Related papers: Numerical homogenization of spatial network models

We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…

The goal of this paper is to create a fruitful bridge between the numerical methods for approximating partial differential equations (PDEs) in fluid dynamics and the (iterative) numerical methods for dealing with the resulting large linear…

We are interested in numerical schemes for the simulation of large scale gas networks. Typical models are based on the isentropic Euler equations with realistic gas constant. The numerical scheme is based on transformation of conservative…

This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…

This paper analyzes an abstract two-level algorithm for hybridizable discontinuous Galerkin (HDG) methods in a unified fashion. We use an extended version of the Xu-Zikatanov (X-Z) identity to derive a sharp estimate of the convergence rate…

We consider a nonlocal linear elastic wave model. We approximate the model using a spectral Galerkin method in space and analyze error in such an approximation. We perform some numerical experiments to demonstrate the scheme.

In image segmentation, there is often more than one plausible solution for a given input. In medical imaging, for example, experts will often disagree about the exact location of object boundaries. Estimating this inherent uncertainty and…

Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to…

In this paper, we study the Boltzmann equation with uncertainties and prove that the spectral convergence of the semi-discretized numerical system holds in a combined velocity and random space, where the Fourier-spectral method is applied…

Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…

High-dimensional transport equations frequently occur in science and engineering. Computing their numerical solution, however, is challenging due to its high dimensionality. In this work we develop an algorithm to efficiently solve the…

This paper investigates a model reduction problem for linear directed network systems, in which the interconnections among the vertices are described by general weakly connected digraphs. First, the definitions of pseudo controllability and…

The subject of this work is a new stochastic Galerkin method for second-order elliptic partial differential equations with random diffusion coefficients. It combines operator compression in the stochastic variables with tree-based spline…

For the nonlinear Richards equation as an unsaturated flow through heterogeneous media, we build a new coarse-scale approximation algorithm utilizing numerical homogenization. This approach follows deep neural networks (DNNs) to quickly and…

Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…

Distributed processing across a networked environment suffers from unpredictable behavior of speedup due to heterogeneous nature of the hardware and software in the remote machines. It is challenging to get a better performance from a…

Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity…

We consider the discretization of a semilinear damped wave equation arising, for instance, in the modeling of gas transport in pipeline networks. For time invariant boundary data, the solutions of the problem are shown to converge…

An efficient $hp$-multigrid scheme is presented for local discontinuous Galerkin (LDG) discretizations of elliptic problems, formulated around the idea of separately coarsening the underlying discrete gradient and divergence operators. We…

Modeling spatial heterogeneity in the data generation process is essential for understanding and predicting geographical phenomena. Despite their prevalence in geospatial tasks, neural network models usually assume spatial stationarity,…