Abstract. A fully discrete a priori analysis of the finite element heterogenenous multiscale method (FE-HMM) introduced in [A. Abdulle, M. Grote, C. Stohrer, Multiscale Model. Simul. 2014] for the wave equation with highly oscillatory coefficients over long time is presented. A sharp a priori convergence rate for the numerical method is derived for long time intervals. The effective model over ...

In this paper, a new algorithm for the multiscale identification of spatio-temporal dynamical systems is derived. It is shown that the input and output observations can be represented in a multiscale manner based on a wavelet multiresolution analysis. The system dynamics at some specific scale of interest can then be identified using an orthogonal forward leastsquares algorithm. This model can ...

Flow through porous media is ubiquitous, occurring from large geological scales down to the microscopic scales. Several critical engineering phenomena like contaminant spread, nuclear waste disposal and oil recovery rely on accurate analysis and prediction of these multiscale phenomena. Such analysis is complicated by inherent uncertainties as well as the limited information available to charac...

Upscaling in situ soil moisture observations (ISMO) to multiscale pixel estimations with kriging is a key step in the comprehensive usage of ISMO and remote sensing (RS) soil moisture data. Scale effects occur and introduce uncertainties during upscaling processes because of spatial heterogeneity and the kriging method. A nested hierarchical scale series was established at the field level, and ...

In this paper, we propose the first numerical study of nanotube-based torsional oscillators via developing a new multiscale model. The edge-to-edge technique was employed in this multiscale method to couple the molecular model, i.e., nanotubes, and the continuum model, i.e., the metal paddle. Without losing accuracy, the metal paddle was treated as the rigid body in the continuum model. Torsion...

We present a multiscale model for numerical simulations of dynamics of crystalline solids. The method combines the continuum nonlinear elasto-dynamics model, which models the stress waves and physical loading conditions, and molecular dynamics model, which provides the nonlinear constitutive relation and resolves the atomic structures near local defects. The coupling of the two models is achiev...

This paper considers the numerical solution of elliptic boundary value problems with a complicated (nonperiodic) diffusion matrix which is smooth but highly oscillating on very different scales. We study the influence of the scales and amplitudes of these oscillations to the regularity of the solution. We introduce weighted Sobolev norms of integer order, where the (p + 1)st seminorm is weighte...