Motivated by fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beam methods which were originally designed for pure initial-value problems of wave equations, we develop fast multiscale Gaussian beam methods for initial boundary value problems of wave equations in bounded convex domains in the high frequency regime. To compute the wave propagation in bounded convex domains, ...

Fuzzy rule-based edge detection using multiscale edge images is proposed. In this method, the edge image is obtained by fuzzy approximate reasoning from multiscale edge images which are obtained by derivative operators with various window sizes. The effect of utilizing multiscale edge images for edge detection is already known, but how to design the rules for deciding edges from multiscale edge...

Mixed variational multiscale methods and multiscale finite elements

1 Corresponding Author, Professor, Associate Chair, The GW Woodruff School of Mechanical Engineering, Savannah Campus, and ASME Fellow Email: [email protected], Phone: (404) 894-8412, Fax: (404) 894-9342 ABSTRACT Simulation Based Engineering Science (SBES) is an evolving interdisciplinary research area rooted in the methods for modeling multiscale, multi-physics events. The objectiv...

Multiscale image registration techniques are presented for the registration of medical images using deformable registration models. The techniques are particularly effective for registration problems in which one or both of the images to be registered contains significant levels of noise. A brief overview of existing deformable registration techniques is presented, and experiments using B-splin...

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Nowadays, multiscale modelling is recognized as the most suitable way to study biological processes. Indeed, almost every phenomenon in nature exhibits a multiscale behaviour, i.e., it is the outcome of interactions that occur at different spatial and temporal scales. Although several ways to provide “multilayer” models have been proposed, only Complex Automata naturally embed spatial informati...

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1 European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*), Bruno Kessler Foundation, Trento, Italy, 2 Faculty of Mathematics and Physics, Charles University in Prague, Prague, Czech Republic, 3 Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, Italy, 4 School of Engineering and Materials Science, Queen Mary University of Lon...

In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM). To solve nonlinear equations, the GMsFEM is used to represent the solution on a coarse grid with mult...