical or computational problems involving interacting behavior or features at multiple spatial, temporal, or other scales.
OpenAlex ID: keywords/multiscale-problems
The Heterognous Multiscale Methods
2003 · Weinan E, Bjorn Engquist · Communications in Mathematical Sciences · 987
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The Periodic Unfolding Method in Homogenization
2008 · D. Cioranescu, A. Damlamian, et al. · SIAM Journal on Mathematical Analysis · 474
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Homogenization of Multiple Integrals
1998 · Andrea Braides, Anneliese Defranceschi · 457
Parallel physics-informed neural networks via domain decomposition
2021 · Khemraj Shukla, Ameya D. Jagtap, et al. · Journal of Computational Physics · 434
Periodic unfolding and homogenization
2002 · Doina Cioranescu, Alain Damlamian, et al. · Comptes Rendus Mathématique · 434
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Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations
2023 · Ben Moseley, Andrew Markham, et al. · Advances in Computational Mathematics · 362
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Tsunami modelling with adaptively refined finite volume methods
2011 · Randall J. LeVeque, David L. George, et al. · Acta Numerica · 301
An Iteration-Free MoM Approach Based on Excitation Independent Characteristic Basis Functions for Solving Large Multiscale Electromagnetic Scattering Problems
2008 · Eugenio Lucente, Agostino Monorchio, et al. · IEEE Transactions on Antennas and Propagation · 262
Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems
2011 · Ivo Babuska, Robert Lipton · Multiscale Modeling and Simulation · 233
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Kolmogorov–Arnold-Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov–Arnold Networks
2024 · Yizheng Wang, Jia Sun, et al. · Computer Methods in Applied Mechanics and Engineering · 215
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A multiscale finite-element method
1997 · E. Rank, R. Krause · Computers & Structures · 196
Asymptotic expansion homogenization for heterogeneous media: computational issues and applications
2001 · Peter W Chung, Kumar K Tamma, et al. · Composites Part A Applied Science and Manufacturing · 160
Chaos and Coarse Graining in Statistical Mechanics
2008 · Patrizia Castiglione, Massimo Falcioni, et al. · Cambridge University Press eBooks · 158
Problems with different time scales for partial differential equations
1980 · Heinz‐Otto Kreiss · Communications on Pure and Applied Mathematics · 152
Heterogeneous multiscale methods for stiff ordinary differential equations
2005 · Bjorn Engquist, Yen-Hsi Tsai · Mathematics of Computation · 148
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Asymptotic and numerical homogenization
2008 · B. Engquist, P. E. Souganidis · Acta Numerica · 143
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
2022 · Zheyuan Hu, Ameya D. Jagtap, et al. · SIAM Journal on Scientific Computing · 141
Numerical Analysis of Multiscale Problems
2012 · Graham, Ivan G., Hou, Thomas Y., et al. · Lecture notes in computational science and engineering · 140
A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes
2007 · G. Capdeville · Journal of Computational Physics · 136
Asymptotic adaptive methods for multi-scale problems in fluid mechanics
2001 · R. Klein, N. Botta, et al. · Journal of Engineering Mathematics · 133
The Periodic Unfolding Method
2018 · Doina Cioranescu, Alain Damlamian, et al. · Series in contemporary mathematics · 132
How Important Are Activation Functions in Regression and Classification? a Survey, Performance Comparison, and Future Directions
2023 · Ameya D. Jagtap, George Em Karniadakis · Journal of Machine Learning for Modeling and Computing · 131
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Problèmes mécaniques multi-échelles: la méthode Arlequin
1998 · Hachmi Ben Dhia · Comptes Rendus de l Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy · 130
Asymptotic adaptive methods for multi-scale problems in fluid mechanics
2001 · R. Klein, N. Botta, et al. · Springer eBooks · 125
Generalized Multiscale Finite Element Methods: Oversampling Strategies
2014 · Yalchin Efendiev, Juan Galvis, et al. · International Journal for Multiscale Computational Engineering · 118
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Works count: 1,288
Citation count: 14,830
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