The mimetic multiscale method for Maxwell’s equations

[1]  I. Babuska,et al.  Special finite element methods for a class of second order elliptic problems with rough coefficients , 1994 .

[2]  Peter Monk,et al.  Finite Element Methods for Maxwell's Equations , 2003 .

[3]  T. Hughes,et al.  The variational multiscale method—a paradigm for computational mechanics , 1998 .

[4]  I. Babuska,et al.  Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods , 1983 .

[5]  D. Fleisch.  A student's guide to Maxwell's equations , 2008 .

[6]  I. Babuska,et al.  Acta Numerica 2003: Survey of meshless and generalized finite element methods: A unified approach , 2003 .

[7]  J. Dendy.  Black box multigrid , 1982 .

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

[9]  A. Brandt,et al.  The Multi-Grid Method for the Diffusion Equation with Strongly Discontinuous Coefficients , 1981 .

[10]  Eldad Haber,et al.  Computational Methods in Geophysical Electromagnetics , 2014, Mathematics in Industry.

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

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

[13]  J. David Moulton,et al.  A multilevel multiscale mimetic (M3) method for two-phase flows in porous media , 2008, J. Comput. Phys..

[14]  Stephan Knapek,et al.  Matrix-Dependent Multigrid Homogenization for Diffusion Problems , 1998, SIAM J. Sci. Comput..

[15]  Panayot S. Vassilevski,et al.  Exact de Rham Sequences of Spaces Defined on Macro-Elements in Two and Three Spatial Dimensions , 2008, SIAM J. Sci. Comput..

[16]  Patrick Jenny,et al.  Multiscale finite-volume method for parabolic problems arising from compressible multiphase flow in porous media , 2009, J. Comput. Phys..

[17]  Lindsey J. Heagy,et al.  A framework for the upscaling of the electrical conductivity in the quasi-static Maxwell's equations , 2016, J. Comput. Appl. Math..

[18]  Jian-Ming Jin,et al.  The Finite Element Method in Electromagnetics , 1993 .

[19]  Eldad Haber,et al.  An oversampling technique for the multiscale finite volume method to simulate electromagnetic responses in the frequency domain , 2016, Computational Geosciences.

[20]  G. W. Hohmann,et al.  4. Electromagnetic Theory for Geophysical Applications , 1987 .

[21]  Eldad Haber,et al.  A multiscale finite volume method for Maxwell's equations at low frequencies , 2014 .

[22]  S. MacLachlan,et al.  Multilevel upscaling through variational coarsening , 2006 .

[23]  Patrick Amestoy,et al.  MUMPS : A General Purpose Distributed Memory Sparse Solver , 2000, PARA.

[24]  E Weinan,et al.  Heterogeneous multiscale methods: A review , 2007 .

[25]  E Weinan,et al.  The heterogeneous multiscale method* , 2012, Acta Numerica.