Generalized Multiscale Finite Element Method for discrete network (graph) models
Copyright policy )Generalized Multiscale Finite Element Method for discrete network (graph) models
In this paper, we consider a time-dependent discrete network model with highly varying connectivity. The approximation by time is performed using an implicit scheme. We propose the coarse scale approximation construction of network models based on the Generalized Multiscale Finite Element Method. An accurate coarse-scale approximation is generated by solving local spectral problems in sub-networks. Convergence analysis of the proposed method is presented for semi-discrete and discrete network models. We establish the stability of the multiscale discrete network. Numerical results are presented for structured and random heterogeneous networks.
Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Applications of graph theory, Random graphs (graph-theoretic aspects), Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, PDEs on graphs and networks (ramified or polygonal spaces), discrete network model, graph upscaling, Finite difference methods for initial value and initial-boundary value problems involving PDEs, multiscale method, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, GMsFEM, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Applications of graph theory, Random graphs (graph-theoretic aspects), Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, PDEs on graphs and networks (ramified or polygonal spaces), discrete network model, graph upscaling, Finite difference methods for initial value and initial-boundary value problems involving PDEs, multiscale method, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, GMsFEM, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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