The heterogeneous multiscale method
Heterogeneous multiscale method for Maxwell’s equations
... Therefore, we approximate the effective behavior of the electromagnetic field without resolving the fine scale behavior. This is done using a Finite Element Heterogeneous Multiscale Method (FE-HMM) ...
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Finite element heterogeneous multiscale method for Elastic Waves in Heterogeneous Media
... element heterogeneous multiscale method (FE-HMM) is proposed for the simulation of time-dependent elastic waves in a rapidly varying heterogeneous elastic ...highly heterogeneous ...
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ANALYSIS OF THE HETEROGENEOUS MULTISCALE METHOD FOR ELLIPTIC HOMOGENIZATION PROBLEMS
... Received by the editors January 2, 2003. 2000 Mathematics Subject Classification. Primary 65N30, 74Q05; Secondary 74Q15, 65C30. Key words and phrases. Heterogeneous multiscale method, homogenization ...
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An adaptive finite element heterogeneous multiscale method for Stokes flow in porous media
... element heterogeneous multiscale method is proposed for solving the Stokes problem in porous ...The method is based on the coupling of an effective Darcy equation on a macroscopic mesh, with ...
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Finite Element Heterogeneous Multiscale Method for the Wave Equation: Long Time Effects
... ELEMENT HETEROGENEOUS MULTISCALE METHOD FOR THE WAVE EQUATION: LONG-TIME EFFECTS ∗ ASSYR ABDULLE † , MARCUS ...element heterogeneous multiscale method (FE-HMM) is proposed for ...
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Analysis of the finite element heterogeneous multiscale method for nonmonotone elliptic homogenization problems
... element heterogeneous multiscale method for a class of quasilin- ear elliptic homogenization problems of nonmonotone type is ...Newton method used to compute the solution is shown to ...
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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 ...the heterogeneous multiscale method (HMM) proposed by E and Engquist in [28], a time-dependent ...
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Heterogeneous multiscale finite element methods for advection-diffusion and nonlinear elliptic multiscale problems
... corresponding heterogeneous multiscale finite element method that was combined with a characteristic ...the method to heterogeneous structures, observing second order convergence in ...
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Coupled continuum hydrodynamics and molecular dynamics method for multiscale simulation
... Hybrid methods can be loosely categorised into: (a) domain-decomposition techniques [5– 8] and (b) heterogeneous multiscale method- ologies (HMM) [9, 10], see Fig 1. Domain- decomposition techniques ...
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A Bayesian numerical homogenization method for elliptic multiscale inverse problems
... MH method one needs multiple evaluations of the cost functional for different realizations of the parameters of ...the method, called the Reduced Basis Finite Element Heterogeneous Multiscale ...
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A multiscale method for compressible liquid-vapor flow with surface tension*
... novel method for its efficient multi-dimensional numerical simulation, at least in the case of moderately curved ...a heterogeneous multiscale method (HMM) in the sense of [21] is an ...
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Multiscale Petrov Galerkin method for high frequency heterogeneous Helmholtz equations
... be heterogeneous. Therefore, in this paper we study a multiscale Petrov-Galerkin method for the Helmholtz equation with large wave numbers k and possibly heterogeneous material coefficients as ...
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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 of ...
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On heterogeneous coupling of multiscale methods for problems with and without scale separation
... this method with a focus on interface control and a numerical strategy based on non-matching meshes in the ...the heterogeneous coupled multiscale method is derived and numerical experiments ...
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Auxiliary variables for 3D multiscale simulations in heterogeneous porous media
... long heterogeneous structures. In particular, the robustness of the multiscale framework in 3D is significantly enhanced with the novel ...basket multiscale method is a special case of the ...
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A hysteretic multiscale formulation for validating computational models of heterogeneous structures
... This is particularly useful in the case of a reliability analysis, which entails processes of a probabilistic nature. These processes usually analyze the effects of the combination of two or more input random variables ...
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Multiscale digital image identification of heterogeneous elastic properties of softwoods
... a method- ology that couples Digital Images Correlation with multi-scale numerical simulations in order to identify a material behaviour that is too complex to obtain at the observation scale but that can be ...
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Multiscale Simulation and Uncertainty Quantification Techniques for Richards' Equation in Heterogeneous Media
... simulate a dependent sequence of random draws from very complicated stochastic models. The good thing about an MCMC algorithm is that it can generate a Markov chain {K s } whose stationary distribution is its target ...
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Heterogeneous Multiscale Methods for modelling surface topography in Elastohydrodynamic Lubrication line contacts
... Fluctuation in pressure in the micro-scale causes deformation to vary as presented in Fig. 6, this variation (±0.01 µm) represents a small proportion of the total deformation magnitude (0.49 µm) which is consistent with ...
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Macroscopic thermal profile of heterogeneous cancerous breasts. A three-dimensional multiscale analysis
... We notice that the numerical solution of the cell problem is found by using COMSOL packages. However, the solutions homogenized and homogeneous problems are computed via the finite element method (FEM) by using ...
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