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Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods [PDF]
Journal of Computational Physics, 2016 In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive.
Chung, Eric +2 more
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msBP: An R Package to Perform Bayesian Nonparametric Inference Using Multiscale Bernstein Polynomials Mixtures [PDF]
Journal of Statistical Software, 2017 msBP is an R package that implements a new method to perform Bayesian multiscale nonparametric inference introduced by Canale and Dunson (2016). The method, based on mixtures of multiscale beta dictionary densities, overcomes the drawbacks of Pólya trees
Antonio Canale
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Baroclinic Instability of a Time-Dependent Zonal Shear Flow
Atmosphere, 2022 In the real atmosphere, the development of large-scale motion is often related to the baroclinic properties of the atmosphere. So, it is necessary to discuss the stability condition of baroclinic flow. It is advantageous to use a layered model to discuss
Chengzhen Guo, Jian Song
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Contrast-Independent Partially Explicit Time Discretizations for Quasi Gas Dynamics
Mathematics, 2022 In the paper, we study a design and stability of contrast-independent partially explicit time discretizations for Quasi-Gas-Dynamics (QGD) Equations in multiscale high-contrast media.
Boris Chetverushkin +2 more
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Computational Multiscale Methods [PDF]
Oberwolfach Reports, 2009 Computational Multiscale Methods play an important role in many modern computer simulations in material sciences with different time scales and different scales in space. Besides various computational challenges, the meeting brought together various applications from many disciplines and scientists from various scientific communities.
Carsten Carstensen, Björn Engquist
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Contrast-Independent, Partially-Explicit Time Discretizations for Nonlinear Multiscale Problems
Mathematics, 2021 This work continues a line of work on developing partially explicit methods for multiscale problems. In our previous works, we considered linear multiscale problems where the spatial heterogeneities are at the subgrid level and are not resolved. In these
Eric T. Chung +3 more
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GKS and UGKS for High-Speed Flows
Aerospace, 2021 The gas-kinetic scheme (GKS) and the unified gas-kinetic scheme (UGKS) are numerical methods based on the gas-kinetic theory, which have been widely used in the numerical simulations of high-speed and non-equilibrium flows.
Yajun Zhu, Chengwen Zhong, Kun Xu
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Fluids, 2021 In this paper, we consider the poroelasticity problem in fractured and heterogeneous media. The mathematical model contains a coupled system of equations for fluid pressures and displacements in heterogeneous media.
Aleksei Tyrylgin +4 more
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DG-GMsFEM for Problems in Perforated Domains with Non-Homogeneous Boundary Conditions
Computation, 2021 Problems in perforated media are complex and require high resolution grid construction to capture complex irregular perforation boundaries leading to the large discrete system of equations. In this paper, we develop a multiscale model reduction technique
Valentin Alekseev +3 more
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Multiscale modeling methods in biomechanics [PDF]
WIREs Systems Biology and Medicine, 2017 More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space–time continuum. We are forced to consider multiple space–time continua, each representing the phenomenon of
Bhattacharya, P., Viceconti, M.
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