Temporal Splitting algorithms for non-stationary multiscale problems

[1]  Yalchin Efendiev,et al.  Splitting methods for solution decomposition in nonstationary problems , 2020, Appl. Math. Comput..

[2]  Eric T. Chung,et al.  Computational multiscale methods for first-order wave equation using mixed CEM-GMsFEM , 2019, J. Comput. Phys..

[3]  Eric T. Chung,et al.  Constraint Energy Minimizing Generalized Multiscale Finite Element Method for high-contrast linear elasticity problem , 2018, 1809.03726.

[4]  Yalchin Efendiev,et al.  Non-local multi-continua upscaling for flows in heterogeneous fractured media , 2017, J. Comput. Phys..

[5]  Yalchin Efendiev,et al.  Fast online generalized multiscale finite element method using constraint energy minimization , 2017, J. Comput. Phys..

[6]  Yalchin Efendiev,et al.  Constraint energy minimizing generalized multiscale finite element method in the mixed formulation , 2017, Computational Geosciences.

[7]  Wotao Yin,et al.  Splitting Methods in Communication, Imaging, Science, and Engineering , 2017 .

[8]  Yalchin Efendiev,et al.  Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods , 2016, J. Comput. Phys..

[9]  Yalchin Efendiev,et al.  Mixed Generalized Multiscale Finite Element Methods and Applications , 2014, Multiscale Model. Simul..

[10]  Frédéric Legoll,et al.  An MsFEM Type Approach for Perforated Domains , 2013, Multiscale Model. Simul..

[11]  Yalchin Efendiev,et al.  Generalized Multiscale Finite Element Methods for Wave Propagation in Heterogeneous Media , 2013, Multiscale Model. Simul..

[12]  Petr N. Vabishchevich,et al.  Additive Operator-Difference Schemes: Splitting Schemes , 2013 .

[13]  Yalchin Efendiev,et al.  Generalized Multiscale Finite Element Methods. Oversampling Strategies , 2013, 1304.4888.

[14]  Yalchin Efendiev,et al.  Generalized multiscale finite element methods (GMsFEM) , 2013, J. Comput. Phys..

[15]  Yalchin Efendiev,et al.  An Efficient Hierarchical Multiscale Finite Element Method for Stokes Equations in Slowly Varying Media , 2013, Multiscale Model. Simul..

[16]  P. Henning,et al.  A localized orthogonal decomposition method for semi-linear elliptic problems , 2012, 1211.3551.

[17]  Yalchin Efendiev,et al.  Coarse-Grid Multiscale Model Reduction Techniques for Flows in Heterogeneous Media and Applications , 2012 .

[18]  Yalchin Efendiev,et al.  Multiscale Finite Element Methods: Theory and Applications , 2009 .

[19]  H. Owhadi,et al.  Metric‐based upscaling , 2007 .

[20]  Ioannis G. Kevrekidis,et al.  General Tooth Boundary Conditions for Equation Free Modeling , 2006, SIAM J. Sci. Comput..

[21]  D. Roose,et al.  Patch dynamics with buffers for homogenization problems , 2004, J. Comput. Phys..

[22]  H. Tchelepi,et al.  Multi-scale finite-volume method for elliptic problems in subsurface flow simulation , 2003 .

[23]  E Weinan,et al.  The Heterognous Multiscale Methods , 2003 .

[24]  Thomas Y. Hou,et al.  A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media , 1997 .

[25]  G. Marchuk Splitting and alternating direction methods , 1990 .

[26]  J. Strikwerda Finite Difference Schemes and Partial Differential Equations , 1989 .

[27]  R. D. Richtmyer,et al.  Survey of the stability of linear finite difference equations , 1956 .