The Multiscale Finite Element Method (MSFEM)
Some Applications of the Generalized Multiscale Finite Element Method
... generalized multiscale finite element method (GMsFEM), is similar to the operator-based approach of Korostyshevskaya and Minkoff ...traditional finite element schemes will apply, ...
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A Generalized Multiscale Finite Element Method for poroelasticity problems II: nonlinear coupling
... the multiscale scale nature of the ...Generalized Multiscale Finite Element Method (GMsFEM) that solves nonlinear problems on a coarse grid by constructing local multiscale basis ...
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Nonconforming multiscale finite element method for Stokes flows in heterogeneous media Part I: Methodologies and numerical experiments
... The multiscale finite element method (MsFEM) is developed in the vein of the Crouzeix–Raviart element for solving viscous incompressible flows in genuine heterogeneous ...a method capable ...
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Analysis of the finite element heterogeneous multiscale method for nonmonotone elliptic homogenization problems
... the multiscale finite element method (MsFEM) [25] for nonlinear elliptic problems of the form −∇ · (a ε (x, uε (x), ∇u ε (x)) = f (x) (a tensor nonlinear also with respect to ∇u ε) have been ...
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Generalization of Mixed Multiscale Finite Element Methods with Applications
... generalized multiscale finite element method, we build a conform- ing multiscale coarse space with strong-symmetry enforcement for the stress on a coarse ...The method is tested ...
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Heterogeneous multiscale finite element methods for advection-diffusion and nonlinear elliptic multiscale problems
... heterogeneous multiscale finite element method for mono- tone elliptic operators with rapid ...This method is formulated in complete analogy to the initial concept suggested by E and ...
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Mixed multiscale finite element methods for stochastic porous media flows
... Although the results presented in this paper are encouraging, there is scope for further exploration. Our intent here was to demonstrate that one can capture the spatial and uncertainty variations of the stochastic flow ...
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The variational multiscale method for mixed finite element formulations
... and element interface terms. If one were to use the obtained multiscale weak formulations as the basis for finite element schemes, then a closure model must be substituted in place of the ...
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Finite element heterogeneous multiscale method for Elastic Waves in Heterogeneous Media
... A finite element heterogeneous multiscale method (FE-HMM) is proposed for the simulation of time-dependent elastic waves in a rapidly varying heterogeneous elastic ...standard finite ...
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An adaptive finite element heterogeneous multiscale method for Stokes flow in porous media
... |e mic | H 1 (Ω) cη mic,Ω Figure 25: Medium C: DS-FE-HMM error analysis (macro: P 1 , micro: P 2 / P 1 , periodic BC). and its computational cost is independent of the pore size. We have focused on a class of problems ...
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Finite Element Heterogeneous Multiscale Method for the Wave Equation: Long Time Effects
... a multiscale FEM for wave propagation in heterogeneous media, which captures not only the short but also the long-time be- havior, yet avoids the high computational cost of fully resolved ...
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A Parallel Multiscale Mixed Finite-Element Method for the Matlab Reservoir Simulation Toolbox
... We have made an attempt to use as much of the built-in functionality in the Parallel Computing Toolbox as is possible. When considering the operation of computing inner products, and then constructing basis functions for ...
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A Large Strains Finite Element Multiscale Approach
... are multiscale approaches dealing with small strains [1, 2, 3, 4, 5, 6], ductile damage [7], plasticity [8, 9, 10], quasi-brittle materials [11, 12, 13, 14], lami- nates [15], filament–wound composites [16], shape ...
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Finite Element Analysis of Multiscale Composite Beams
... The Finite Element Analysis (FEA) finds out the solutions for various parameters like temperature, stresses, or other needed unknown parameters ...specific finite element ...the finite ...
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Multiscale Characterization of a Polycrystalline Aggregate Subjected to Severe Plastic Deformation with the Finite Element Method
... FE method is representative, the deformation state of the mi- crostructure is considered in addition to the macroscopic re- sponse and evolution of the crystallographic texture 21,22) ...
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Discontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales
... various multiscale approaches have been proposed – see [6, 9] and the references ...heterogeneous multiscale method (HMM) proposed by E and Engquist in [28], a time-dependent advection-diffusion ...
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A multiscale finite element technique for nonlinear multi-phase materials
... Keywords: Finite Element Method (FEM), Voids, Plasticity, Multiscale, homogenisation, condensation technique 1. Introduction The heterogeneous nature of materials has a significant impact on ...
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Stabilized finite element methods based on multiscale enrichment for the Stokes problem
... The plan of the paper is as follows. In section 2 we present the general framework and derive a general form of the method. In sections 3 and 4 this framework is applied to derive concrete stabilized finite ...
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Adaptivity and Online Basis Construction for Generalized Multiscale Finite Element Methods
... posed method is to construct the online basis functions by solving local problems based on a computed ...online multiscale basis function is constructed by solving local problems with a right hand side that ...
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Mesoscopic Distinct Element Method for Multiscale Modeling of Carbon Nanotubes
... enable multiscale simulations by fill- ing the current gap between atomistic molecular dynamics (MD) and continuum finite element modeling (FEM) ...
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