Residual-driven online generalized multiscale finite element methods [PDF]
Journal of Computational Physics, 2015 The construction of local reduced-order models via multiscale basis functions has been an area of active research. In this paper, we propose online multiscale basis functions which are constructed using the offline space and the current residual. Online multiscale basis functions are constructed adaptively in some selected regions based on our error ...
Chung, Eric T. +2 more
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Proper generalized decomposition of time-multiscale models [PDF]
, 2011 Models encountered in computational mechanics could involve many time scales. When these time scales cannot be separated, one must solve the evolution model in the entire time interval by using the finest time step that the model implies.
CHINESTA SORIA, Francisco +8 more
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Nonconforming generalized multiscale finite element methods
Journal of Computational and Applied Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chak Shing Lee, Dongwoo Sheen
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Multiscale Geometric Integration of Deterministic and Stochastic Systems [PDF]
, 2011 In order to accelerate computations and improve long time accuracy of numerical simulations, this thesis develops multiscale geometric integrators. For general multiscale stiff ODEs, SDEs, and PDEs, FLow AVeraging integratORs (FLAVORs) have been ...
Tao, Molei
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Space–time proper generalized decompositions for the resolution of transient elastodynamic models [PDF]
, 2013 In this paper, we investigate ability of proper generalized decomposition (PGD) to solve transient elastodynamic models in space–time domain. Classical methods use time integration schemes and an incremental resolution process.
BOUCINHA, Lucas +2 more
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Generalized Multiscale Finite Element Methods for Wave Propagation in Heterogeneous Media [PDF]
Multiscale Modeling & Simulation, 2014 Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop efficient and accurate methods that allow the use of coarse grids.
Chung, Eric T. +2 more
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Prediction of Discretization of GMsFEM Using Deep Learning
Mathematics, 2019 In this paper, we propose a deep-learning-based approach to a class of multiscale problems. The generalized multiscale finite element method (GMsFEM) has been proven successful as a model reduction technique of flow problems in heterogeneous and high ...
Min Wang +5 more
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Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice [PDF]
, 2013 We present an a priori error analysis of a practical energy based atomistic/continuum coupling method (A. V. Shapeev, Multiscale Model. Simul., 9(3):905-932, 2011) in two dimensions, for finite-range pair-potential interactions, in the presence of ...
Ortner, C. +2 more
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A weak Galerkin generalized multiscale finite element method
Journal of Computational and Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin Mu 0002, Junping Wang, Xiu Ye
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A two-level enriched finite element method for a mixed problem
, 2011 The simplest pair of spaces is made inf-sup stable for the mixed form of the Darcy equation. The key ingredient is to enhance the finite element spaces inside a Petrov-Galerkin framework with functions satisfying element-wise local Darcy problems with ...
Barrenechea, Gabriel +3 more
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